id	sid	tid	token	lemma	pos
ejpam-5509	1	1	european	european	PROPN
ejpam-5509	1	2	journal	journal	PROPN
ejpam-5509	1	3	of	of	ADP
ejpam-5509	1	4	pure	pure	ADJ
ejpam-5509	1	5	and	and	CCONJ
ejpam-5509	1	6	applied	applied	ADJ
ejpam-5509	1	7	mathematics	mathematic	NOUN
ejpam-5509	1	8	2025	2025	NUM
ejpam-5509	1	9	,	,	PUNCT
ejpam-5509	1	10	vol	vol	NOUN
ejpam-5509	1	11	.	.	PROPN
ejpam-5509	1	12	18	18	NUM
ejpam-5509	1	13	,	,	PUNCT
ejpam-5509	1	14	issue	issue	NOUN
ejpam-5509	1	15	1	1	NUM
ejpam-5509	1	16	,	,	PUNCT
ejpam-5509	1	17	article	article	NOUN
ejpam-5509	1	18	number	number	NOUN
ejpam-5509	1	19	5509	5509	NUM
ejpam-5509	1	20	issn	issn	VERB
ejpam-5509	1	21	1307	1307	NUM
ejpam-5509	1	22	-	-	SYM
ejpam-5509	1	23	5543	5543	NUM
ejpam-5509	1	24	–	–	PUNCT
ejpam-5509	1	25	ejpam.com	ejpam.com	X
ejpam-5509	1	26	published	publish	VERB
ejpam-5509	1	27	by	by	ADP
ejpam-5509	1	28	new	new	PROPN
ejpam-5509	1	29	york	york	PROPN
ejpam-5509	1	30	business	business	PROPN
ejpam-5509	1	31	global	global	PROPN
ejpam-5509	1	32	numerical	numerical	PROPN
ejpam-5509	1	33	investigation	investigation	NOUN
ejpam-5509	1	34	of	of	ADP
ejpam-5509	1	35	the	the	DET
ejpam-5509	1	36	dynamical	dynamical	ADJ
ejpam-5509	1	37	behavior	behavior	NOUN
ejpam-5509	1	38	of	of	ADP
ejpam-5509	1	39	hepatitis	hepatitis	PROPN
ejpam-5509	1	40	b	b	PROPN
ejpam-5509	1	41	virus	virus	NOUN
ejpam-5509	1	42	via	via	ADP
ejpam-5509	1	43	caputo	caputo	PROPN
ejpam-5509	1	44	-	-	PUNCT
ejpam-5509	1	45	fabrizio	fabrizio	PROPN
ejpam-5509	1	46	fractional	fractional	PROPN
ejpam-5509	1	47	derivative	derivative	PROPN
ejpam-5509	1	48	imtiaz	imtiaz	PROPN
ejpam-5509	1	49	ahmad1	ahmad1	PROPN
ejpam-5509	1	50	,	,	PUNCT
ejpam-5509	1	51	rashid	rashid	PROPN
ejpam-5509	1	52	jan2,3	jan2,3	PROPN
ejpam-5509	1	53	,	,	PUNCT
ejpam-5509	1	54	normy	normy	PROPN
ejpam-5509	1	55	norfiza	norfiza	PROPN
ejpam-5509	1	56	abdul	abdul	PROPN
ejpam-5509	1	57	razak2	razak2	PROPN
ejpam-5509	1	58	,	,	PUNCT
ejpam-5509	1	59	aziz	aziz	PROPN
ejpam-5509	1	60	khan4	khan4	PROPN
ejpam-5509	1	61	,	,	PUNCT
ejpam-5509	1	62	thabet	thabet	NOUN
ejpam-5509	1	63	abdeljawad5,4,6,7	abdeljawad5,4,6,7	ADJ
ejpam-5509	1	64	1	1	NUM
ejpam-5509	1	65	institute	institute	PROPN
ejpam-5509	1	66	of	of	ADP
ejpam-5509	1	67	informatics	informatic	NOUN
ejpam-5509	1	68	and	and	CCONJ
ejpam-5509	1	69	computing	compute	VERB
ejpam-5509	1	70	in	in	ADP
ejpam-5509	1	71	energy	energy	NOUN
ejpam-5509	1	72	(	(	PUNCT
ejpam-5509	1	73	iice	iice	NOUN
ejpam-5509	1	74	)	)	PUNCT
ejpam-5509	1	75	,	,	PUNCT
ejpam-5509	1	76	universiti	universiti	PROPN
ejpam-5509	1	77	tenaga	tenaga	PROPN
ejpam-5509	1	78	nasional	nasional	PROPN
ejpam-5509	1	79	,	,	PUNCT
ejpam-5509	1	80	kajang	kajang	PROPN
ejpam-5509	1	81	,	,	PUNCT
ejpam-5509	1	82	selangor	selangor	PROPN
ejpam-5509	1	83	,	,	PUNCT
ejpam-5509	1	84	malaysia	malaysia	PROPN
ejpam-5509	1	85	2	2	NUM
ejpam-5509	1	86	institute	institute	NOUN
ejpam-5509	1	87	of	of	ADP
ejpam-5509	1	88	energy	energy	NOUN
ejpam-5509	1	89	infrastructure	infrastructure	NOUN
ejpam-5509	1	90	(	(	PUNCT
ejpam-5509	1	91	iei	iei	PROPN
ejpam-5509	1	92	)	)	PUNCT
ejpam-5509	1	93	,	,	PUNCT
ejpam-5509	1	94	department	department	NOUN
ejpam-5509	1	95	of	of	ADP
ejpam-5509	1	96	civil	civil	ADJ
ejpam-5509	1	97	engineering	engineering	NOUN
ejpam-5509	1	98	,	,	PUNCT
ejpam-5509	1	99	college	college	NOUN
ejpam-5509	1	100	of	of	ADP
ejpam-5509	1	101	engineering	engineering	PROPN
ejpam-5509	1	102	,	,	PUNCT
ejpam-5509	1	103	universiti	universiti	PROPN
ejpam-5509	1	104	tenaga	tenaga	PROPN
ejpam-5509	1	105	nasional	nasional	PROPN
ejpam-5509	1	106	(	(	PUNCT
ejpam-5509	1	107	uniten	uniten	PROPN
ejpam-5509	1	108	)	)	PUNCT
ejpam-5509	1	109	,	,	PUNCT
ejpam-5509	1	110	putrajaya	putrajaya	PROPN
ejpam-5509	1	111	campus	campus	PROPN
ejpam-5509	1	112	,	,	PUNCT
ejpam-5509	1	113	jalan	jalan	PROPN
ejpam-5509	1	114	ikram	ikram	PROPN
ejpam-5509	1	115	-	-	PUNCT
ejpam-5509	1	116	uniten	uniten	VERB
ejpam-5509	1	117	,	,	PUNCT
ejpam-5509	1	118	43000	43000	NUM
ejpam-5509	1	119	kajang	kajang	PROPN
ejpam-5509	1	120	,	,	PUNCT
ejpam-5509	1	121	selangor	selangor	PROPN
ejpam-5509	1	122	,	,	PUNCT
ejpam-5509	1	123	malaysia	malaysia	PROPN
ejpam-5509	1	124	3	3	NUM
ejpam-5509	1	125	mathematics	mathematics	PROPN
ejpam-5509	1	126	research	research	NOUN
ejpam-5509	1	127	center	center	NOUN
ejpam-5509	1	128	,	,	PUNCT
ejpam-5509	1	129	near	near	ADP
ejpam-5509	1	130	east	east	PROPN
ejpam-5509	1	131	university	university	PROPN
ejpam-5509	1	132	trnc	trnc	NOUN
ejpam-5509	1	133	,	,	PUNCT
ejpam-5509	1	134	mersin	mersin	PROPN
ejpam-5509	1	135	10	10	NUM
ejpam-5509	1	136	,	,	PUNCT
ejpam-5509	1	137	nicosia	nicosia	PROPN
ejpam-5509	1	138	99138	99138	NUM
ejpam-5509	1	139	,	,	PUNCT
ejpam-5509	1	140	turkey	turkey	PROPN
ejpam-5509	1	141	4	4	NUM
ejpam-5509	1	142	department	department	NOUN
ejpam-5509	1	143	of	of	ADP
ejpam-5509	1	144	mathematics	mathematic	NOUN
ejpam-5509	1	145	and	and	CCONJ
ejpam-5509	1	146	sciences	science	NOUN
ejpam-5509	1	147	,	,	PUNCT
ejpam-5509	1	148	prince	prince	PROPN
ejpam-5509	1	149	sultan	sultan	PROPN
ejpam-5509	1	150	university	university	PROPN
ejpam-5509	1	151	,	,	PUNCT
ejpam-5509	1	152	p.o	p.o	PROPN
ejpam-5509	1	153	.	.	PROPN
ejpam-5509	1	154	box	box	PROPN
ejpam-5509	1	155	66833	66833	NUM
ejpam-5509	1	156	,	,	PUNCT
ejpam-5509	1	157	11586	11586	NUM
ejpam-5509	1	158	riyadh	riyadh	NOUN
ejpam-5509	1	159	,	,	PUNCT
ejpam-5509	1	160	saudi	saudi	PROPN
ejpam-5509	1	161	arabia	arabia	PROPN
ejpam-5509	1	162	5	5	NUM
ejpam-5509	1	163	department	department	NOUN
ejpam-5509	1	164	of	of	ADP
ejpam-5509	1	165	mathematics	mathematic	NOUN
ejpam-5509	1	166	,	,	PUNCT
ejpam-5509	1	167	saveetha	saveetha	PROPN
ejpam-5509	1	168	school	school	PROPN
ejpam-5509	1	169	of	of	ADP
ejpam-5509	1	170	engineering	engineering	PROPN
ejpam-5509	1	171	,	,	PUNCT
ejpam-5509	1	172	saveetha	saveetha	PROPN
ejpam-5509	1	173	institute	institute	PROPN
ejpam-5509	1	174	of	of	ADP
ejpam-5509	1	175	medical	medical	ADJ
ejpam-5509	1	176	and	and	CCONJ
ejpam-5509	1	177	technical	technical	ADJ
ejpam-5509	1	178	sciences	science	NOUN
ejpam-5509	1	179	,	,	PUNCT
ejpam-5509	1	180	saveetha	saveetha	PROPN
ejpam-5509	1	181	university	university	PROPN
ejpam-5509	1	182	,	,	PUNCT
ejpam-5509	1	183	chennai	chennai	NOUN
ejpam-5509	1	184	602105	602105	NUM
ejpam-5509	1	185	,	,	PUNCT
ejpam-5509	1	186	tamil	tamil	PROPN
ejpam-5509	1	187	nadu	nadu	PROPN
ejpam-5509	1	188	,	,	PUNCT
ejpam-5509	1	189	india	india	PROPN
ejpam-5509	1	190	6	6	NUM
ejpam-5509	1	191	center	center	NOUN
ejpam-5509	1	192	for	for	ADP
ejpam-5509	1	193	applied	applied	ADJ
ejpam-5509	1	194	mathematics	mathematic	NOUN
ejpam-5509	1	195	and	and	CCONJ
ejpam-5509	1	196	bioinformatics	bioinformatics	NOUN
ejpam-5509	1	197	(	(	PUNCT
ejpam-5509	1	198	camb	camb	PROPN
ejpam-5509	1	199	)	)	PUNCT
ejpam-5509	1	200	,	,	PUNCT
ejpam-5509	1	201	gulf	gulf	PROPN
ejpam-5509	1	202	university	university	PROPN
ejpam-5509	1	203	for	for	ADP
ejpam-5509	1	204	science	science	NOUN
ejpam-5509	1	205	and	and	CCONJ
ejpam-5509	1	206	technology	technology	NOUN
ejpam-5509	1	207	,	,	PUNCT
ejpam-5509	1	208	hawally	hawally	ADV
ejpam-5509	1	209	,	,	PUNCT
ejpam-5509	1	210	32093	32093	NUM
ejpam-5509	1	211	,	,	PUNCT
ejpam-5509	1	212	kuwait	kuwait	PROPN
ejpam-5509	1	213	7	7	NUM
ejpam-5509	1	214	department	department	NOUN
ejpam-5509	1	215	of	of	ADP
ejpam-5509	1	216	mathematics	mathematic	NOUN
ejpam-5509	1	217	and	and	CCONJ
ejpam-5509	1	218	applied	apply	VERB
ejpam-5509	1	219	mathematics	mathematic	NOUN
ejpam-5509	1	220	,	,	PUNCT
ejpam-5509	1	221	sefako	sefako	VERB
ejpam-5509	1	222	makgatho	makgatho	PROPN
ejpam-5509	1	223	health	health	PROPN
ejpam-5509	1	224	sciences	sciences	PROPN
ejpam-5509	1	225	university	university	PROPN
ejpam-5509	1	226	,	,	PUNCT
ejpam-5509	1	227	garankuwa	garankuwa	NOUN
ejpam-5509	1	228	,	,	PUNCT
ejpam-5509	1	229	medusa	medusa	NOUN
ejpam-5509	1	230	0204	0204	NUM
ejpam-5509	1	231	,	,	PUNCT
ejpam-5509	1	232	south	south	PROPN
ejpam-5509	1	233	africa	africa	PROPN
ejpam-5509	1	234	abstract	abstract	PROPN
ejpam-5509	1	235	.	.	PUNCT
ejpam-5509	2	1	hepatitis	hepatitis	PROPN
ejpam-5509	2	2	b	b	PROPN
ejpam-5509	2	3	is	be	AUX
ejpam-5509	2	4	a	a	DET
ejpam-5509	2	5	viral	viral	ADJ
ejpam-5509	2	6	infection	infection	NOUN
ejpam-5509	2	7	that	that	PRON
ejpam-5509	2	8	primarily	primarily	ADV
ejpam-5509	2	9	targets	target	VERB
ejpam-5509	2	10	the	the	DET
ejpam-5509	2	11	liver	liver	NOUN
ejpam-5509	2	12	,	,	PUNCT
ejpam-5509	2	13	potentially	potentially	ADV
ejpam-5509	2	14	leading	lead	VERB
ejpam-5509	2	15	to	to	ADP
ejpam-5509	2	16	acute	acute	ADJ
ejpam-5509	2	17	or	or	CCONJ
ejpam-5509	2	18	chronic	chronic	ADJ
ejpam-5509	2	19	liver	liver	NOUN
ejpam-5509	2	20	diseases	disease	NOUN
ejpam-5509	2	21	with	with	ADP
ejpam-5509	2	22	severe	severe	ADJ
ejpam-5509	2	23	complications	complication	NOUN
ejpam-5509	2	24	,	,	PUNCT
ejpam-5509	2	25	such	such	ADJ
ejpam-5509	2	26	as	as	ADP
ejpam-5509	2	27	cirrhosis	cirrhosis	NOUN
ejpam-5509	2	28	and	and	CCONJ
ejpam-5509	2	29	liver	liver	NOUN
ejpam-5509	2	30	cancer	cancer	NOUN
ejpam-5509	2	31	.	.	PUNCT
ejpam-5509	3	1	its	its	PRON
ejpam-5509	3	2	persistent	persistent	ADJ
ejpam-5509	3	3	prevalence	prevalence	NOUN
ejpam-5509	3	4	underscores	underscore	VERB
ejpam-5509	3	5	its	its	PRON
ejpam-5509	3	6	status	status	NOUN
ejpam-5509	3	7	as	as	ADP
ejpam-5509	3	8	a	a	DET
ejpam-5509	3	9	significant	significant	ADJ
ejpam-5509	3	10	global	global	ADJ
ejpam-5509	3	11	health	health	NOUN
ejpam-5509	3	12	issue	issue	NOUN
ejpam-5509	3	13	.	.	PUNCT
ejpam-5509	4	1	this	this	DET
ejpam-5509	4	2	research	research	NOUN
ejpam-5509	4	3	constructs	construct	VERB
ejpam-5509	4	4	a	a	DET
ejpam-5509	4	5	mathematical	mathematical	ADJ
ejpam-5509	4	6	model	model	NOUN
ejpam-5509	4	7	for	for	ADP
ejpam-5509	4	8	the	the	DET
ejpam-5509	4	9	progression	progression	NOUN
ejpam-5509	4	10	of	of	ADP
ejpam-5509	4	11	hepatitis	hepatitis	PROPN
ejpam-5509	4	12	b	b	PROPN
ejpam-5509	4	13	using	use	VERB
ejpam-5509	4	14	fractional	fractional	ADJ
ejpam-5509	4	15	derivatives	derivative	NOUN
ejpam-5509	4	16	,	,	PUNCT
ejpam-5509	4	17	accounting	account	VERB
ejpam-5509	4	18	for	for	ADP
ejpam-5509	4	19	a	a	DET
ejpam-5509	4	20	two	two	NUM
ejpam-5509	4	21	-	-	PUNCT
ejpam-5509	4	22	dose	dose	VERB
ejpam-5509	4	23	vaccine	vaccine	NOUN
ejpam-5509	4	24	regimen	regiman	NOUN
ejpam-5509	4	25	.	.	PUNCT
ejpam-5509	5	1	the	the	DET
ejpam-5509	5	2	basic	basic	ADJ
ejpam-5509	5	3	concepts	concept	NOUN
ejpam-5509	5	4	of	of	ADP
ejpam-5509	5	5	the	the	DET
ejpam-5509	5	6	caputo	caputo	PROPN
ejpam-5509	5	7	-	-	PUNCT
ejpam-5509	5	8	fabrizio	fabrizio	PROPN
ejpam-5509	5	9	(	(	PUNCT
ejpam-5509	5	10	cf	cf	NOUN
ejpam-5509	5	11	)	)	PUNCT
ejpam-5509	5	12	derivative	derivative	NOUN
ejpam-5509	5	13	are	be	AUX
ejpam-5509	5	14	presented	present	VERB
ejpam-5509	5	15	for	for	ADP
ejpam-5509	5	16	the	the	DET
ejpam-5509	5	17	model	model	NOUN
ejpam-5509	5	18	’s	’s	PART
ejpam-5509	5	19	analysis	analysis	NOUN
ejpam-5509	5	20	.	.	PUNCT
ejpam-5509	6	1	the	the	DET
ejpam-5509	6	2	infection	infection	NOUN
ejpam-5509	6	3	-	-	PUNCT
ejpam-5509	6	4	free	free	ADJ
ejpam-5509	6	5	equilibrium	equilibrium	NOUN
ejpam-5509	6	6	is	be	AUX
ejpam-5509	6	7	investigated	investigate	VERB
ejpam-5509	6	8	,	,	PUNCT
ejpam-5509	6	9	and	and	CCONJ
ejpam-5509	6	10	the	the	DET
ejpam-5509	6	11	endemic	endemic	ADJ
ejpam-5509	6	12	indicator	indicator	NOUN
ejpam-5509	6	13	of	of	ADP
ejpam-5509	6	14	the	the	DET
ejpam-5509	6	15	system	system	NOUN
ejpam-5509	6	16	,	,	PUNCT
ejpam-5509	6	17	r0	r0	NOUN
ejpam-5509	6	18	,	,	PUNCT
ejpam-5509	6	19	is	be	AUX
ejpam-5509	6	20	determined	determine	VERB
ejpam-5509	6	21	using	use	VERB
ejpam-5509	6	22	the	the	DET
ejpam-5509	6	23	next	next	ADJ
ejpam-5509	6	24	-	-	PUNCT
ejpam-5509	6	25	generation	generation	NOUN
ejpam-5509	6	26	matrix	matrix	NOUN
ejpam-5509	6	27	method	method	NOUN
ejpam-5509	6	28	.	.	PUNCT
ejpam-5509	7	1	the	the	DET
ejpam-5509	7	2	model	model	NOUN
ejpam-5509	7	3	exhibits	exhibit	VERB
ejpam-5509	7	4	local	local	ADJ
ejpam-5509	7	5	asymptotic	asymptotic	ADJ
ejpam-5509	7	6	stability	stability	NOUN
ejpam-5509	7	7	at	at	ADP
ejpam-5509	7	8	the	the	DET
ejpam-5509	7	9	infection	infection	NOUN
ejpam-5509	7	10	-	-	PUNCT
ejpam-5509	7	11	free	free	ADJ
ejpam-5509	7	12	equilibrium	equilibrium	NOUN
ejpam-5509	7	13	when	when	SCONJ
ejpam-5509	7	14	r0	r0	NOUN
ejpam-5509	7	15	<	<	X
ejpam-5509	7	16	1	1	NUM
ejpam-5509	7	17	,	,	PUNCT
ejpam-5509	7	18	and	and	CCONJ
ejpam-5509	7	19	instability	instability	NOUN
ejpam-5509	7	20	otherwise	otherwise	ADV
ejpam-5509	7	21	.	.	PUNCT
ejpam-5509	8	1	conditions	condition	NOUN
ejpam-5509	8	2	ensuring	ensure	VERB
ejpam-5509	8	3	the	the	DET
ejpam-5509	8	4	existence	existence	NOUN
ejpam-5509	8	5	and	and	CCONJ
ejpam-5509	8	6	uniqueness	uniqueness	NOUN
ejpam-5509	8	7	of	of	ADP
ejpam-5509	8	8	solutions	solution	NOUN
ejpam-5509	8	9	for	for	ADP
ejpam-5509	8	10	the	the	DET
ejpam-5509	8	11	proposed	propose	VERB
ejpam-5509	8	12	fractional	fractional	ADJ
ejpam-5509	8	13	dynamics	dynamic	NOUN
ejpam-5509	8	14	model	model	NOUN
ejpam-5509	8	15	are	be	AUX
ejpam-5509	8	16	established	establish	VERB
ejpam-5509	8	17	.	.	PUNCT
ejpam-5509	9	1	a	a	DET
ejpam-5509	9	2	new	new	ADJ
ejpam-5509	9	3	numerical	numerical	ADJ
ejpam-5509	9	4	method	method	NOUN
ejpam-5509	9	5	for	for	ADP
ejpam-5509	9	6	analyzing	analyze	VERB
ejpam-5509	9	7	the	the	DET
ejpam-5509	9	8	time	time	NOUN
ejpam-5509	9	9	series	series	NOUN
ejpam-5509	9	10	of	of	ADP
ejpam-5509	9	11	the	the	DET
ejpam-5509	9	12	system	system	NOUN
ejpam-5509	9	13	is	be	AUX
ejpam-5509	9	14	also	also	ADV
ejpam-5509	9	15	presented	present	VERB
ejpam-5509	9	16	.	.	PUNCT
ejpam-5509	10	1	the	the	DET
ejpam-5509	10	2	study	study	NOUN
ejpam-5509	10	3	elucidates	elucidate	VERB
ejpam-5509	10	4	the	the	DET
ejpam-5509	10	5	impact	impact	NOUN
ejpam-5509	10	6	of	of	ADP
ejpam-5509	10	7	input	input	NOUN
ejpam-5509	10	8	variables	variable	NOUN
ejpam-5509	10	9	on	on	ADP
ejpam-5509	10	10	the	the	DET
ejpam-5509	10	11	system	system	NOUN
ejpam-5509	10	12	’s	’s	PART
ejpam-5509	10	13	dynamic	dynamic	ADJ
ejpam-5509	10	14	behavior	behavior	NOUN
ejpam-5509	10	15	and	and	CCONJ
ejpam-5509	10	16	identifies	identify	VERB
ejpam-5509	10	17	critical	critical	ADJ
ejpam-5509	10	18	factors	factor	NOUN
ejpam-5509	10	19	within	within	ADP
ejpam-5509	10	20	the	the	DET
ejpam-5509	10	21	model	model	NOUN
ejpam-5509	10	22	,	,	PUNCT
ejpam-5509	10	23	highlighting	highlight	VERB
ejpam-5509	10	24	key	key	ADJ
ejpam-5509	10	25	parameters	parameter	NOUN
ejpam-5509	10	26	that	that	PRON
ejpam-5509	10	27	can	can	AUX
ejpam-5509	10	28	be	be	AUX
ejpam-5509	10	29	targeted	target	VERB
ejpam-5509	10	30	for	for	ADP
ejpam-5509	10	31	the	the	DET
ejpam-5509	10	32	control	control	NOUN
ejpam-5509	10	33	and	and	CCONJ
ejpam-5509	10	34	management	management	NOUN
ejpam-5509	10	35	of	of	ADP
ejpam-5509	10	36	hepatitis	hepatitis	PROPN
ejpam-5509	10	37	b	b	NOUN
ejpam-5509	10	38	infection	infection	NOUN
ejpam-5509	10	39	.	.	PUNCT
ejpam-5509	11	1	2020	2020	NUM
ejpam-5509	11	2	mathematics	mathematic	NOUN
ejpam-5509	11	3	subject	subject	NOUN
ejpam-5509	11	4	classifications	classification	NOUN
ejpam-5509	11	5	:	:	PUNCT
ejpam-5509	11	6	92d30	92d30	NUM
ejpam-5509	11	7	,	,	PUNCT
ejpam-5509	11	8	34a08	34a08	NUM
ejpam-5509	11	9	,	,	PUNCT
ejpam-5509	11	10	34d20	34d20	NUM
ejpam-5509	11	11	,	,	PUNCT
ejpam-5509	11	12	37n25	37n25	NUM
ejpam-5509	11	13	,	,	PUNCT
ejpam-5509	11	14	65l05	65l05	NUM
ejpam-5509	11	15	doi	doi	NOUN
ejpam-5509	11	16	:	:	PUNCT
ejpam-5509	11	17	https://doi.org/10.29020/nybg.ejpam.v18i1.5509	https://doi.org/10.29020/nybg.ejpam.v18i1.5509	ADP
ejpam-5509	11	18	email	email	NOUN
ejpam-5509	11	19	addresses	address	VERB
ejpam-5509	11	20	:	:	PUNCT
ejpam-5509	11	21	imtiazkakakhil@gmail.com	imtiazkakakhil@gmail.com	PROPN
ejpam-5509	11	22	(	(	PUNCT
ejpam-5509	11	23	i.	i.	PROPN
ejpam-5509	11	24	ahmad	ahmad	PROPN
ejpam-5509	11	25	)	)	PUNCT
ejpam-5509	11	26	,	,	PUNCT
ejpam-5509	11	27	rashid.jan@uniten.edu.my	rashid.jan@uniten.edu.my	NOUN
ejpam-5509	11	28	(	(	PUNCT
ejpam-5509	11	29	r.	r.	PROPN
ejpam-5509	11	30	jan	jan	PROPN
ejpam-5509	11	31	)	)	PUNCT
ejpam-5509	11	32	,	,	PUNCT
ejpam-5509	11	33	tabdeljawad@psu.edu.sa	tabdeljawad@psu.edu.sa	PROPN
ejpam-5509	11	34	(	(	PUNCT
ejpam-5509	11	35	t.	t.	NOUN
ejpam-5509	11	36	abdeljawad	abdeljawad	PROPN
ejpam-5509	11	37	)	)	PUNCT
ejpam-5509	11	38	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5509	12	1	1	1	NUM
ejpam-5509	12	2	copyright	copyright	NOUN
ejpam-5509	12	3	:	:	PUNCT
ejpam-5509	12	4	©	©	PROPN
ejpam-5509	12	5	2025	2025	NUM
ejpam-5509	12	6	the	the	DET
ejpam-5509	12	7	author(s	author(s	NOUN
ejpam-5509	12	8	)	)	PUNCT
ejpam-5509	12	9	.	.	PUNCT
ejpam-5509	13	1	(	(	PUNCT
ejpam-5509	13	2	cc	cc	NOUN
ejpam-5509	13	3	by	by	ADP
ejpam-5509	13	4	-	-	PUNCT
ejpam-5509	13	5	nc	nc	PROPN
ejpam-5509	13	6	4.0	4.0	NUM
ejpam-5509	13	7	)	)	PUNCT
ejpam-5509	13	8	i.	i.	PROPN
ejpam-5509	13	9	ahmad	ahmad	PROPN
ejpam-5509	13	10	et	et	PROPN
ejpam-5509	13	11	al	al	PROPN
ejpam-5509	13	12	.	.	PUNCT
ejpam-5509	13	13	/	/	SYM
ejpam-5509	13	14	eur	eur	PROPN
ejpam-5509	13	15	.	.	PUNCT
ejpam-5509	14	1	j.	j.	PROPN
ejpam-5509	14	2	pure	pure	PROPN
ejpam-5509	14	3	appl	appl	PROPN
ejpam-5509	14	4	.	.	PROPN
ejpam-5509	14	5	math	math	PROPN
ejpam-5509	14	6	,	,	PUNCT
ejpam-5509	14	7	18	18	NUM
ejpam-5509	14	8	(	(	PUNCT
ejpam-5509	14	9	1	1	NUM
ejpam-5509	14	10	)	)	PUNCT
ejpam-5509	14	11	(	(	PUNCT
ejpam-5509	14	12	2025	2025	NUM
ejpam-5509	14	13	)	)	PUNCT
ejpam-5509	14	14	,	,	PUNCT
ejpam-5509	14	15	5509	5509	NUM
ejpam-5509	14	16	2	2	NUM
ejpam-5509	14	17	of	of	ADP
ejpam-5509	14	18	27	27	NUM
ejpam-5509	14	19	key	key	ADJ
ejpam-5509	14	20	words	word	NOUN
ejpam-5509	14	21	and	and	CCONJ
ejpam-5509	14	22	phrases	phrase	NOUN
ejpam-5509	14	23	:	:	PUNCT
ejpam-5509	14	24	hepatitis	hepatitis	PROPN
ejpam-5509	14	25	b	b	PROPN
ejpam-5509	14	26	,	,	PUNCT
ejpam-5509	14	27	fractional	fractional	ADJ
ejpam-5509	14	28	dynamics	dynamic	NOUN
ejpam-5509	14	29	,	,	PUNCT
ejpam-5509	14	30	caputo	caputo	PROPN
ejpam-5509	14	31	-	-	PUNCT
ejpam-5509	14	32	fabrizio	fabrizio	PROPN
ejpam-5509	14	33	derivative	derivative	NOUN
ejpam-5509	14	34	,	,	PUNCT
ejpam-5509	14	35	model	model	NOUN
ejpam-5509	14	36	analysis	analysis	NOUN
ejpam-5509	14	37	,	,	PUNCT
ejpam-5509	14	38	dynamical	dynamical	ADJ
ejpam-5509	14	39	behavior	behavior	NOUN
ejpam-5509	14	40	1	1	NUM
ejpam-5509	14	41	.	.	PUNCT
ejpam-5509	14	42	introduction	introduction	NOUN
ejpam-5509	14	43	several	several	ADJ
ejpam-5509	14	44	globally	globally	ADV
ejpam-5509	14	45	significant	significant	ADJ
ejpam-5509	14	46	infectious	infectious	ADJ
ejpam-5509	14	47	diseases	disease	NOUN
ejpam-5509	14	48	,	,	PUNCT
ejpam-5509	14	49	including	include	VERB
ejpam-5509	14	50	hepatitis	hepatitis	PROPN
ejpam-5509	14	51	b	b	PROPN
ejpam-5509	14	52	(	(	PUNCT
ejpam-5509	14	53	hb	hb	X
ejpam-5509	14	54	)	)	PUNCT
ejpam-5509	15	1	[	[	X
ejpam-5509	15	2	22	22	NUM
ejpam-5509	15	3	]	]	PUNCT
ejpam-5509	15	4	,	,	PUNCT
ejpam-5509	15	5	pose	pose	VERB
ejpam-5509	15	6	a	a	DET
ejpam-5509	15	7	threat	threat	NOUN
ejpam-5509	15	8	to	to	ADP
ejpam-5509	15	9	human	human	ADJ
ejpam-5509	15	10	life	life	NOUN
ejpam-5509	15	11	.	.	PUNCT
ejpam-5509	16	1	hepatitis	hepatitis	PROPN
ejpam-5509	16	2	b	b	PROPN
ejpam-5509	16	3	results	result	VERB
ejpam-5509	16	4	from	from	ADP
ejpam-5509	16	5	an	an	DET
ejpam-5509	16	6	infection	infection	NOUN
ejpam-5509	16	7	instigated	instigate	VERB
ejpam-5509	16	8	by	by	ADP
ejpam-5509	16	9	the	the	DET
ejpam-5509	16	10	hepatitis	hepatitis	PROPN
ejpam-5509	16	11	b	b	PROPN
ejpam-5509	16	12	virus	virus	NOUN
ejpam-5509	16	13	(	(	PUNCT
ejpam-5509	16	14	hbv	hbv	NOUN
ejpam-5509	16	15	)	)	PUNCT
ejpam-5509	16	16	,	,	PUNCT
ejpam-5509	16	17	leading	lead	VERB
ejpam-5509	16	18	to	to	ADP
ejpam-5509	16	19	hepatic	hepatic	ADJ
ejpam-5509	16	20	impairment	impairment	NOUN
ejpam-5509	16	21	and	and	CCONJ
ejpam-5509	16	22	the	the	DET
ejpam-5509	16	23	potential	potential	ADJ
ejpam-5509	16	24	progression	progression	NOUN
ejpam-5509	16	25	of	of	ADP
ejpam-5509	16	26	both	both	CCONJ
ejpam-5509	16	27	acute	acute	ADJ
ejpam-5509	16	28	and	and	CCONJ
ejpam-5509	16	29	chronic	chronic	ADJ
ejpam-5509	16	30	infections	infection	NOUN
ejpam-5509	16	31	.	.	PUNCT
ejpam-5509	17	1	despite	despite	SCONJ
ejpam-5509	17	2	the	the	DET
ejpam-5509	17	3	asymptomatic	asymptomatic	ADJ
ejpam-5509	17	4	nature	nature	NOUN
ejpam-5509	17	5	in	in	ADP
ejpam-5509	17	6	the	the	DET
ejpam-5509	17	7	early	early	ADJ
ejpam-5509	17	8	phases	phase	NOUN
ejpam-5509	17	9	of	of	ADP
ejpam-5509	17	10	hb	hb	NOUN
ejpam-5509	17	11	infection	infection	NOUN
ejpam-5509	17	12	for	for	ADP
ejpam-5509	17	13	many	many	ADJ
ejpam-5509	17	14	individuals	individual	NOUN
ejpam-5509	17	15	,	,	PUNCT
ejpam-5509	17	16	certain	certain	ADJ
ejpam-5509	17	17	cases	case	NOUN
ejpam-5509	17	18	may	may	AUX
ejpam-5509	17	19	subsequently	subsequently	ADV
ejpam-5509	17	20	manifest	manifest	VERB
ejpam-5509	17	21	abrupt	abrupt	ADJ
ejpam-5509	17	22	clinical	clinical	ADJ
ejpam-5509	17	23	symptoms	symptom	NOUN
ejpam-5509	17	24	,	,	PUNCT
ejpam-5509	17	25	encompassing	encompass	VERB
ejpam-5509	17	26	nausea	nausea	NOUN
ejpam-5509	17	27	,	,	PUNCT
ejpam-5509	17	28	jaundice	jaundice	NOUN
ejpam-5509	17	29	,	,	PUNCT
ejpam-5509	17	30	fatigue	fatigue	NOUN
ejpam-5509	17	31	,	,	PUNCT
ejpam-5509	17	32	darkened	darken	VERB
ejpam-5509	17	33	urine	urine	NOUN
ejpam-5509	17	34	,	,	PUNCT
ejpam-5509	17	35	and	and	CCONJ
ejpam-5509	17	36	abdominal	abdominal	ADJ
ejpam-5509	17	37	discomfort	discomfort	NOUN
ejpam-5509	17	38	[	[	X
ejpam-5509	17	39	40	40	NUM
ejpam-5509	17	40	]	]	PUNCT
ejpam-5509	17	41	.	.	PUNCT
ejpam-5509	18	1	roughly	roughly	ADV
ejpam-5509	18	2	one	one	NUM
ejpam-5509	18	3	-	-	PUNCT
ejpam-5509	18	4	third	third	NOUN
ejpam-5509	18	5	of	of	ADP
ejpam-5509	18	6	the	the	DET
ejpam-5509	18	7	world	world	NOUN
ejpam-5509	18	8	’s	’s	PART
ejpam-5509	18	9	population	population	NOUN
ejpam-5509	18	10	is	be	AUX
ejpam-5509	18	11	estimated	estimate	VERB
ejpam-5509	18	12	to	to	PART
ejpam-5509	18	13	experience	experience	VERB
ejpam-5509	18	14	infection	infection	NOUN
ejpam-5509	18	15	at	at	ADP
ejpam-5509	18	16	some	some	DET
ejpam-5509	18	17	point	point	NOUN
ejpam-5509	18	18	in	in	ADP
ejpam-5509	18	19	their	their	PRON
ejpam-5509	18	20	lives	life	NOUN
ejpam-5509	18	21	,	,	PUNCT
ejpam-5509	18	22	with	with	ADP
ejpam-5509	18	23	240	240	NUM
ejpam-5509	18	24	-	-	SYM
ejpam-5509	18	25	350	350	NUM
ejpam-5509	18	26	million	million	NUM
ejpam-5509	18	27	individuals	individual	NOUN
ejpam-5509	18	28	afflicted	afflict	VERB
ejpam-5509	18	29	by	by	ADP
ejpam-5509	18	30	chronic	chronic	ADJ
ejpam-5509	18	31	infections	infection	NOUN
ejpam-5509	18	32	[	[	X
ejpam-5509	18	33	40	40	NUM
ejpam-5509	18	34	]	]	PUNCT
ejpam-5509	18	35	.	.	PUNCT
ejpam-5509	19	1	in	in	ADP
ejpam-5509	19	2	comparison	comparison	NOUN
ejpam-5509	19	3	to	to	ADP
ejpam-5509	19	4	the	the	DET
ejpam-5509	19	5	extensive	extensive	ADJ
ejpam-5509	19	6	global	global	ADJ
ejpam-5509	19	7	effort	effort	NOUN
ejpam-5509	19	8	directed	direct	VERB
ejpam-5509	19	9	towards	towards	ADP
ejpam-5509	19	10	hiv	hiv	PROPN
ejpam-5509	19	11	by	by	ADP
ejpam-5509	19	12	public	public	ADJ
ejpam-5509	19	13	health	health	NOUN
ejpam-5509	19	14	planners	planner	NOUN
ejpam-5509	19	15	,	,	PUNCT
ejpam-5509	19	16	it	it	PRON
ejpam-5509	19	17	is	be	AUX
ejpam-5509	19	18	noteworthy	noteworthy	ADJ
ejpam-5509	19	19	that	that	SCONJ
ejpam-5509	19	20	hbv	hbv	NOUN
ejpam-5509	19	21	and	and	CCONJ
ejpam-5509	19	22	hcv	hcv	NOUN
ejpam-5509	19	23	,	,	PUNCT
ejpam-5509	19	24	while	while	SCONJ
ejpam-5509	19	25	equally	equally	ADV
ejpam-5509	19	26	transmissible	transmissible	ADJ
ejpam-5509	19	27	,	,	PUNCT
ejpam-5509	19	28	are	be	AUX
ejpam-5509	19	29	significantly	significantly	ADV
ejpam-5509	19	30	more	more	ADJ
ejpam-5509	19	31	infectious-100	infectious-100	ADJ
ejpam-5509	19	32	times	time	NOUN
ejpam-5509	19	33	more	more	ADJ
ejpam-5509	19	34	for	for	ADP
ejpam-5509	19	35	hbv	hbv	NOUN
ejpam-5509	19	36	and	and	CCONJ
ejpam-5509	19	37	10	10	NUM
ejpam-5509	19	38	times	time	NOUN
ejpam-5509	19	39	more	more	ADJ
ejpam-5509	19	40	for	for	ADP
ejpam-5509	19	41	hcv	hcv	NOUN
ejpam-5509	19	42	[	[	X
ejpam-5509	19	43	30	30	NUM
ejpam-5509	19	44	]	]	PUNCT
ejpam-5509	19	45	.	.	PUNCT
ejpam-5509	20	1	in	in	ADP
ejpam-5509	20	2	areas	area	NOUN
ejpam-5509	20	3	with	with	ADP
ejpam-5509	20	4	a	a	DET
ejpam-5509	20	5	significant	significant	ADJ
ejpam-5509	20	6	prevalence	prevalence	NOUN
ejpam-5509	20	7	of	of	ADP
ejpam-5509	20	8	hbv	hbv	NOUN
ejpam-5509	20	9	,	,	PUNCT
ejpam-5509	20	10	the	the	DET
ejpam-5509	20	11	primary	primary	ADJ
ejpam-5509	20	12	transmission	transmission	NOUN
ejpam-5509	20	13	routes	route	NOUN
ejpam-5509	20	14	involve	involve	VERB
ejpam-5509	20	15	the	the	DET
ejpam-5509	20	16	transfer	transfer	NOUN
ejpam-5509	20	17	of	of	ADP
ejpam-5509	20	18	the	the	DET
ejpam-5509	20	19	virus	virus	NOUN
ejpam-5509	20	20	from	from	ADP
ejpam-5509	20	21	mother	mother	NOUN
ejpam-5509	20	22	to	to	ADP
ejpam-5509	20	23	child	child	NOUN
ejpam-5509	20	24	,	,	PUNCT
ejpam-5509	20	25	exposure	exposure	NOUN
ejpam-5509	20	26	to	to	ADP
ejpam-5509	20	27	contaminated	contaminate	VERB
ejpam-5509	20	28	blood	blood	NOUN
ejpam-5509	20	29	or	or	CCONJ
ejpam-5509	20	30	bodily	bodily	ADJ
ejpam-5509	20	31	fluids	fluid	NOUN
ejpam-5509	20	32	through	through	ADP
ejpam-5509	20	33	percutaneous	percutaneous	ADJ
ejpam-5509	20	34	means	mean	NOUN
ejpam-5509	20	35	,	,	PUNCT
ejpam-5509	20	36	and	and	CCONJ
ejpam-5509	20	37	sexual	sexual	ADJ
ejpam-5509	20	38	contact	contact	NOUN
ejpam-5509	20	39	[	[	X
ejpam-5509	20	40	30	30	NUM
ejpam-5509	20	41	]	]	PUNCT
ejpam-5509	20	42	.	.	PUNCT
ejpam-5509	21	1	in	in	ADP
ejpam-5509	21	2	the	the	DET
ejpam-5509	21	3	year	year	NOUN
ejpam-5509	21	4	2015	2015	NUM
ejpam-5509	21	5	,	,	PUNCT
ejpam-5509	21	6	there	there	PRON
ejpam-5509	21	7	were	be	VERB
ejpam-5509	21	8	approximately	approximately	ADV
ejpam-5509	21	9	900,000	900,000	NUM
ejpam-5509	21	10	fatalities	fatality	NOUN
ejpam-5509	21	11	attributed	attribute	VERB
ejpam-5509	21	12	to	to	ADP
ejpam-5509	21	13	hbv	hbv	NOUN
ejpam-5509	21	14	infection	infection	NOUN
ejpam-5509	21	15	,	,	PUNCT
ejpam-5509	21	16	predominantly	predominantly	ADV
ejpam-5509	21	17	resulting	result	VERB
ejpam-5509	21	18	from	from	ADP
ejpam-5509	21	19	the	the	DET
ejpam-5509	21	20	development	development	NOUN
ejpam-5509	21	21	of	of	ADP
ejpam-5509	21	22	hepatocellular	hepatocellular	ADJ
ejpam-5509	21	23	carcinoma	carcinoma	NOUN
ejpam-5509	21	24	(	(	PUNCT
ejpam-5509	21	25	hcc	hcc	NOUN
ejpam-5509	21	26	)	)	PUNCT
ejpam-5509	21	27	and	and	CCONJ
ejpam-5509	21	28	cirrhosis	cirrhosis	NOUN
ejpam-5509	21	29	[	[	X
ejpam-5509	21	30	29	29	NUM
ejpam-5509	21	31	]	]	PUNCT
ejpam-5509	21	32	.	.	PUNCT
ejpam-5509	22	1	the	the	DET
ejpam-5509	22	2	implementation	implementation	NOUN
ejpam-5509	22	3	of	of	ADP
ejpam-5509	22	4	hb	hb	NOUN
ejpam-5509	22	5	birth	birth	NOUN
ejpam-5509	22	6	immunization	immunization	NOUN
ejpam-5509	22	7	is	be	AUX
ejpam-5509	22	8	pivotal	pivotal	ADJ
ejpam-5509	22	9	in	in	ADP
ejpam-5509	22	10	preventing	prevent	VERB
ejpam-5509	22	11	the	the	DET
ejpam-5509	22	12	transmission	transmission	NOUN
ejpam-5509	22	13	of	of	ADP
ejpam-5509	22	14	hbv	hbv	NOUN
ejpam-5509	22	15	from	from	ADP
ejpam-5509	22	16	mother	mother	NOUN
ejpam-5509	22	17	to	to	ADP
ejpam-5509	22	18	child	child	NOUN
ejpam-5509	22	19	and	and	CCONJ
ejpam-5509	22	20	between	between	ADP
ejpam-5509	22	21	individuals	individual	NOUN
ejpam-5509	22	22	.	.	PUNCT
ejpam-5509	23	1	it	it	PRON
ejpam-5509	23	2	is	be	AUX
ejpam-5509	23	3	imperative	imperative	ADJ
ejpam-5509	23	4	for	for	SCONJ
ejpam-5509	23	5	healthcare	healthcare	NOUN
ejpam-5509	23	6	systems	system	NOUN
ejpam-5509	23	7	to	to	PART
ejpam-5509	23	8	enhance	enhance	VERB
ejpam-5509	23	9	their	their	PRON
ejpam-5509	23	10	efforts	effort	NOUN
ejpam-5509	23	11	in	in	ADP
ejpam-5509	23	12	the	the	DET
ejpam-5509	23	13	treatment	treatment	NOUN
ejpam-5509	23	14	and	and	CCONJ
ejpam-5509	23	15	prevention	prevention	NOUN
ejpam-5509	23	16	of	of	ADP
ejpam-5509	23	17	viral	viral	ADJ
ejpam-5509	23	18	hepatitis	hepatitis	NOUN
ejpam-5509	23	19	[	[	X
ejpam-5509	23	20	36	36	NUM
ejpam-5509	23	21	]	]	PUNCT
ejpam-5509	23	22	.	.	PUNCT
ejpam-5509	24	1	additionally	additionally	ADV
ejpam-5509	24	2	,	,	PUNCT
ejpam-5509	24	3	current	current	ADJ
ejpam-5509	24	4	investigations	investigation	NOUN
ejpam-5509	24	5	are	be	AUX
ejpam-5509	24	6	exploring	explore	VERB
ejpam-5509	24	7	the	the	DET
ejpam-5509	24	8	application	application	NOUN
ejpam-5509	24	9	of	of	ADP
ejpam-5509	24	10	antiviral	antiviral	ADJ
ejpam-5509	24	11	treatments	treatment	NOUN
ejpam-5509	24	12	,	,	PUNCT
ejpam-5509	24	13	including	include	VERB
ejpam-5509	24	14	tenofovir	tenofovir	NOUN
ejpam-5509	24	15	,	,	PUNCT
ejpam-5509	24	16	telbivudine	telbivudine	NOUN
ejpam-5509	24	17	,	,	PUNCT
ejpam-5509	24	18	and	and	CCONJ
ejpam-5509	24	19	lamivudine	lamivudine	NOUN
ejpam-5509	24	20	,	,	PUNCT
ejpam-5509	24	21	as	as	ADP
ejpam-5509	24	22	prospective	prospective	ADJ
ejpam-5509	24	23	approaches	approach	NOUN
ejpam-5509	24	24	to	to	PART
ejpam-5509	24	25	alleviate	alleviate	VERB
ejpam-5509	24	26	perinatal	perinatal	ADJ
ejpam-5509	24	27	transmission	transmission	NOUN
ejpam-5509	24	28	of	of	ADP
ejpam-5509	24	29	hbv	hbv	NOUN
ejpam-5509	24	30	in	in	ADP
ejpam-5509	24	31	expectant	expectant	ADJ
ejpam-5509	24	32	women	woman	NOUN
ejpam-5509	24	33	exhibiting	exhibit	VERB
ejpam-5509	24	34	elevated	elevated	ADJ
ejpam-5509	24	35	hbv	hbv	NOUN
ejpam-5509	24	36	dna	dna	PROPN
ejpam-5509	24	37	levels	level	NOUN
ejpam-5509	24	38	.	.	PUNCT
ejpam-5509	25	1	screening	screen	VERB
ejpam-5509	25	2	for	for	ADP
ejpam-5509	25	3	hbv	hbv	NOUN
ejpam-5509	25	4	is	be	AUX
ejpam-5509	25	5	crucial	crucial	ADJ
ejpam-5509	25	6	due	due	ADP
ejpam-5509	25	7	to	to	ADP
ejpam-5509	25	8	the	the	DET
ejpam-5509	25	9	highly	highly	ADV
ejpam-5509	25	10	contagious	contagious	ADJ
ejpam-5509	25	11	nature	nature	NOUN
ejpam-5509	25	12	of	of	ADP
ejpam-5509	25	13	the	the	DET
ejpam-5509	25	14	disease	disease	NOUN
ejpam-5509	25	15	and	and	CCONJ
ejpam-5509	25	16	its	its	PRON
ejpam-5509	25	17	severe	severe	ADJ
ejpam-5509	25	18	public	public	ADJ
ejpam-5509	25	19	health	health	NOUN
ejpam-5509	25	20	implications	implication	NOUN
ejpam-5509	25	21	.	.	PUNCT
ejpam-5509	26	1	emphasizing	emphasize	VERB
ejpam-5509	26	2	vaccination	vaccination	NOUN
ejpam-5509	26	3	as	as	ADP
ejpam-5509	26	4	a	a	DET
ejpam-5509	26	5	preventive	preventive	ADJ
ejpam-5509	26	6	measure	measure	NOUN
ejpam-5509	26	7	against	against	ADP
ejpam-5509	26	8	hbv	hbv	NOUN
ejpam-5509	26	9	infection	infection	NOUN
ejpam-5509	26	10	and	and	CCONJ
ejpam-5509	26	11	its	its	PRON
ejpam-5509	26	12	associated	associated	ADJ
ejpam-5509	26	13	complications	complication	NOUN
ejpam-5509	26	14	is	be	AUX
ejpam-5509	26	15	imperative	imperative	ADJ
ejpam-5509	26	16	[	[	X
ejpam-5509	26	17	36	36	NUM
ejpam-5509	26	18	,	,	PUNCT
ejpam-5509	26	19	40	40	NUM
ejpam-5509	26	20	]	]	PUNCT
ejpam-5509	26	21	.	.	PUNCT
ejpam-5509	27	1	the	the	DET
ejpam-5509	27	2	primary	primary	ADJ
ejpam-5509	27	3	objectives	objective	NOUN
ejpam-5509	27	4	of	of	ADP
ejpam-5509	27	5	hbv	hbv	NOUN
ejpam-5509	27	6	screening	screening	NOUN
ejpam-5509	27	7	encompass	encompass	VERB
ejpam-5509	27	8	the	the	DET
ejpam-5509	27	9	detection	detection	NOUN
ejpam-5509	27	10	of	of	ADP
ejpam-5509	27	11	individuals	individual	NOUN
ejpam-5509	27	12	with	with	ADP
ejpam-5509	27	13	chronic	chronic	ADJ
ejpam-5509	27	14	infections	infection	NOUN
ejpam-5509	27	15	,	,	PUNCT
ejpam-5509	27	16	who	who	PRON
ejpam-5509	27	17	could	could	AUX
ejpam-5509	27	18	benefit	benefit	VERB
ejpam-5509	27	19	from	from	ADP
ejpam-5509	27	20	treatment	treatment	NOUN
ejpam-5509	27	21	or	or	CCONJ
ejpam-5509	27	22	receive	receive	VERB
ejpam-5509	27	23	education	education	NOUN
ejpam-5509	27	24	on	on	ADP
ejpam-5509	27	25	lifestyle	lifestyle	NOUN
ejpam-5509	27	26	modifications	modification	NOUN
ejpam-5509	27	27	to	to	PART
ejpam-5509	27	28	reduce	reduce	VERB
ejpam-5509	27	29	transmission	transmission	NOUN
ejpam-5509	27	30	risks	risk	NOUN
ejpam-5509	27	31	.	.	PUNCT
ejpam-5509	28	1	furthermore	furthermore	ADV
ejpam-5509	28	2	,	,	PUNCT
ejpam-5509	28	3	it	it	PRON
ejpam-5509	28	4	strives	strive	VERB
ejpam-5509	28	5	to	to	PART
ejpam-5509	28	6	pinpoint	pinpoint	VERB
ejpam-5509	28	7	close	close	ADJ
ejpam-5509	28	8	contacts	contact	NOUN
ejpam-5509	28	9	of	of	ADP
ejpam-5509	28	10	infected	infect	VERB
ejpam-5509	28	11	individuals	individual	NOUN
ejpam-5509	28	12	for	for	ADP
ejpam-5509	28	13	vaccination	vaccination	NOUN
ejpam-5509	28	14	and	and	CCONJ
ejpam-5509	28	15	offer	offer	VERB
ejpam-5509	28	16	care	care	NOUN
ejpam-5509	28	17	for	for	ADP
ejpam-5509	28	18	chronic	chronic	ADJ
ejpam-5509	28	19	hb	hb	X
ejpam-5509	28	20	cases	case	NOUN
ejpam-5509	28	21	,	,	PUNCT
ejpam-5509	28	22	along	along	ADP
ejpam-5509	28	23	with	with	ADP
ejpam-5509	28	24	ongoing	ongoing	ADJ
ejpam-5509	28	25	monitoring	monitoring	NOUN
ejpam-5509	28	26	of	of	ADP
ejpam-5509	28	27	disease	disease	NOUN
ejpam-5509	28	28	activity	activity	NOUN
ejpam-5509	28	29	and	and	CCONJ
ejpam-5509	28	30	surveillance	surveillance	NOUN
ejpam-5509	28	31	for	for	ADP
ejpam-5509	28	32	hcc	hcc	PROPN
ejpam-5509	28	33	[	[	X
ejpam-5509	28	34	32	32	NUM
ejpam-5509	28	35	]	]	PUNCT
ejpam-5509	28	36	.	.	PUNCT
ejpam-5509	29	1	focused	focused	ADJ
ejpam-5509	29	2	screening	screening	NOUN
ejpam-5509	29	3	of	of	ADP
ejpam-5509	29	4	at	at	ADP
ejpam-5509	29	5	-	-	PUNCT
ejpam-5509	29	6	risk	risk	NOUN
ejpam-5509	29	7	populations	population	NOUN
ejpam-5509	29	8	,	,	PUNCT
ejpam-5509	29	9	such	such	ADJ
ejpam-5509	29	10	as	as	ADP
ejpam-5509	29	11	migrants	migrant	NOUN
ejpam-5509	29	12	,	,	PUNCT
ejpam-5509	29	13	could	could	AUX
ejpam-5509	29	14	enhance	enhance	VERB
ejpam-5509	29	15	the	the	DET
ejpam-5509	29	16	identification	identification	NOUN
ejpam-5509	29	17	of	of	ADP
ejpam-5509	29	18	cases	case	NOUN
ejpam-5509	29	19	.	.	PUNCT
ejpam-5509	30	1	a	a	DET
ejpam-5509	30	2	cost	cost	NOUN
ejpam-5509	30	3	-	-	PUNCT
ejpam-5509	30	4	effectiveness	effectiveness	NOUN
ejpam-5509	30	5	evaluation	evaluation	NOUN
ejpam-5509	30	6	of	of	ADP
ejpam-5509	30	7	screening	screen	VERB
ejpam-5509	30	8	for	for	ADP
ejpam-5509	30	9	viral	viral	ADJ
ejpam-5509	30	10	hepatitis	hepatitis	NOUN
ejpam-5509	30	11	among	among	ADP
ejpam-5509	30	12	immigrants	immigrant	NOUN
ejpam-5509	30	13	originating	originate	VERB
ejpam-5509	30	14	from	from	ADP
ejpam-5509	30	15	regions	region	NOUN
ejpam-5509	30	16	with	with	ADP
ejpam-5509	30	17	moderate	moderate	ADJ
ejpam-5509	30	18	to	to	PART
ejpam-5509	30	19	high	high	ADJ
ejpam-5509	30	20	prevalence	prevalence	NOUN
ejpam-5509	30	21	emphasizes	emphasize	VERB
ejpam-5509	30	22	the	the	DET
ejpam-5509	30	23	significance	significance	NOUN
ejpam-5509	30	24	of	of	ADP
ejpam-5509	30	25	screening	screen	VERB
ejpam-5509	30	26	as	as	ADP
ejpam-5509	30	27	a	a	DET
ejpam-5509	30	28	secondary	secondary	ADJ
ejpam-5509	30	29	prevention	prevention	NOUN
ejpam-5509	30	30	measure	measure	NOUN
ejpam-5509	30	31	[	[	X
ejpam-5509	30	32	33	33	NUM
ejpam-5509	30	33	]	]	PUNCT
ejpam-5509	30	34	.	.	PUNCT
ejpam-5509	31	1	numerous	numerous	ADJ
ejpam-5509	31	2	scholars	scholar	NOUN
ejpam-5509	31	3	have	have	AUX
ejpam-5509	31	4	explored	explore	VERB
ejpam-5509	31	5	the	the	DET
ejpam-5509	31	6	patterns	pattern	NOUN
ejpam-5509	31	7	of	of	ADP
ejpam-5509	31	8	hb	hb	NOUN
ejpam-5509	31	9	transmission	transmission	NOUN
ejpam-5509	31	10	in	in	ADP
ejpam-5509	31	11	different	different	ADJ
ejpam-5509	31	12	geographical	geographical	ADJ
ejpam-5509	31	13	areas	area	NOUN
ejpam-5509	31	14	,	,	PUNCT
ejpam-5509	31	15	as	as	ADV
ejpam-5509	31	16	well	well	ADV
ejpam-5509	31	17	as	as	ADP
ejpam-5509	31	18	the	the	DET
ejpam-5509	31	19	immune	immune	ADJ
ejpam-5509	31	20	system	system	NOUN
ejpam-5509	31	21	’s	’s	PART
ejpam-5509	31	22	response	response	NOUN
ejpam-5509	31	23	to	to	ADP
ejpam-5509	31	24	infection	infection	NOUN
ejpam-5509	31	25	,	,	PUNCT
ejpam-5509	31	26	through	through	ADP
ejpam-5509	31	27	the	the	DET
ejpam-5509	31	28	application	application	NOUN
ejpam-5509	31	29	of	of	ADP
ejpam-5509	31	30	mathematical	mathematical	ADJ
ejpam-5509	31	31	models	model	NOUN
ejpam-5509	31	32	.	.	PUNCT
ejpam-5509	32	1	anderson	anderson	PROPN
ejpam-5509	32	2	and	and	CCONJ
ejpam-5509	32	3	may	may	AUX
ejpam-5509	32	4	,	,	PUNCT
ejpam-5509	32	5	in	in	ADP
ejpam-5509	32	6	their	their	PRON
ejpam-5509	32	7	research	research	NOUN
ejpam-5509	32	8	,	,	PUNCT
ejpam-5509	32	9	elucidated	elucidate	VERB
ejpam-5509	32	10	the	the	DET
ejpam-5509	32	11	outcomes	outcome	NOUN
ejpam-5509	32	12	of	of	ADP
ejpam-5509	32	13	hb	hb	PROPN
ejpam-5509	32	14	transmission	transmission	NOUN
ejpam-5509	32	15	among	among	ADP
ejpam-5509	32	16	carriers	carrier	NOUN
ejpam-5509	32	17	by	by	ADP
ejpam-5509	32	18	employing	employ	VERB
ejpam-5509	32	19	a	a	DET
ejpam-5509	32	20	basic	basic	ADJ
ejpam-5509	32	21	mathematical	mathematical	ADJ
ejpam-5509	32	22	model	model	NOUN
ejpam-5509	32	23	i.	i.	PROPN
ejpam-5509	32	24	ahmad	ahmad	PROPN
ejpam-5509	32	25	et	et	PROPN
ejpam-5509	32	26	al	al	PROPN
ejpam-5509	32	27	.	.	PUNCT
ejpam-5509	32	28	/	/	SYM
ejpam-5509	32	29	eur	eur	PROPN
ejpam-5509	32	30	.	.	PUNCT
ejpam-5509	33	1	j.	j.	PROPN
ejpam-5509	33	2	pure	pure	PROPN
ejpam-5509	33	3	appl	appl	PROPN
ejpam-5509	33	4	.	.	PROPN
ejpam-5509	33	5	math	math	PROPN
ejpam-5509	33	6	,	,	PUNCT
ejpam-5509	33	7	18	18	NUM
ejpam-5509	33	8	(	(	PUNCT
ejpam-5509	33	9	1	1	NUM
ejpam-5509	33	10	)	)	PUNCT
ejpam-5509	33	11	(	(	PUNCT
ejpam-5509	33	12	2025	2025	NUM
ejpam-5509	33	13	)	)	PUNCT
ejpam-5509	33	14	,	,	PUNCT
ejpam-5509	33	15	5509	5509	NUM
ejpam-5509	33	16	3	3	NUM
ejpam-5509	33	17	of	of	ADP
ejpam-5509	33	18	27	27	NUM
ejpam-5509	34	1	[	[	X
ejpam-5509	34	2	11	11	NUM
ejpam-5509	34	3	]	]	PUNCT
ejpam-5509	34	4	.	.	PUNCT
ejpam-5509	35	1	anderson	anderson	PROPN
ejpam-5509	35	2	and	and	CCONJ
ejpam-5509	35	3	williams	williams	PROPN
ejpam-5509	35	4	,	,	PUNCT
ejpam-5509	35	5	in	in	ADP
ejpam-5509	35	6	their	their	PRON
ejpam-5509	35	7	modeling	modeling	NOUN
ejpam-5509	35	8	of	of	ADP
ejpam-5509	35	9	sexual	sexual	ADJ
ejpam-5509	35	10	transmission	transmission	NOUN
ejpam-5509	35	11	of	of	ADP
ejpam-5509	35	12	hb	hb	PROPN
ejpam-5509	35	13	,	,	PUNCT
ejpam-5509	35	14	integrated	integrate	VERB
ejpam-5509	35	15	a	a	DET
ejpam-5509	35	16	range	range	NOUN
ejpam-5509	35	17	of	of	ADP
ejpam-5509	35	18	variables	variable	NOUN
ejpam-5509	35	19	encompassing	encompass	VERB
ejpam-5509	35	20	sexual	sexual	ADJ
ejpam-5509	35	21	behavior	behavior	NOUN
ejpam-5509	35	22	and	and	CCONJ
ejpam-5509	35	23	age	age	NOUN
ejpam-5509	36	1	[	[	X
ejpam-5509	36	2	41	41	NUM
ejpam-5509	36	3	]	]	PUNCT
ejpam-5509	36	4	.	.	PUNCT
ejpam-5509	37	1	the	the	DET
ejpam-5509	37	2	age	age	NOUN
ejpam-5509	37	3	of	of	ADP
ejpam-5509	37	4	hb	hb	PROPN
ejpam-5509	37	5	infection	infection	NOUN
ejpam-5509	37	6	and	and	CCONJ
ejpam-5509	37	7	the	the	DET
ejpam-5509	37	8	development	development	NOUN
ejpam-5509	37	9	of	of	ADP
ejpam-5509	37	10	the	the	DET
ejpam-5509	37	11	carrier	carrier	NOUN
ejpam-5509	37	12	state	state	NOUN
ejpam-5509	37	13	were	be	AUX
ejpam-5509	37	14	found	find	VERB
ejpam-5509	37	15	to	to	PART
ejpam-5509	37	16	be	be	AUX
ejpam-5509	37	17	related	relate	VERB
ejpam-5509	37	18	by	by	ADP
ejpam-5509	37	19	edmunds	edmund	NOUN
ejpam-5509	37	20	et	et	PROPN
ejpam-5509	37	21	al	al	PROPN
ejpam-5509	37	22	.	.	PUNCT
ejpam-5509	38	1	[	[	X
ejpam-5509	38	2	21	21	NUM
ejpam-5509	38	3	]	]	PUNCT
ejpam-5509	38	4	.	.	PUNCT
ejpam-5509	39	1	medley	medley	PROPN
ejpam-5509	39	2	et	et	PROPN
ejpam-5509	39	3	al	al	PROPN
ejpam-5509	39	4	.	.	PROPN
ejpam-5509	39	5	introduced	introduce	VERB
ejpam-5509	39	6	a	a	DET
ejpam-5509	39	7	feedback	feedback	NOUN
ejpam-5509	39	8	mechanism	mechanism	NOUN
ejpam-5509	39	9	model	model	NOUN
ejpam-5509	39	10	that	that	PRON
ejpam-5509	39	11	links	link	VERB
ejpam-5509	39	12	the	the	DET
ejpam-5509	39	13	probability	probability	NOUN
ejpam-5509	39	14	of	of	ADP
ejpam-5509	39	15	carrierclass	carrierclass	NOUN
ejpam-5509	39	16	formation	formation	NOUN
ejpam-5509	39	17	after	after	ADP
ejpam-5509	39	18	infection	infection	NOUN
ejpam-5509	39	19	to	to	ADP
ejpam-5509	39	20	factors	factor	NOUN
ejpam-5509	39	21	such	such	ADJ
ejpam-5509	39	22	as	as	ADP
ejpam-5509	39	23	transmission	transmission	NOUN
ejpam-5509	39	24	rate	rate	NOUN
ejpam-5509	39	25	,	,	PUNCT
ejpam-5509	39	26	average	average	ADJ
ejpam-5509	39	27	age	age	NOUN
ejpam-5509	39	28	of	of	ADP
ejpam-5509	39	29	infection	infection	NOUN
ejpam-5509	39	30	,	,	PUNCT
ejpam-5509	39	31	and	and	CCONJ
ejpam-5509	39	32	infection	infection	NOUN
ejpam-5509	39	33	prevalence	prevalence	NOUN
ejpam-5509	39	34	[	[	X
ejpam-5509	39	35	31	31	NUM
ejpam-5509	39	36	]	]	PUNCT
ejpam-5509	39	37	,	,	PUNCT
ejpam-5509	39	38	whereas	whereas	SCONJ
ejpam-5509	39	39	din	din	VERB
ejpam-5509	39	40	and	and	CCONJ
ejpam-5509	39	41	abidin	abidin	PROPN
ejpam-5509	40	1	[	[	X
ejpam-5509	40	2	18	18	NUM
ejpam-5509	40	3	]	]	PUNCT
ejpam-5509	40	4	used	use	VERB
ejpam-5509	40	5	the	the	DET
ejpam-5509	40	6	mittag	mittag	ADJ
ejpam-5509	40	7	-	-	PUNCT
ejpam-5509	40	8	leffler	leffler	NOUN
ejpam-5509	40	9	kernel	kernel	NOUN
ejpam-5509	40	10	to	to	PART
ejpam-5509	40	11	model	model	VERB
ejpam-5509	40	12	an	an	DET
ejpam-5509	40	13	epidemic	epidemic	NOUN
ejpam-5509	40	14	of	of	ADP
ejpam-5509	40	15	hb	hb	PROPN
ejpam-5509	40	16	vaccination	vaccination	NOUN
ejpam-5509	40	17	.	.	PUNCT
ejpam-5509	41	1	transmission	transmission	NOUN
ejpam-5509	41	2	dynamics	dynamic	NOUN
ejpam-5509	41	3	of	of	ADP
ejpam-5509	41	4	hepatitis	hepatitis	PROPN
ejpam-5509	41	5	b	b	PROPN
ejpam-5509	41	6	differ	differ	VERB
ejpam-5509	41	7	between	between	ADP
ejpam-5509	41	8	industrialized	industrialize	VERB
ejpam-5509	41	9	nations	nation	NOUN
ejpam-5509	41	10	and	and	CCONJ
ejpam-5509	41	11	developing	develop	VERB
ejpam-5509	41	12	countries	country	NOUN
ejpam-5509	41	13	.	.	PUNCT
ejpam-5509	42	1	in	in	ADP
ejpam-5509	42	2	their	their	PRON
ejpam-5509	42	3	study	study	NOUN
ejpam-5509	42	4	,	,	PUNCT
ejpam-5509	42	5	edmunds	edmund	VERB
ejpam-5509	42	6	et	et	PROPN
ejpam-5509	42	7	al	al	PROPN
ejpam-5509	42	8	.	.	PUNCT
ejpam-5509	43	1	[	[	X
ejpam-5509	43	2	19	19	NUM
ejpam-5509	43	3	]	]	PUNCT
ejpam-5509	43	4	primarily	primarily	ADV
ejpam-5509	43	5	considered	consider	VERB
ejpam-5509	43	6	childhood	childhood	NOUN
ejpam-5509	43	7	hb	hb	NOUN
ejpam-5509	43	8	transmission	transmission	NOUN
ejpam-5509	43	9	rates	rate	NOUN
ejpam-5509	43	10	as	as	ADP
ejpam-5509	43	11	a	a	DET
ejpam-5509	43	12	key	key	ADJ
ejpam-5509	43	13	determinant	determinant	NOUN
ejpam-5509	43	14	of	of	ADP
ejpam-5509	43	15	epidemic	epidemic	NOUN
ejpam-5509	43	16	levels	level	NOUN
ejpam-5509	43	17	in	in	ADP
ejpam-5509	43	18	developing	develop	VERB
ejpam-5509	43	19	countries	country	NOUN
ejpam-5509	43	20	,	,	PUNCT
ejpam-5509	43	21	complemented	complement	VERB
ejpam-5509	43	22	by	by	ADP
ejpam-5509	43	23	the	the	DET
ejpam-5509	43	24	assessment	assessment	NOUN
ejpam-5509	43	25	of	of	ADP
ejpam-5509	43	26	sexual	sexual	ADJ
ejpam-5509	43	27	contact	contact	NOUN
ejpam-5509	43	28	rates	rate	NOUN
ejpam-5509	43	29	.	.	PUNCT
ejpam-5509	44	1	it	it	PRON
ejpam-5509	44	2	is	be	AUX
ejpam-5509	44	3	noteworthy	noteworthy	ADJ
ejpam-5509	44	4	that	that	SCONJ
ejpam-5509	44	5	data	datum	NOUN
ejpam-5509	44	6	on	on	ADP
ejpam-5509	44	7	sexual	sexual	ADJ
ejpam-5509	44	8	contact	contact	NOUN
ejpam-5509	44	9	rates	rate	NOUN
ejpam-5509	44	10	in	in	ADP
ejpam-5509	44	11	developing	develop	VERB
ejpam-5509	44	12	nations	nation	NOUN
ejpam-5509	44	13	are	be	AUX
ejpam-5509	44	14	limited	limited	ADJ
ejpam-5509	44	15	.	.	PUNCT
ejpam-5509	45	1	while	while	SCONJ
ejpam-5509	45	2	williams	williams	PROPN
ejpam-5509	45	3	et	et	PROPN
ejpam-5509	45	4	al	al	PROPN
ejpam-5509	45	5	.	.	PUNCT
ejpam-5509	46	1	[	[	X
ejpam-5509	46	2	20	20	NUM
ejpam-5509	46	3	]	]	PUNCT
ejpam-5509	46	4	provided	provide	VERB
ejpam-5509	46	5	a	a	DET
ejpam-5509	46	6	mathematical	mathematical	ADJ
ejpam-5509	46	7	model	model	NOUN
ejpam-5509	46	8	for	for	ADP
ejpam-5509	46	9	assessing	assess	VERB
ejpam-5509	46	10	the	the	DET
ejpam-5509	46	11	transmission	transmission	NOUN
ejpam-5509	46	12	dynamics	dynamic	NOUN
ejpam-5509	46	13	of	of	ADP
ejpam-5509	46	14	hb	hb	PROPN
ejpam-5509	46	15	in	in	ADP
ejpam-5509	46	16	the	the	DET
ejpam-5509	46	17	uk	uk	PROPN
ejpam-5509	46	18	.	.	PROPN
ejpam-5509	46	19	coupe	coupe	PROPN
ejpam-5509	46	20	et	et	PROPN
ejpam-5509	46	21	al	al	PROPN
ejpam-5509	46	22	.	.	PUNCT
ejpam-5509	47	1	[	[	X
ejpam-5509	47	2	17	17	NUM
ejpam-5509	47	3	]	]	PUNCT
ejpam-5509	47	4	constructed	construct	VERB
ejpam-5509	47	5	a	a	DET
ejpam-5509	47	6	standard	standard	ADJ
ejpam-5509	47	7	model	model	NOUN
ejpam-5509	47	8	of	of	ADP
ejpam-5509	47	9	immune	immune	ADJ
ejpam-5509	47	10	response	response	NOUN
ejpam-5509	47	11	to	to	PART
ejpam-5509	47	12	investigate	investigate	VERB
ejpam-5509	47	13	the	the	DET
ejpam-5509	47	14	temporal	temporal	ADJ
ejpam-5509	47	15	aspects	aspect	NOUN
ejpam-5509	47	16	of	of	ADP
ejpam-5509	47	17	effector	effector	NOUN
ejpam-5509	47	18	cell	cell	NOUN
ejpam-5509	47	19	activation	activation	NOUN
ejpam-5509	47	20	,	,	PUNCT
ejpam-5509	47	21	the	the	DET
ejpam-5509	47	22	course	course	NOUN
ejpam-5509	47	23	of	of	ADP
ejpam-5509	47	24	the	the	DET
ejpam-5509	47	25	disease	disease	NOUN
ejpam-5509	47	26	,	,	PUNCT
ejpam-5509	47	27	the	the	DET
ejpam-5509	47	28	induction	induction	NOUN
ejpam-5509	47	29	of	of	ADP
ejpam-5509	47	30	antibodies	antibody	NOUN
ejpam-5509	47	31	by	by	ADP
ejpam-5509	47	32	the	the	DET
ejpam-5509	47	33	vaccine	vaccine	NOUN
ejpam-5509	47	34	,	,	PUNCT
ejpam-5509	47	35	and	and	CCONJ
ejpam-5509	47	36	the	the	DET
ejpam-5509	47	37	role	role	NOUN
ejpam-5509	47	38	of	of	ADP
ejpam-5509	47	39	preexisting	preexist	VERB
ejpam-5509	47	40	conditions	condition	NOUN
ejpam-5509	47	41	in	in	ADP
ejpam-5509	47	42	preventing	prevent	VERB
ejpam-5509	47	43	hb	hb	PROPN
ejpam-5509	47	44	.	.	PUNCT
ejpam-5509	48	1	subsequently	subsequently	ADV
ejpam-5509	48	2	,	,	PUNCT
ejpam-5509	48	3	gourley	gourley	PROPN
ejpam-5509	48	4	et	et	PROPN
ejpam-5509	48	5	al	al	PROPN
ejpam-5509	48	6	.	.	PROPN
ejpam-5509	48	7	later	later	ADV
ejpam-5509	48	8	expanded	expand	VERB
ejpam-5509	48	9	on	on	ADP
ejpam-5509	48	10	this	this	DET
ejpam-5509	48	11	model	model	NOUN
ejpam-5509	48	12	with	with	ADP
ejpam-5509	48	13	a	a	DET
ejpam-5509	48	14	time	time	NOUN
ejpam-5509	48	15	-	-	PUNCT
ejpam-5509	48	16	delayed	delay	VERB
ejpam-5509	48	17	variation	variation	NOUN
ejpam-5509	48	18	,	,	PUNCT
ejpam-5509	48	19	while	while	SCONJ
ejpam-5509	48	20	min	min	PROPN
ejpam-5509	48	21	et	et	PROPN
ejpam-5509	48	22	al	al	PROPN
ejpam-5509	48	23	.	.	PROPN
ejpam-5509	49	1	used	use	VERB
ejpam-5509	49	2	a	a	DET
ejpam-5509	49	3	traditional	traditional	ADJ
ejpam-5509	49	4	model	model	NOUN
ejpam-5509	49	5	function	function	NOUN
ejpam-5509	49	6	instead	instead	ADV
ejpam-5509	49	7	of	of	ADP
ejpam-5509	49	8	mass	mass	ADJ
ejpam-5509	49	9	action	action	NOUN
ejpam-5509	49	10	to	to	PART
ejpam-5509	49	11	elucidate	elucidate	VERB
ejpam-5509	49	12	susceptibility	susceptibility	NOUN
ejpam-5509	49	13	to	to	ADP
ejpam-5509	49	14	hb	hb	PROPN
ejpam-5509	49	15	infection	infection	NOUN
ejpam-5509	50	1	[	[	X
ejpam-5509	50	2	23	23	NUM
ejpam-5509	50	3	]	]	PUNCT
ejpam-5509	50	4	.	.	PUNCT
ejpam-5509	51	1	in	in	ADP
ejpam-5509	51	2	order	order	NOUN
ejpam-5509	51	3	to	to	PART
ejpam-5509	51	4	improve	improve	VERB
ejpam-5509	51	5	the	the	DET
ejpam-5509	51	6	precision	precision	NOUN
ejpam-5509	51	7	of	of	ADP
ejpam-5509	51	8	the	the	DET
ejpam-5509	51	9	baseline	baseline	ADJ
ejpam-5509	51	10	reproduction	reproduction	NOUN
ejpam-5509	51	11	number	number	NOUN
ejpam-5509	51	12	estimations	estimation	NOUN
ejpam-5509	51	13	for	for	ADP
ejpam-5509	51	14	the	the	DET
ejpam-5509	51	15	hb	hb	PROPN
ejpam-5509	51	16	population	population	NOUN
ejpam-5509	51	17	,	,	PUNCT
ejpam-5509	51	18	hews	hew	VERB
ejpam-5509	51	19	et	et	PROPN
ejpam-5509	51	20	al	al	PROPN
ejpam-5509	51	21	.	.	PROPN
ejpam-5509	51	22	employed	employ	VERB
ejpam-5509	51	23	a	a	DET
ejpam-5509	51	24	logistic	logistic	ADJ
ejpam-5509	51	25	growth	growth	NOUN
ejpam-5509	51	26	model	model	NOUN
ejpam-5509	51	27	and	and	CCONJ
ejpam-5509	51	28	a	a	DET
ejpam-5509	51	29	conventional	conventional	ADJ
ejpam-5509	51	30	methodology	methodology	NOUN
ejpam-5509	51	31	,	,	PUNCT
ejpam-5509	51	32	thereby	thereby	ADV
ejpam-5509	51	33	enhancing	enhance	VERB
ejpam-5509	51	34	the	the	DET
ejpam-5509	51	35	model	model	NOUN
ejpam-5509	51	36	’s	’s	PART
ejpam-5509	51	37	concordance	concordance	NOUN
ejpam-5509	51	38	with	with	ADP
ejpam-5509	51	39	the	the	DET
ejpam-5509	51	40	available	available	ADJ
ejpam-5509	51	41	data	datum	NOUN
ejpam-5509	52	1	[	[	X
ejpam-5509	52	2	25	25	NUM
ejpam-5509	52	3	]	]	PUNCT
ejpam-5509	52	4	.	.	PUNCT
ejpam-5509	53	1	in	in	ADP
ejpam-5509	53	2	this	this	DET
ejpam-5509	53	3	study	study	NOUN
ejpam-5509	53	4	,	,	PUNCT
ejpam-5509	53	5	we	we	PRON
ejpam-5509	53	6	will	will	AUX
ejpam-5509	53	7	formulate	formulate	VERB
ejpam-5509	53	8	a	a	DET
ejpam-5509	53	9	mathematical	mathematical	ADJ
ejpam-5509	53	10	model	model	NOUN
ejpam-5509	53	11	to	to	PART
ejpam-5509	53	12	analyze	analyze	VERB
ejpam-5509	53	13	the	the	DET
ejpam-5509	53	14	transmission	transmission	NOUN
ejpam-5509	53	15	dynamics	dynamic	NOUN
ejpam-5509	53	16	of	of	ADP
ejpam-5509	53	17	hepatitis	hepatitis	PROPN
ejpam-5509	53	18	b	b	PROPN
ejpam-5509	53	19	(	(	PUNCT
ejpam-5509	53	20	hb	hb	PROPN
ejpam-5509	53	21	)	)	PUNCT
ejpam-5509	53	22	,	,	PUNCT
ejpam-5509	53	23	incorporating	incorporate	VERB
ejpam-5509	53	24	double	double	ADJ
ejpam-5509	53	25	-	-	PUNCT
ejpam-5509	53	26	dose	dose	NOUN
ejpam-5509	53	27	vaccination	vaccination	NOUN
ejpam-5509	53	28	and	and	CCONJ
ejpam-5509	53	29	the	the	DET
ejpam-5509	53	30	presence	presence	NOUN
ejpam-5509	53	31	of	of	ADP
ejpam-5509	53	32	asymptomatic	asymptomatic	ADJ
ejpam-5509	53	33	carriers	carrier	NOUN
ejpam-5509	53	34	.	.	PUNCT
ejpam-5509	54	1	the	the	DET
ejpam-5509	54	2	model	model	NOUN
ejpam-5509	54	3	will	will	AUX
ejpam-5509	54	4	account	account	VERB
ejpam-5509	54	5	for	for	ADP
ejpam-5509	54	6	the	the	DET
ejpam-5509	54	7	role	role	NOUN
ejpam-5509	54	8	of	of	ADP
ejpam-5509	54	9	asymptomatic	asymptomatic	ADJ
ejpam-5509	54	10	individuals	individual	NOUN
ejpam-5509	54	11	in	in	ADP
ejpam-5509	54	12	disease	disease	NOUN
ejpam-5509	54	13	spread	spread	VERB
ejpam-5509	54	14	and	and	CCONJ
ejpam-5509	54	15	evaluate	evaluate	VERB
ejpam-5509	54	16	the	the	DET
ejpam-5509	54	17	effectiveness	effectiveness	NOUN
ejpam-5509	54	18	of	of	ADP
ejpam-5509	54	19	a	a	DET
ejpam-5509	54	20	two	two	NUM
ejpam-5509	54	21	-	-	PUNCT
ejpam-5509	54	22	dose	dose	NOUN
ejpam-5509	54	23	vaccination	vaccination	NOUN
ejpam-5509	54	24	strategy	strategy	NOUN
ejpam-5509	54	25	in	in	ADP
ejpam-5509	54	26	controlling	control	VERB
ejpam-5509	54	27	the	the	DET
ejpam-5509	54	28	infection	infection	NOUN
ejpam-5509	54	29	.	.	PUNCT
ejpam-5509	55	1	by	by	ADP
ejpam-5509	55	2	integrating	integrate	VERB
ejpam-5509	55	3	these	these	DET
ejpam-5509	55	4	factors	factor	NOUN
ejpam-5509	55	5	,	,	PUNCT
ejpam-5509	55	6	the	the	DET
ejpam-5509	55	7	proposed	propose	VERB
ejpam-5509	55	8	model	model	NOUN
ejpam-5509	55	9	aims	aim	VERB
ejpam-5509	55	10	to	to	PART
ejpam-5509	55	11	provide	provide	VERB
ejpam-5509	55	12	a	a	DET
ejpam-5509	55	13	comprehensive	comprehensive	ADJ
ejpam-5509	55	14	understanding	understanding	NOUN
ejpam-5509	55	15	of	of	ADP
ejpam-5509	55	16	hb	hb	NOUN
ejpam-5509	55	17	transmission	transmission	NOUN
ejpam-5509	55	18	and	and	CCONJ
ejpam-5509	55	19	inform	inform	VERB
ejpam-5509	55	20	public	public	ADJ
ejpam-5509	55	21	health	health	NOUN
ejpam-5509	55	22	strategies	strategy	NOUN
ejpam-5509	55	23	for	for	ADP
ejpam-5509	55	24	disease	disease	NOUN
ejpam-5509	55	25	prevention	prevention	NOUN
ejpam-5509	55	26	and	and	CCONJ
ejpam-5509	55	27	management	management	NOUN
ejpam-5509	55	28	.	.	PUNCT
ejpam-5509	56	1	the	the	DET
ejpam-5509	56	2	application	application	NOUN
ejpam-5509	56	3	of	of	ADP
ejpam-5509	56	4	fractional	fractional	ADJ
ejpam-5509	56	5	derivatives	derivative	NOUN
ejpam-5509	56	6	extends	extend	VERB
ejpam-5509	56	7	beyond	beyond	ADP
ejpam-5509	56	8	theoretical	theoretical	ADJ
ejpam-5509	56	9	mathematics	mathematic	NOUN
ejpam-5509	56	10	and	and	CCONJ
ejpam-5509	56	11	finds	find	VERB
ejpam-5509	56	12	relevance	relevance	NOUN
ejpam-5509	56	13	in	in	ADP
ejpam-5509	56	14	various	various	ADJ
ejpam-5509	56	15	real	real	ADJ
ejpam-5509	56	16	-	-	PUNCT
ejpam-5509	56	17	world	world	NOUN
ejpam-5509	56	18	problems	problem	NOUN
ejpam-5509	56	19	across	across	ADP
ejpam-5509	56	20	diverse	diverse	ADJ
ejpam-5509	56	21	fields	field	NOUN
ejpam-5509	57	1	[	[	X
ejpam-5509	57	2	4–7	4–7	NOUN
ejpam-5509	57	3	,	,	PUNCT
ejpam-5509	57	4	10	10	NUM
ejpam-5509	57	5	,	,	PUNCT
ejpam-5509	57	6	14	14	NUM
ejpam-5509	57	7	,	,	PUNCT
ejpam-5509	57	8	26	26	NUM
ejpam-5509	57	9	,	,	PUNCT
ejpam-5509	57	10	34	34	NUM
ejpam-5509	57	11	]	]	PUNCT
ejpam-5509	57	12	.	.	PUNCT
ejpam-5509	58	1	these	these	DET
ejpam-5509	58	2	applications	application	NOUN
ejpam-5509	58	3	highlight	highlight	VERB
ejpam-5509	58	4	the	the	DET
ejpam-5509	58	5	versatility	versatility	NOUN
ejpam-5509	58	6	of	of	ADP
ejpam-5509	58	7	fractional	fractional	ADJ
ejpam-5509	58	8	calculus	calculus	NOUN
ejpam-5509	58	9	in	in	ADP
ejpam-5509	58	10	addressing	address	VERB
ejpam-5509	58	11	real	real	ADJ
ejpam-5509	58	12	-	-	PUNCT
ejpam-5509	58	13	world	world	NOUN
ejpam-5509	58	14	problems	problem	NOUN
ejpam-5509	58	15	across	across	ADP
ejpam-5509	58	16	disciplines	discipline	NOUN
ejpam-5509	58	17	,	,	PUNCT
ejpam-5509	58	18	offering	offer	VERB
ejpam-5509	58	19	a	a	DET
ejpam-5509	58	20	powerful	powerful	ADJ
ejpam-5509	58	21	tool	tool	NOUN
ejpam-5509	58	22	for	for	ADP
ejpam-5509	58	23	modeling	model	VERB
ejpam-5509	58	24	complex	complex	ADJ
ejpam-5509	58	25	phenomena	phenomenon	NOUN
ejpam-5509	58	26	and	and	CCONJ
ejpam-5509	58	27	improving	improve	VERB
ejpam-5509	58	28	the	the	DET
ejpam-5509	58	29	understanding	understanding	NOUN
ejpam-5509	58	30	of	of	ADP
ejpam-5509	58	31	intricate	intricate	ADJ
ejpam-5509	58	32	dynamic	dynamic	ADJ
ejpam-5509	58	33	systems	system	NOUN
ejpam-5509	58	34	[	[	X
ejpam-5509	58	35	1–3	1–3	NOUN
ejpam-5509	58	36	,	,	PUNCT
ejpam-5509	58	37	8	8	NUM
ejpam-5509	58	38	,	,	PUNCT
ejpam-5509	58	39	9	9	NUM
ejpam-5509	58	40	,	,	PUNCT
ejpam-5509	58	41	15	15	NUM
ejpam-5509	58	42	,	,	PUNCT
ejpam-5509	58	43	37	37	NUM
ejpam-5509	58	44	,	,	PUNCT
ejpam-5509	58	45	39	39	NUM
ejpam-5509	58	46	]	]	PUNCT
ejpam-5509	58	47	.	.	PUNCT
ejpam-5509	59	1	the	the	DET
ejpam-5509	59	2	utilization	utilization	NOUN
ejpam-5509	59	3	of	of	ADP
ejpam-5509	59	4	fractional	fractional	ADJ
ejpam-5509	59	5	derivatives	derivative	NOUN
ejpam-5509	59	6	in	in	ADP
ejpam-5509	59	7	epidemic	epidemic	NOUN
ejpam-5509	59	8	models	model	NOUN
ejpam-5509	59	9	represents	represent	VERB
ejpam-5509	59	10	a	a	DET
ejpam-5509	59	11	sophisticated	sophisticated	ADJ
ejpam-5509	59	12	approach	approach	NOUN
ejpam-5509	59	13	to	to	ADP
ejpam-5509	59	14	capturing	capture	VERB
ejpam-5509	59	15	non	non	ADJ
ejpam-5509	59	16	-	-	ADJ
ejpam-5509	59	17	integer	integer	ADJ
ejpam-5509	59	18	order	order	NOUN
ejpam-5509	59	19	dynamics	dynamic	NOUN
ejpam-5509	59	20	inherent	inherent	ADJ
ejpam-5509	59	21	in	in	ADP
ejpam-5509	59	22	certain	certain	ADJ
ejpam-5509	59	23	biological	biological	ADJ
ejpam-5509	59	24	and	and	CCONJ
ejpam-5509	59	25	epidemiological	epidemiological	ADJ
ejpam-5509	59	26	systems	system	NOUN
ejpam-5509	59	27	[	[	X
ejpam-5509	59	28	27	27	NUM
ejpam-5509	59	29	,	,	PUNCT
ejpam-5509	59	30	35	35	NUM
ejpam-5509	59	31	]	]	PUNCT
ejpam-5509	59	32	.	.	PUNCT
ejpam-5509	60	1	unlike	unlike	ADP
ejpam-5509	60	2	traditional	traditional	ADJ
ejpam-5509	60	3	integer	integer	NOUN
ejpam-5509	60	4	-	-	PUNCT
ejpam-5509	60	5	order	order	NOUN
ejpam-5509	60	6	derivatives	derivative	NOUN
ejpam-5509	60	7	,	,	PUNCT
ejpam-5509	60	8	fractional	fractional	ADJ
ejpam-5509	60	9	derivatives	derivative	NOUN
ejpam-5509	60	10	involve	involve	VERB
ejpam-5509	60	11	non	non	ADJ
ejpam-5509	60	12	-	-	ADJ
ejpam-5509	60	13	integer	integer	ADJ
ejpam-5509	60	14	orders	order	NOUN
ejpam-5509	60	15	,	,	PUNCT
ejpam-5509	60	16	allowing	allow	VERB
ejpam-5509	60	17	for	for	ADP
ejpam-5509	60	18	a	a	DET
ejpam-5509	60	19	more	more	ADV
ejpam-5509	60	20	nuanced	nuanced	ADJ
ejpam-5509	60	21	representation	representation	NOUN
ejpam-5509	60	22	of	of	ADP
ejpam-5509	60	23	complex	complex	ADJ
ejpam-5509	60	24	behaviors	behavior	NOUN
ejpam-5509	60	25	and	and	CCONJ
ejpam-5509	60	26	long	long	ADJ
ejpam-5509	60	27	-	-	PUNCT
ejpam-5509	60	28	range	range	NOUN
ejpam-5509	60	29	dependencies	dependency	NOUN
ejpam-5509	60	30	observed	observe	VERB
ejpam-5509	60	31	in	in	ADP
ejpam-5509	60	32	epidemic	epidemic	NOUN
ejpam-5509	60	33	spread	spread	NOUN
ejpam-5509	60	34	.	.	PUNCT
ejpam-5509	61	1	in	in	ADP
ejpam-5509	61	2	the	the	DET
ejpam-5509	61	3	context	context	NOUN
ejpam-5509	61	4	of	of	ADP
ejpam-5509	61	5	epidemic	epidemic	NOUN
ejpam-5509	61	6	modeling	modeling	NOUN
ejpam-5509	61	7	,	,	PUNCT
ejpam-5509	61	8	the	the	DET
ejpam-5509	61	9	fractional	fractional	ADJ
ejpam-5509	61	10	derivative	derivative	NOUN
ejpam-5509	61	11	is	be	AUX
ejpam-5509	61	12	employed	employ	VERB
ejpam-5509	61	13	to	to	PART
ejpam-5509	61	14	describe	describe	VERB
ejpam-5509	61	15	the	the	DET
ejpam-5509	61	16	rate	rate	NOUN
ejpam-5509	61	17	of	of	ADP
ejpam-5509	61	18	change	change	NOUN
ejpam-5509	61	19	of	of	ADP
ejpam-5509	61	20	infected	infected	ADJ
ejpam-5509	61	21	or	or	CCONJ
ejpam-5509	61	22	susceptible	susceptible	ADJ
ejpam-5509	61	23	populations	population	NOUN
ejpam-5509	61	24	with	with	ADP
ejpam-5509	61	25	respect	respect	NOUN
ejpam-5509	61	26	to	to	ADP
ejpam-5509	61	27	time	time	NOUN
ejpam-5509	61	28	,	,	PUNCT
ejpam-5509	61	29	considering	consider	VERB
ejpam-5509	61	30	fractional	fractional	ADJ
ejpam-5509	61	31	orders	order	NOUN
ejpam-5509	61	32	that	that	PRON
ejpam-5509	61	33	may	may	AUX
ejpam-5509	61	34	reflect	reflect	VERB
ejpam-5509	61	35	memory	memory	NOUN
ejpam-5509	61	36	effects	effect	NOUN
ejpam-5509	61	37	or	or	CCONJ
ejpam-5509	61	38	non	non	ADJ
ejpam-5509	61	39	-	-	ADJ
ejpam-5509	61	40	local	local	ADJ
ejpam-5509	61	41	interactions	interaction	NOUN
ejpam-5509	61	42	.	.	PUNCT
ejpam-5509	62	1	this	this	DET
ejpam-5509	62	2	mathematical	mathematical	ADJ
ejpam-5509	62	3	framework	framework	NOUN
ejpam-5509	62	4	offers	offer	VERB
ejpam-5509	62	5	a	a	DET
ejpam-5509	62	6	more	more	ADV
ejpam-5509	62	7	accurate	accurate	ADJ
ejpam-5509	62	8	portrayal	portrayal	NOUN
ejpam-5509	62	9	of	of	ADP
ejpam-5509	62	10	epidemic	epidemic	NOUN
ejpam-5509	62	11	dynamics	dynamic	NOUN
ejpam-5509	62	12	,	,	PUNCT
ejpam-5509	62	13	particularly	particularly	ADV
ejpam-5509	62	14	when	when	SCONJ
ejpam-5509	62	15	conventional	conventional	ADJ
ejpam-5509	62	16	models	model	NOUN
ejpam-5509	62	17	fall	fall	VERB
ejpam-5509	62	18	short	short	ADV
ejpam-5509	62	19	in	in	ADP
ejpam-5509	62	20	capturing	capture	VERB
ejpam-5509	62	21	the	the	DET
ejpam-5509	62	22	intricate	intricate	ADJ
ejpam-5509	62	23	patterns	pattern	NOUN
ejpam-5509	62	24	exhibited	exhibit	VERB
ejpam-5509	62	25	by	by	ADP
ejpam-5509	62	26	real	real	ADJ
ejpam-5509	62	27	-	-	PUNCT
ejpam-5509	62	28	world	world	NOUN
ejpam-5509	62	29	epidemics	epidemic	NOUN
ejpam-5509	62	30	.	.	PUNCT
ejpam-5509	63	1	therefore	therefore	ADV
ejpam-5509	63	2	,	,	PUNCT
ejpam-5509	63	3	we	we	PRON
ejpam-5509	63	4	have	have	VERB
ejpam-5509	63	5	i.	i.	PROPN
ejpam-5509	63	6	ahmad	ahmad	PROPN
ejpam-5509	63	7	et	et	PROPN
ejpam-5509	63	8	al	al	PROPN
ejpam-5509	63	9	.	.	PUNCT
ejpam-5509	63	10	/	/	SYM
ejpam-5509	63	11	eur	eur	PROPN
ejpam-5509	63	12	.	.	PUNCT
ejpam-5509	64	1	j.	j.	PROPN
ejpam-5509	64	2	pure	pure	PROPN
ejpam-5509	64	3	appl	appl	PROPN
ejpam-5509	64	4	.	.	PROPN
ejpam-5509	64	5	math	math	PROPN
ejpam-5509	64	6	,	,	PUNCT
ejpam-5509	64	7	18	18	NUM
ejpam-5509	64	8	(	(	PUNCT
ejpam-5509	64	9	1	1	NUM
ejpam-5509	64	10	)	)	PUNCT
ejpam-5509	64	11	(	(	PUNCT
ejpam-5509	64	12	2025	2025	NUM
ejpam-5509	64	13	)	)	PUNCT
ejpam-5509	64	14	,	,	PUNCT
ejpam-5509	64	15	5509	5509	NUM
ejpam-5509	64	16	4	4	NUM
ejpam-5509	64	17	of	of	ADP
ejpam-5509	64	18	27	27	NUM
ejpam-5509	64	19	chosen	choose	VERB
ejpam-5509	64	20	to	to	PART
ejpam-5509	64	21	model	model	VERB
ejpam-5509	64	22	the	the	DET
ejpam-5509	64	23	dynamics	dynamic	NOUN
ejpam-5509	64	24	of	of	ADP
ejpam-5509	64	25	hepatitis	hepatitis	PROPN
ejpam-5509	64	26	b	b	PROPN
ejpam-5509	64	27	(	(	PUNCT
ejpam-5509	64	28	hb	hb	X
ejpam-5509	64	29	)	)	PUNCT
ejpam-5509	64	30	using	use	VERB
ejpam-5509	64	31	a	a	DET
ejpam-5509	64	32	fractional	fractional	ADJ
ejpam-5509	64	33	-	-	PUNCT
ejpam-5509	64	34	order	order	NOUN
ejpam-5509	64	35	framework	framework	NOUN
ejpam-5509	64	36	to	to	PART
ejpam-5509	64	37	achieve	achieve	VERB
ejpam-5509	64	38	more	more	ADV
ejpam-5509	64	39	accurate	accurate	ADJ
ejpam-5509	64	40	and	and	CCONJ
ejpam-5509	64	41	precise	precise	ADJ
ejpam-5509	64	42	results	result	NOUN
ejpam-5509	64	43	.	.	PUNCT
ejpam-5509	65	1	the	the	DET
ejpam-5509	65	2	fractional	fractional	ADJ
ejpam-5509	65	3	approach	approach	NOUN
ejpam-5509	65	4	allows	allow	VERB
ejpam-5509	65	5	for	for	ADP
ejpam-5509	65	6	better	well	ADJ
ejpam-5509	65	7	representation	representation	NOUN
ejpam-5509	65	8	of	of	ADP
ejpam-5509	65	9	the	the	DET
ejpam-5509	65	10	memory	memory	NOUN
ejpam-5509	65	11	effects	effect	NOUN
ejpam-5509	65	12	and	and	CCONJ
ejpam-5509	65	13	complex	complex	ADJ
ejpam-5509	65	14	dynamics	dynamic	NOUN
ejpam-5509	65	15	inherent	inherent	ADJ
ejpam-5509	65	16	in	in	ADP
ejpam-5509	65	17	disease	disease	NOUN
ejpam-5509	65	18	transmission	transmission	NOUN
ejpam-5509	65	19	,	,	PUNCT
ejpam-5509	65	20	providing	provide	VERB
ejpam-5509	65	21	enhanced	enhanced	ADJ
ejpam-5509	65	22	insights	insight	NOUN
ejpam-5509	65	23	into	into	ADP
ejpam-5509	65	24	the	the	DET
ejpam-5509	65	25	behavior	behavior	NOUN
ejpam-5509	65	26	of	of	ADP
ejpam-5509	65	27	the	the	DET
ejpam-5509	65	28	infection	infection	NOUN
ejpam-5509	65	29	and	and	CCONJ
ejpam-5509	65	30	the	the	DET
ejpam-5509	65	31	impact	impact	NOUN
ejpam-5509	65	32	of	of	ADP
ejpam-5509	65	33	control	control	NOUN
ejpam-5509	65	34	measures	measure	NOUN
ejpam-5509	65	35	.	.	PUNCT
ejpam-5509	66	1	the	the	DET
ejpam-5509	66	2	present	present	ADJ
ejpam-5509	66	3	study	study	NOUN
ejpam-5509	66	4	is	be	AUX
ejpam-5509	66	5	organized	organize	VERB
ejpam-5509	66	6	as	as	SCONJ
ejpam-5509	66	7	follows	follow	VERB
ejpam-5509	66	8	:	:	PUNCT
ejpam-5509	66	9	section	section	NOUN
ejpam-5509	66	10	2	2	NUM
ejpam-5509	66	11	elucidates	elucidate	VERB
ejpam-5509	66	12	definitions	definition	NOUN
ejpam-5509	66	13	and	and	CCONJ
ejpam-5509	66	14	concepts	concept	NOUN
ejpam-5509	66	15	pertinent	pertinent	VERB
ejpam-5509	66	16	to	to	ADP
ejpam-5509	66	17	fractional	fractional	ADJ
ejpam-5509	66	18	theory	theory	NOUN
ejpam-5509	66	19	in	in	ADP
ejpam-5509	66	20	the	the	DET
ejpam-5509	66	21	context	context	NOUN
ejpam-5509	66	22	of	of	ADP
ejpam-5509	66	23	this	this	DET
ejpam-5509	66	24	research	research	NOUN
ejpam-5509	66	25	.	.	PUNCT
ejpam-5509	67	1	section	section	NOUN
ejpam-5509	67	2	3	3	NUM
ejpam-5509	67	3	introduces	introduce	NOUN
ejpam-5509	67	4	the	the	DET
ejpam-5509	67	5	developed	develop	VERB
ejpam-5509	67	6	hb	hb	PROPN
ejpam-5509	67	7	model	model	NOUN
ejpam-5509	67	8	.	.	PUNCT
ejpam-5509	68	1	section	section	NOUN
ejpam-5509	68	2	4	4	NUM
ejpam-5509	68	3	employs	employ	VERB
ejpam-5509	68	4	caputo	caputo	PROPN
ejpam-5509	68	5	-	-	PUNCT
ejpam-5509	68	6	fabrizio	fabrizio	PROPN
ejpam-5509	68	7	derivatives	derivative	NOUN
ejpam-5509	68	8	to	to	PART
ejpam-5509	68	9	portray	portray	VERB
ejpam-5509	68	10	the	the	DET
ejpam-5509	68	11	dynamics	dynamic	NOUN
ejpam-5509	68	12	,	,	PUNCT
ejpam-5509	68	13	computes	compute	VERB
ejpam-5509	68	14	the	the	DET
ejpam-5509	68	15	threshold	threshold	NOUN
ejpam-5509	68	16	parameter	parameter	NOUN
ejpam-5509	68	17	r0	r0	NOUN
ejpam-5509	68	18	,	,	PUNCT
ejpam-5509	68	19	and	and	CCONJ
ejpam-5509	68	20	investigates	investigate	VERB
ejpam-5509	68	21	the	the	DET
ejpam-5509	68	22	equilibria	equilibrium	NOUN
ejpam-5509	68	23	.	.	PUNCT
ejpam-5509	69	1	section	section	NOUN
ejpam-5509	69	2	5	5	NUM
ejpam-5509	69	3	delves	delf	NOUN
ejpam-5509	69	4	into	into	ADP
ejpam-5509	69	5	the	the	DET
ejpam-5509	69	6	uniqueness	uniqueness	NOUN
ejpam-5509	69	7	and	and	CCONJ
ejpam-5509	69	8	existence	existence	NOUN
ejpam-5509	69	9	of	of	ADP
ejpam-5509	69	10	solutions	solution	NOUN
ejpam-5509	69	11	,	,	PUNCT
ejpam-5509	69	12	employing	employ	VERB
ejpam-5509	69	13	fixed	fix	VERB
ejpam-5509	69	14	point	point	NOUN
ejpam-5509	69	15	theory	theory	NOUN
ejpam-5509	69	16	.	.	PUNCT
ejpam-5509	70	1	finally	finally	ADV
ejpam-5509	70	2	,	,	PUNCT
ejpam-5509	70	3	section	section	NOUN
ejpam-5509	70	4	6	6	NUM
ejpam-5509	70	5	provides	provide	VERB
ejpam-5509	70	6	a	a	DET
ejpam-5509	70	7	synthesis	synthesis	NOUN
ejpam-5509	70	8	of	of	ADP
ejpam-5509	70	9	the	the	DET
ejpam-5509	70	10	findings	finding	NOUN
ejpam-5509	70	11	and	and	CCONJ
ejpam-5509	70	12	concludes	conclude	VERB
ejpam-5509	70	13	the	the	DET
ejpam-5509	70	14	research	research	NOUN
ejpam-5509	70	15	.	.	PUNCT
ejpam-5509	71	1	2	2	X
ejpam-5509	71	2	.	.	X
ejpam-5509	71	3	theory	theory	NOUN
ejpam-5509	71	4	and	and	CCONJ
ejpam-5509	71	5	concepts	concept	NOUN
ejpam-5509	71	6	here	here	ADV
ejpam-5509	71	7	,	,	PUNCT
ejpam-5509	71	8	we	we	PRON
ejpam-5509	71	9	introduce	introduce	VERB
ejpam-5509	71	10	the	the	DET
ejpam-5509	71	11	fundamental	fundamental	ADJ
ejpam-5509	71	12	concept	concept	NOUN
ejpam-5509	71	13	of	of	ADP
ejpam-5509	71	14	the	the	DET
ejpam-5509	71	15	caputo	caputo	PROPN
ejpam-5509	71	16	-	-	PUNCT
ejpam-5509	71	17	fabrizio	fabrizio	PROPN
ejpam-5509	71	18	(	(	PUNCT
ejpam-5509	71	19	cf	cf	NOUN
ejpam-5509	71	20	)	)	PUNCT
ejpam-5509	71	21	fractional	fractional	ADJ
ejpam-5509	71	22	operator	operator	NOUN
ejpam-5509	71	23	for	for	ADP
ejpam-5509	71	24	the	the	DET
ejpam-5509	71	25	examination	examination	NOUN
ejpam-5509	71	26	of	of	ADP
ejpam-5509	71	27	our	our	PRON
ejpam-5509	71	28	proposed	propose	VERB
ejpam-5509	71	29	hb	hb	PROPN
ejpam-5509	71	30	model	model	PROPN
ejpam-5509	71	31	.	.	PUNCT
ejpam-5509	72	1	the	the	DET
ejpam-5509	72	2	theory	theory	NOUN
ejpam-5509	72	3	and	and	CCONJ
ejpam-5509	72	4	principles	principle	NOUN
ejpam-5509	72	5	underlying	underlie	VERB
ejpam-5509	72	6	the	the	DET
ejpam-5509	72	7	fractional	fractional	ADJ
ejpam-5509	72	8	cf	cf	NOUN
ejpam-5509	72	9	derivative	derivative	NOUN
ejpam-5509	72	10	are	be	AUX
ejpam-5509	72	11	outlined	outline	VERB
ejpam-5509	72	12	as	as	SCONJ
ejpam-5509	72	13	follows	follow	VERB
ejpam-5509	72	14	:	:	PUNCT
ejpam-5509	72	15	definition	definition	NOUN
ejpam-5509	72	16	1	1	NUM
ejpam-5509	72	17	.	.	PUNCT
ejpam-5509	72	18	assume	assume	VERB
ejpam-5509	72	19	a	a	DET
ejpam-5509	72	20	function	function	NOUN
ejpam-5509	72	21	k	k	PROPN
ejpam-5509	72	22	∈	∈	PROPN
ejpam-5509	72	23	h1(a	h1(a	PROPN
ejpam-5509	72	24	,	,	PUNCT
ejpam-5509	72	25	b	b	NOUN
ejpam-5509	72	26	)	)	PUNCT
ejpam-5509	72	27	,	,	PUNCT
ejpam-5509	72	28	subject	subject	ADJ
ejpam-5509	72	29	to	to	ADP
ejpam-5509	72	30	the	the	DET
ejpam-5509	72	31	condition	condition	NOUN
ejpam-5509	72	32	that	that	SCONJ
ejpam-5509	72	33	a	a	PRON
ejpam-5509	72	34	is	be	AUX
ejpam-5509	72	35	less	less	ADJ
ejpam-5509	72	36	than	than	ADP
ejpam-5509	72	37	b.	b.	PROPN
ejpam-5509	72	38	in	in	ADP
ejpam-5509	72	39	this	this	DET
ejpam-5509	72	40	case	case	NOUN
ejpam-5509	72	41	,	,	PUNCT
ejpam-5509	72	42	the	the	DET
ejpam-5509	72	43	cf	cf	NOUN
ejpam-5509	72	44	derivative	derivative	NOUN
ejpam-5509	72	45	is	be	AUX
ejpam-5509	72	46	given	give	VERB
ejpam-5509	72	47	by	by	ADP
ejpam-5509	72	48	dς	dς	PROPN
ejpam-5509	72	49	t	t	PROPN
ejpam-5509	72	50	(	(	PUNCT
ejpam-5509	72	51	k(t	k(t	NOUN
ejpam-5509	72	52	)	)	PUNCT
ejpam-5509	72	53	)	)	PUNCT
ejpam-5509	73	1	=	=	SYM
ejpam-5509	73	2	u(ς	u(ς	PROPN
ejpam-5509	73	3	)	)	PUNCT
ejpam-5509	73	4	1−	1−	NUM
ejpam-5509	73	5	ς	ς	PROPN
ejpam-5509	73	6	∫	∫	PROPN
ejpam-5509	73	7	t	t	PROPN
ejpam-5509	73	8	a	a	DET
ejpam-5509	73	9	k′(x	k′(x	NOUN
ejpam-5509	73	10	)	)	PUNCT
ejpam-5509	73	11	exp	exp	NOUN
ejpam-5509	73	12	(	(	PUNCT
ejpam-5509	73	13	−	−	PROPN
ejpam-5509	73	14	ς	ς	PROPN
ejpam-5509	73	15	t−	t−	PROPN
ejpam-5509	73	16	x	x	SYM
ejpam-5509	73	17	1−	1−	NUM
ejpam-5509	73	18	ς	ς	PROPN
ejpam-5509	73	19	)	)	PUNCT
ejpam-5509	73	20	dx	dx	PROPN
ejpam-5509	73	21	,	,	PUNCT
ejpam-5509	73	22	(	(	PUNCT
ejpam-5509	73	23	1	1	X
ejpam-5509	73	24	)	)	PUNCT
ejpam-5509	73	25	with	with	ADP
ejpam-5509	73	26	the	the	DET
ejpam-5509	73	27	condition	condition	NOUN
ejpam-5509	73	28	that	that	SCONJ
ejpam-5509	73	29	ς	ς	PROPN
ejpam-5509	73	30	∈	∈	PROPN
ejpam-5509	73	31	[	[	X
ejpam-5509	73	32	0	0	NUM
ejpam-5509	73	33	,	,	PUNCT
ejpam-5509	73	34	1	1	NUM
ejpam-5509	73	35	]	]	PUNCT
ejpam-5509	73	36	and	and	CCONJ
ejpam-5509	73	37	u(τ	u(τ	NUM
ejpam-5509	73	38	)	)	PUNCT
ejpam-5509	73	39	indicates	indicate	VERB
ejpam-5509	73	40	the	the	DET
ejpam-5509	73	41	normality	normality	NOUN
ejpam-5509	73	42	holding	hold	VERB
ejpam-5509	73	43	u(0	u(0	NOUN
ejpam-5509	73	44	)	)	PUNCT
ejpam-5509	73	45	=	=	SYM
ejpam-5509	74	1	u(1	u(1	PROPN
ejpam-5509	74	2	)	)	PUNCT
ejpam-5509	74	3	=	=	SYM
ejpam-5509	74	4	1	1	NUM
ejpam-5509	75	1	[	[	X
ejpam-5509	75	2	16	16	NUM
ejpam-5509	75	3	]	]	PUNCT
ejpam-5509	75	4	.	.	PUNCT
ejpam-5509	76	1	otherwise	otherwise	ADV
ejpam-5509	76	2	,	,	PUNCT
ejpam-5509	76	3	if	if	SCONJ
ejpam-5509	76	4	k	k	PROPN
ejpam-5509	76	5	/∈	/∈	VERB
ejpam-5509	76	6	h1(a	h1(a	PROPN
ejpam-5509	76	7	,	,	PUNCT
ejpam-5509	76	8	b	b	NOUN
ejpam-5509	76	9	)	)	PUNCT
ejpam-5509	76	10	,	,	PUNCT
ejpam-5509	76	11	then	then	ADV
ejpam-5509	76	12	dς	dς	X
ejpam-5509	76	13	t	t	PROPN
ejpam-5509	76	14	(	(	PUNCT
ejpam-5509	76	15	k(t	k(t	NOUN
ejpam-5509	76	16	)	)	PUNCT
ejpam-5509	76	17	)	)	PUNCT
ejpam-5509	76	18	=	=	SYM
ejpam-5509	77	1	ςu(ς	ςu(ς	X
ejpam-5509	77	2	)	)	PUNCT
ejpam-5509	77	3	1−	1−	NUM
ejpam-5509	77	4	ς	ς	PROPN
ejpam-5509	77	5	∫	∫	PROPN
ejpam-5509	77	6	t	t	PROPN
ejpam-5509	77	7	a	a	PRON
ejpam-5509	77	8	(	(	PUNCT
ejpam-5509	77	9	k(t)−	k(t)−	PROPN
ejpam-5509	77	10	k(x	k(x	PROPN
ejpam-5509	77	11	)	)	PUNCT
ejpam-5509	77	12	)	)	PUNCT
ejpam-5509	77	13	exp	exp	NOUN
ejpam-5509	77	14	(	(	PUNCT
ejpam-5509	77	15	−	−	PROPN
ejpam-5509	77	16	ς	ς	PROPN
ejpam-5509	77	17	t−	t−	PROPN
ejpam-5509	77	18	x	x	SYM
ejpam-5509	77	19	1−	1−	NUM
ejpam-5509	77	20	ς	ς	PROPN
ejpam-5509	77	21	)	)	PUNCT
ejpam-5509	77	22	dx	dx	PROPN
ejpam-5509	77	23	.	.	PUNCT
ejpam-5509	78	1	(	(	PUNCT
ejpam-5509	78	2	2	2	X
ejpam-5509	78	3	)	)	PUNCT
ejpam-5509	78	4	remark	remark	NOUN
ejpam-5509	78	5	1	1	NUM
ejpam-5509	78	6	.	.	PUNCT
ejpam-5509	79	1	if	if	SCONJ
ejpam-5509	79	2	α	α	PRON
ejpam-5509	79	3	=	=	SYM
ejpam-5509	79	4	1−ς	1−ς	NUM
ejpam-5509	79	5	ς	ς	PROPN
ejpam-5509	79	6	∈	∈	PROPN
ejpam-5509	79	7	[	[	X
ejpam-5509	79	8	0,∞	0,∞	NOUN
ejpam-5509	79	9	)	)	PUNCT
ejpam-5509	79	10	and	and	CCONJ
ejpam-5509	80	1	ς	ς	PROPN
ejpam-5509	80	2	=	=	SYM
ejpam-5509	80	3	1	1	NUM
ejpam-5509	80	4	1+α	1+α	NUM
ejpam-5509	80	5	∈	∈	PROPN
ejpam-5509	81	1	[	[	X
ejpam-5509	81	2	0	0	NUM
ejpam-5509	81	3	,	,	PUNCT
ejpam-5509	81	4	1	1	NUM
ejpam-5509	81	5	]	]	PUNCT
ejpam-5509	81	6	,	,	PUNCT
ejpam-5509	81	7	then	then	ADV
ejpam-5509	81	8	the	the	DET
ejpam-5509	81	9	above	above	ADJ
ejpam-5509	81	10	(	(	PUNCT
ejpam-5509	81	11	2	2	X
ejpam-5509	81	12	)	)	PUNCT
ejpam-5509	81	13	suggest	suggest	VERB
ejpam-5509	81	14	dς	dς	PROPN
ejpam-5509	81	15	t	t	PROPN
ejpam-5509	81	16	(	(	PUNCT
ejpam-5509	81	17	k(t	k(t	NOUN
ejpam-5509	81	18	)	)	PUNCT
ejpam-5509	81	19	)	)	PUNCT
ejpam-5509	82	1	=	=	SYM
ejpam-5509	82	2	m(α	m(α	PROPN
ejpam-5509	82	3	)	)	PUNCT
ejpam-5509	83	1	α	α	PROPN
ejpam-5509	83	2	∫	∫	PROPN
ejpam-5509	83	3	t	t	PROPN
ejpam-5509	83	4	a	a	DET
ejpam-5509	83	5	k′(x)e[−	k′(x)e[−	PROPN
ejpam-5509	83	6	t−x	t−x	PROPN
ejpam-5509	83	7	α	α	NOUN
ejpam-5509	83	8	]	]	X
ejpam-5509	83	9	dx	dx	PROPN
ejpam-5509	83	10	,	,	PUNCT
ejpam-5509	83	11	m(0	m(0	PROPN
ejpam-5509	83	12	)	)	PUNCT
ejpam-5509	83	13	=	=	SYM
ejpam-5509	83	14	m(∞	m(∞	X
ejpam-5509	83	15	)	)	PUNCT
ejpam-5509	83	16	=	=	SYM
ejpam-5509	83	17	1	1	X
ejpam-5509	83	18	.	.	PUNCT
ejpam-5509	83	19	(	(	PUNCT
ejpam-5509	83	20	3	3	X
ejpam-5509	83	21	)	)	PUNCT
ejpam-5509	83	22	moreover	moreover	ADV
ejpam-5509	83	23	,	,	PUNCT
ejpam-5509	83	24	we	we	PRON
ejpam-5509	83	25	have	have	VERB
ejpam-5509	83	26	lim	lim	PROPN
ejpam-5509	83	27	α−→0	α−→0	PROPN
ejpam-5509	83	28	1	1	NUM
ejpam-5509	83	29	α	α	NOUN
ejpam-5509	83	30	exp	exp	NOUN
ejpam-5509	83	31	(	(	PUNCT
ejpam-5509	83	32	−	−	PROPN
ejpam-5509	83	33	t−	t−	PROPN
ejpam-5509	83	34	x	x	SYM
ejpam-5509	83	35	α	α	NOUN
ejpam-5509	83	36	)	)	PUNCT
ejpam-5509	84	1	=	=	SYM
ejpam-5509	84	2	δ(x−	δ(x−	X
ejpam-5509	84	3	t	t	PROPN
ejpam-5509	84	4	)	)	PUNCT
ejpam-5509	84	5	.	.	PUNCT
ejpam-5509	85	1	(	(	PUNCT
ejpam-5509	85	2	4	4	X
ejpam-5509	85	3	)	)	PUNCT
ejpam-5509	85	4	definition	definition	NOUN
ejpam-5509	85	5	2	2	NUM
ejpam-5509	85	6	.	.	PUNCT
ejpam-5509	86	1	[	[	X
ejpam-5509	86	2	28	28	NUM
ejpam-5509	86	3	]	]	PUNCT
ejpam-5509	86	4	.	.	PUNCT
ejpam-5509	87	1	the	the	DET
ejpam-5509	87	2	fractional	fractional	ADJ
ejpam-5509	87	3	integral	integral	NOUN
ejpam-5509	87	4	of	of	ADP
ejpam-5509	87	5	a	a	DET
ejpam-5509	87	6	given	give	VERB
ejpam-5509	87	7	function	function	NOUN
ejpam-5509	87	8	is	be	AUX
ejpam-5509	87	9	expressed	express	VERB
ejpam-5509	87	10	as	as	SCONJ
ejpam-5509	87	11	follows	follow	VERB
ejpam-5509	87	12	.	.	PUNCT
ejpam-5509	88	1	iςt	iςt	VERB
ejpam-5509	88	2	(	(	PUNCT
ejpam-5509	88	3	k(t	k(t	NOUN
ejpam-5509	88	4	)	)	PUNCT
ejpam-5509	88	5	)	)	PUNCT
ejpam-5509	89	1	=	=	PUNCT
ejpam-5509	90	1	2(1−	2(1−	NUM
ejpam-5509	90	2	ς	ς	NOUN
ejpam-5509	90	3	)	)	PUNCT
ejpam-5509	90	4	(	(	PUNCT
ejpam-5509	90	5	2−	2−	NUM
ejpam-5509	90	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	90	7	)	)	PUNCT
ejpam-5509	90	8	k(t	k(t	NOUN
ejpam-5509	90	9	)	)	PUNCT
ejpam-5509	91	1	+	+	CCONJ
ejpam-5509	91	2	2ς	2ς	NUM
ejpam-5509	91	3	(	(	PUNCT
ejpam-5509	91	4	2−	2−	NUM
ejpam-5509	91	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	91	6	)	)	PUNCT
ejpam-5509	91	7	∫	∫	PROPN
ejpam-5509	91	8	t	t	PROPN
ejpam-5509	91	9	0	0	NUM
ejpam-5509	91	10	k(u)du	k(u)du	PROPN
ejpam-5509	91	11	,	,	PUNCT
ejpam-5509	91	12	t	t	PROPN
ejpam-5509	91	13	≥	≥	PROPN
ejpam-5509	91	14	0	0	NUM
ejpam-5509	91	15	.	.	PUNCT
ejpam-5509	92	1	(	(	PUNCT
ejpam-5509	92	2	5	5	NUM
ejpam-5509	92	3	)	)	PUNCT
ejpam-5509	92	4	next	next	ADV
ejpam-5509	92	5	,	,	PUNCT
ejpam-5509	92	6	we	we	PRON
ejpam-5509	92	7	move	move	VERB
ejpam-5509	92	8	to	to	ADP
ejpam-5509	92	9	the	the	DET
ejpam-5509	92	10	following	follow	VERB
ejpam-5509	92	11	remark	remark	NOUN
ejpam-5509	92	12	:	:	PUNCT
ejpam-5509	92	13	i.	i.	PROPN
ejpam-5509	92	14	ahmad	ahmad	PROPN
ejpam-5509	92	15	et	et	PROPN
ejpam-5509	92	16	al	al	PROPN
ejpam-5509	92	17	.	.	PUNCT
ejpam-5509	92	18	/	/	SYM
ejpam-5509	92	19	eur	eur	PROPN
ejpam-5509	92	20	.	.	PUNCT
ejpam-5509	93	1	j.	j.	PROPN
ejpam-5509	93	2	pure	pure	PROPN
ejpam-5509	93	3	appl	appl	PROPN
ejpam-5509	93	4	.	.	PROPN
ejpam-5509	93	5	math	math	PROPN
ejpam-5509	93	6	,	,	PUNCT
ejpam-5509	93	7	18	18	NUM
ejpam-5509	93	8	(	(	PUNCT
ejpam-5509	93	9	1	1	NUM
ejpam-5509	93	10	)	)	PUNCT
ejpam-5509	93	11	(	(	PUNCT
ejpam-5509	93	12	2025	2025	NUM
ejpam-5509	93	13	)	)	PUNCT
ejpam-5509	93	14	,	,	PUNCT
ejpam-5509	93	15	5509	5509	NUM
ejpam-5509	93	16	5	5	NUM
ejpam-5509	93	17	of	of	ADP
ejpam-5509	93	18	27	27	NUM
ejpam-5509	93	19	remark	remark	NOUN
ejpam-5509	93	20	2	2	NUM
ejpam-5509	93	21	.	.	PUNCT
ejpam-5509	94	1	the	the	DET
ejpam-5509	94	2	definition	definition	NOUN
ejpam-5509	94	3	2	2	NUM
ejpam-5509	94	4	provided	provide	VERB
ejpam-5509	94	5	above	above	ADP
ejpam-5509	94	6	yields	yield	NOUN
ejpam-5509	94	7	the	the	DET
ejpam-5509	94	8	following	follow	VERB
ejpam-5509	94	9	result	result	NOUN
ejpam-5509	94	10	.	.	PUNCT
ejpam-5509	95	1	2(1−	2(1−	X
ejpam-5509	95	2	ς	ς	X
ejpam-5509	95	3	)	)	PUNCT
ejpam-5509	95	4	(	(	PUNCT
ejpam-5509	95	5	2−	2−	NUM
ejpam-5509	95	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	95	7	)	)	PUNCT
ejpam-5509	96	1	+	+	NUM
ejpam-5509	96	2	2ς	2ς	NUM
ejpam-5509	96	3	(	(	PUNCT
ejpam-5509	96	4	2−	2−	NUM
ejpam-5509	96	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	96	6	)	)	PUNCT
ejpam-5509	96	7	=	=	SYM
ejpam-5509	96	8	1	1	NUM
ejpam-5509	96	9	,	,	PUNCT
ejpam-5509	96	10	(	(	PUNCT
ejpam-5509	96	11	6	6	NUM
ejpam-5509	96	12	)	)	PUNCT
ejpam-5509	96	13	with	with	ADP
ejpam-5509	96	14	the	the	DET
ejpam-5509	96	15	condition	condition	NOUN
ejpam-5509	96	16	that	that	SCONJ
ejpam-5509	96	17	u(ς	u(ς	PROPN
ejpam-5509	96	18	)	)	PUNCT
ejpam-5509	96	19	=	=	PROPN
ejpam-5509	96	20	2	2	NUM
ejpam-5509	96	21	2−ς	2−ς	NUM
ejpam-5509	96	22	.	.	PUNCT
ejpam-5509	97	1	in	in	ADP
ejpam-5509	97	2	[	[	X
ejpam-5509	97	3	28	28	NUM
ejpam-5509	97	4	]	]	X
ejpam-5509	97	5	,	,	PUNCT
ejpam-5509	97	6	new	new	ADJ
ejpam-5509	97	7	operator	operator	NOUN
ejpam-5509	97	8	has	have	AUX
ejpam-5509	97	9	been	be	AUX
ejpam-5509	97	10	developed	develop	VERB
ejpam-5509	97	11	by	by	ADP
ejpam-5509	97	12	utilizing	utilize	VERB
ejpam-5509	97	13	(	(	PUNCT
ejpam-5509	97	14	6	6	NUM
ejpam-5509	97	15	)	)	PUNCT
ejpam-5509	97	16	as	as	SCONJ
ejpam-5509	97	17	follows	follow	VERB
ejpam-5509	97	18	dς	dς	PROPN
ejpam-5509	97	19	t	t	PROPN
ejpam-5509	97	20	(	(	PUNCT
ejpam-5509	97	21	k(t	k(t	NOUN
ejpam-5509	97	22	)	)	PUNCT
ejpam-5509	97	23	)	)	PUNCT
ejpam-5509	98	1	=	=	PUNCT
ejpam-5509	98	2	1	1	NUM
ejpam-5509	98	3	1−	1−	NUM
ejpam-5509	98	4	ς	ς	PROPN
ejpam-5509	98	5	∫	∫	PROPN
ejpam-5509	98	6	t	t	PROPN
ejpam-5509	98	7	0	0	NUM
ejpam-5509	98	8	k′(x	k′(x	NOUN
ejpam-5509	98	9	)	)	PUNCT
ejpam-5509	98	10	exp	exp	NOUN
ejpam-5509	98	11	(	(	PUNCT
ejpam-5509	98	12	ς	ς	PROPN
ejpam-5509	98	13	t−	t−	PROPN
ejpam-5509	98	14	x	x	PROPN
ejpam-5509	98	15	1−	1−	NUM
ejpam-5509	98	16	ς	ς	PROPN
ejpam-5509	98	17	)	)	PUNCT
ejpam-5509	98	18	dx	dx	PROPN
ejpam-5509	98	19	.	.	PUNCT
ejpam-5509	99	1	(	(	PUNCT
ejpam-5509	99	2	7	7	X
ejpam-5509	99	3	)	)	PUNCT
ejpam-5509	99	4	in	in	ADP
ejpam-5509	99	5	this	this	DET
ejpam-5509	99	6	context	context	NOUN
ejpam-5509	99	7	,	,	PUNCT
ejpam-5509	99	8	the	the	DET
ejpam-5509	99	9	fractional	fractional	ADJ
ejpam-5509	99	10	order	order	NOUN
ejpam-5509	99	11	adheres	adhere	VERB
ejpam-5509	99	12	to	to	ADP
ejpam-5509	99	13	the	the	DET
ejpam-5509	99	14	requirement	requirement	NOUN
ejpam-5509	99	15	that	that	SCONJ
ejpam-5509	99	16	0	0	PUNCT
ejpam-5509	99	17	<	<	X
ejpam-5509	99	18	ς	ς	X
ejpam-5509	99	19	<	<	X
ejpam-5509	99	20	1	1	NUM
ejpam-5509	99	21	.	.	PUNCT
ejpam-5509	100	1	in	in	ADP
ejpam-5509	100	2	the	the	DET
ejpam-5509	100	3	literature	literature	NOUN
ejpam-5509	100	4	,	,	PUNCT
ejpam-5509	100	5	various	various	ADJ
ejpam-5509	100	6	authors	author	NOUN
ejpam-5509	100	7	have	have	AUX
ejpam-5509	100	8	introduced	introduce	VERB
ejpam-5509	100	9	several	several	ADJ
ejpam-5509	100	10	fractional	fractional	ADJ
ejpam-5509	100	11	operators	operator	NOUN
ejpam-5509	100	12	.	.	PUNCT
ejpam-5509	101	1	some	some	DET
ejpam-5509	101	2	novel	novel	ADJ
ejpam-5509	101	3	fractional	fractional	ADJ
ejpam-5509	101	4	operators	operator	NOUN
ejpam-5509	101	5	are	be	AUX
ejpam-5509	101	6	defined	define	VERB
ejpam-5509	101	7	below	below	ADP
ejpam-5509	101	8	:	:	PUNCT
ejpam-5509	101	9	definition	definition	NOUN
ejpam-5509	101	10	3	3	NUM
ejpam-5509	101	11	.	.	PUNCT
ejpam-5509	102	1	the	the	DET
ejpam-5509	102	2	atangana	atangana	PROPN
ejpam-5509	102	3	-	-	PUNCT
ejpam-5509	102	4	beleanu	beleanu	NOUN
ejpam-5509	102	5	fractional	fractional	ADJ
ejpam-5509	102	6	operator	operator	NOUN
ejpam-5509	102	7	in	in	ADP
ejpam-5509	102	8	the	the	DET
ejpam-5509	102	9	caputo	caputo	PROPN
ejpam-5509	102	10	form	form	NOUN
ejpam-5509	102	11	is	be	AUX
ejpam-5509	102	12	given	give	VERB
ejpam-5509	102	13	by	by	ADP
ejpam-5509	102	14	:	:	PUNCT
ejpam-5509	102	15	abc	abc	PROPN
ejpam-5509	102	16	p	p	PROPN
ejpam-5509	102	17	dς	dς	PROPN
ejpam-5509	102	18	t	t	PROPN
ejpam-5509	102	19	g(t	g(t	PROPN
ejpam-5509	102	20	)	)	PUNCT
ejpam-5509	103	1	=	=	SYM
ejpam-5509	103	2	b(ς	b(ς	PROPN
ejpam-5509	103	3	)	)	PUNCT
ejpam-5509	103	4	1−	1−	NUM
ejpam-5509	104	1	ς	ς	PROPN
ejpam-5509	104	2	∫	∫	PROPN
ejpam-5509	104	3	t	t	PROPN
ejpam-5509	104	4	p	p	PROPN
ejpam-5509	104	5	g′(κ)eς	g′(κ)eς	PROPN
ejpam-5509	104	6	[	[	PUNCT
ejpam-5509	104	7	−	−	PROPN
ejpam-5509	104	8	ς	ς	PROPN
ejpam-5509	104	9	(	(	PUNCT
ejpam-5509	104	10	t−	t−	PROPN
ejpam-5509	104	11	κ)ς	κ)ς	NOUN
ejpam-5509	105	1	1−	1−	NUM
ejpam-5509	105	2	ς	ς	X
ejpam-5509	105	3	]	]	PUNCT
ejpam-5509	105	4	dκ	dκ	PROPN
ejpam-5509	105	5	.	.	PROPN
ejpam-5509	106	1	in	in	ADP
ejpam-5509	106	2	which	which	PRON
ejpam-5509	106	3	g	g	PROPN
ejpam-5509	106	4	∈	∈	PROPN
ejpam-5509	106	5	h1(p	h1(p	PROPN
ejpam-5509	106	6	,	,	PUNCT
ejpam-5509	106	7	q	q	NOUN
ejpam-5509	106	8	)	)	PUNCT
ejpam-5509	106	9	,	,	PUNCT
ejpam-5509	106	10	q	q	X
ejpam-5509	106	11	>	>	X
ejpam-5509	106	12	p	p	X
ejpam-5509	106	13	,	,	PUNCT
ejpam-5509	106	14	and	and	CCONJ
ejpam-5509	106	15	∈	∈	PROPN
ejpam-5509	107	1	[	[	X
ejpam-5509	107	2	0	0	NUM
ejpam-5509	107	3	,	,	PUNCT
ejpam-5509	107	4	1	1	NUM
ejpam-5509	107	5	]	]	PUNCT
ejpam-5509	107	6	.	.	PUNCT
ejpam-5509	108	1	definition	definition	NOUN
ejpam-5509	108	2	4	4	NUM
ejpam-5509	108	3	.	.	PUNCT
ejpam-5509	109	1	[	[	X
ejpam-5509	109	2	24	24	NUM
ejpam-5509	109	3	]	]	PUNCT
ejpam-5509	109	4	.	.	PUNCT
ejpam-5509	110	1	the	the	DET
ejpam-5509	110	2	he	he	PRON
ejpam-5509	110	3	’s	’s	PART
ejpam-5509	110	4	fractional	fractional	ADJ
ejpam-5509	110	5	operator	operator	NOUN
ejpam-5509	110	6	is	be	AUX
ejpam-5509	110	7	defined	define	VERB
ejpam-5509	110	8	as	as	SCONJ
ejpam-5509	110	9	follows	follow	VERB
ejpam-5509	110	10	:	:	PUNCT
ejpam-5509	110	11	dς	dς	PROPN
ejpam-5509	110	12	t	t	PROPN
ejpam-5509	110	13	g(t	g(t	PROPN
ejpam-5509	110	14	)	)	PUNCT
ejpam-5509	111	1	=	=	SYM
ejpam-5509	111	2	1	1	NUM
ejpam-5509	111	3	γ(1−	γ(1−	NOUN
ejpam-5509	111	4	ς	ς	NOUN
ejpam-5509	111	5	)	)	PUNCT
ejpam-5509	112	1	dn	dn	PROPN
ejpam-5509	112	2	dtn	dtn	PROPN
ejpam-5509	112	3	∫	∫	PROPN
ejpam-5509	112	4	t	t	PROPN
ejpam-5509	112	5	t0	t0	PROPN
ejpam-5509	112	6	(	(	PUNCT
ejpam-5509	112	7	s−	s−	NOUN
ejpam-5509	112	8	t)n−ς−1[g0(s)−	t)n−ς−1[g0(s)−	NOUN
ejpam-5509	112	9	g(s)]ds	g(s)]ds	PROPN
ejpam-5509	112	10	.	.	PUNCT
ejpam-5509	113	1	where	where	SCONJ
ejpam-5509	113	2	ς	ς	PROPN
ejpam-5509	113	3	is	be	AUX
ejpam-5509	113	4	the	the	DET
ejpam-5509	113	5	fractional	fractional	ADJ
ejpam-5509	113	6	order	order	NOUN
ejpam-5509	113	7	and	and	CCONJ
ejpam-5509	113	8	g0	g0	NOUN
ejpam-5509	113	9	is	be	AUX
ejpam-5509	113	10	a	a	DET
ejpam-5509	113	11	known	know	VERB
ejpam-5509	113	12	function	function	NOUN
ejpam-5509	113	13	.	.	PUNCT
ejpam-5509	114	1	3	3	X
ejpam-5509	114	2	.	.	X
ejpam-5509	114	3	formulation	formulation	NOUN
ejpam-5509	114	4	of	of	ADP
ejpam-5509	114	5	the	the	DET
ejpam-5509	114	6	model	model	NOUN
ejpam-5509	114	7	we	we	PRON
ejpam-5509	114	8	constructed	construct	VERB
ejpam-5509	114	9	a	a	DET
ejpam-5509	114	10	compartmental	compartmental	ADJ
ejpam-5509	114	11	mathematical	mathematical	ADJ
ejpam-5509	114	12	model	model	NOUN
ejpam-5509	114	13	to	to	PART
ejpam-5509	114	14	simulate	simulate	VERB
ejpam-5509	114	15	the	the	DET
ejpam-5509	114	16	dynamics	dynamic	NOUN
ejpam-5509	114	17	of	of	ADP
ejpam-5509	114	18	hepatitis	hepatitis	PROPN
ejpam-5509	114	19	b	b	PROPN
ejpam-5509	114	20	transmission	transmission	NOUN
ejpam-5509	114	21	based	base	VERB
ejpam-5509	114	22	on	on	ADP
ejpam-5509	114	23	various	various	ADJ
ejpam-5509	114	24	transmission	transmission	NOUN
ejpam-5509	114	25	routes	route	NOUN
ejpam-5509	114	26	.	.	PUNCT
ejpam-5509	115	1	the	the	DET
ejpam-5509	115	2	total	total	ADJ
ejpam-5509	115	3	population	population	NOUN
ejpam-5509	115	4	,	,	PUNCT
ejpam-5509	115	5	denoted	denote	VERB
ejpam-5509	115	6	as	as	ADP
ejpam-5509	115	7	n(t	n(t	PROPN
ejpam-5509	115	8	)	)	PUNCT
ejpam-5509	115	9	,	,	PUNCT
ejpam-5509	115	10	is	be	AUX
ejpam-5509	115	11	partitioned	partition	VERB
ejpam-5509	115	12	into	into	ADP
ejpam-5509	115	13	six	six	NUM
ejpam-5509	115	14	distinct	distinct	ADJ
ejpam-5509	115	15	classes	class	NOUN
ejpam-5509	115	16	:	:	PUNCT
ejpam-5509	115	17	s(t	s(t	PROPN
ejpam-5509	115	18	)	)	PUNCT
ejpam-5509	115	19	,	,	PUNCT
ejpam-5509	115	20	v1(t	v1(t	CCONJ
ejpam-5509	115	21	)	)	PUNCT
ejpam-5509	115	22	,	,	PUNCT
ejpam-5509	115	23	v2(t	v2(t	NOUN
ejpam-5509	115	24	)	)	PUNCT
ejpam-5509	115	25	,	,	PUNCT
ejpam-5509	115	26	i(t	i(t	PROPN
ejpam-5509	115	27	)	)	PUNCT
ejpam-5509	115	28	,	,	PUNCT
ejpam-5509	115	29	c(t	c(t	PROPN
ejpam-5509	115	30	)	)	PUNCT
ejpam-5509	115	31	,	,	PUNCT
ejpam-5509	115	32	and	and	CCONJ
ejpam-5509	115	33	r(t	r(t	NOUN
ejpam-5509	115	34	)	)	PUNCT
ejpam-5509	115	35	.	.	PUNCT
ejpam-5509	116	1	consequently	consequently	ADV
ejpam-5509	116	2	,	,	PUNCT
ejpam-5509	116	3	n(t	n(t	PROPN
ejpam-5509	116	4	)	)	PUNCT
ejpam-5509	116	5	can	can	AUX
ejpam-5509	116	6	be	be	AUX
ejpam-5509	116	7	described	describe	VERB
ejpam-5509	116	8	as	as	SCONJ
ejpam-5509	116	9	follows	follow	VERB
ejpam-5509	116	10	:	:	PUNCT
ejpam-5509	116	11	n(t	n(t	X
ejpam-5509	116	12	)	)	PUNCT
ejpam-5509	116	13	=	=	SYM
ejpam-5509	116	14	s(t	s(t	PROPN
ejpam-5509	116	15	)	)	PUNCT
ejpam-5509	116	16	+	+	NUM
ejpam-5509	116	17	v1(t	v1(t	X
ejpam-5509	116	18	)	)	PUNCT
ejpam-5509	116	19	+	+	PUNCT
ejpam-5509	117	1	v2(t	v2(t	X
ejpam-5509	117	2	)	)	PUNCT
ejpam-5509	117	3	+	+	CCONJ
ejpam-5509	117	4	i(t	i(t	NOUN
ejpam-5509	117	5	)	)	PUNCT
ejpam-5509	118	1	+	+	X
ejpam-5509	118	2	c(t	c(t	PROPN
ejpam-5509	118	3	)	)	PUNCT
ejpam-5509	118	4	+	+	NOUN
ejpam-5509	118	5	r(t	r(t	NOUN
ejpam-5509	118	6	)	)	PUNCT
ejpam-5509	118	7	.	.	PUNCT
ejpam-5509	119	1	(	(	PUNCT
ejpam-5509	119	2	8)	8)	NUM
ejpam-5509	119	3	additionally	additionally	ADV
ejpam-5509	119	4	,	,	PUNCT
ejpam-5509	119	5	s(t	s(t	PROPN
ejpam-5509	119	6	)	)	PUNCT
ejpam-5509	119	7	stands	stand	VERB
ejpam-5509	119	8	for	for	ADP
ejpam-5509	119	9	individuals	individual	NOUN
ejpam-5509	119	10	who	who	PRON
ejpam-5509	119	11	have	have	AUX
ejpam-5509	119	12	not	not	PART
ejpam-5509	119	13	encountered	encounter	VERB
ejpam-5509	119	14	the	the	DET
ejpam-5509	119	15	infection	infection	NOUN
ejpam-5509	119	16	yet	yet	ADV
ejpam-5509	119	17	and	and	CCONJ
ejpam-5509	119	18	remain	remain	VERB
ejpam-5509	119	19	susceptible	susceptible	ADJ
ejpam-5509	119	20	to	to	ADP
ejpam-5509	119	21	infection	infection	NOUN
ejpam-5509	119	22	.	.	PUNCT
ejpam-5509	120	1	v1(t	v1(t	X
ejpam-5509	120	2	)	)	PUNCT
ejpam-5509	120	3	denotes	denote	VERB
ejpam-5509	120	4	those	those	PRON
ejpam-5509	120	5	who	who	PRON
ejpam-5509	120	6	have	have	AUX
ejpam-5509	120	7	been	be	AUX
ejpam-5509	120	8	administered	administer	VERB
ejpam-5509	120	9	the	the	DET
ejpam-5509	120	10	initial	initial	ADJ
ejpam-5509	120	11	vaccine	vaccine	NOUN
ejpam-5509	120	12	dose	dose	VERB
ejpam-5509	120	13	,	,	PUNCT
ejpam-5509	120	14	whereas	whereas	SCONJ
ejpam-5509	120	15	v2(t	v2(t	X
ejpam-5509	120	16	)	)	PUNCT
ejpam-5509	120	17	represents	represent	VERB
ejpam-5509	120	18	individuals	individual	NOUN
ejpam-5509	120	19	who	who	PRON
ejpam-5509	120	20	have	have	AUX
ejpam-5509	120	21	successfully	successfully	ADV
ejpam-5509	120	22	received	receive	VERB
ejpam-5509	120	23	both	both	DET
ejpam-5509	120	24	doses	dose	NOUN
ejpam-5509	120	25	of	of	ADP
ejpam-5509	120	26	the	the	DET
ejpam-5509	120	27	vaccine	vaccine	NOUN
ejpam-5509	120	28	,	,	PUNCT
ejpam-5509	120	29	usually	usually	ADV
ejpam-5509	120	30	with	with	ADP
ejpam-5509	120	31	a	a	DET
ejpam-5509	120	32	one	one	NUM
ejpam-5509	120	33	-	-	PUNCT
ejpam-5509	120	34	month	month	NOUN
ejpam-5509	120	35	interval	interval	NOUN
ejpam-5509	120	36	between	between	ADP
ejpam-5509	120	37	them	they	PRON
ejpam-5509	120	38	.	.	PUNCT
ejpam-5509	121	1	i(t	i(t	NOUN
ejpam-5509	121	2	)	)	PUNCT
ejpam-5509	121	3	denotes	denote	VERB
ejpam-5509	121	4	those	those	PRON
ejpam-5509	121	5	who	who	PRON
ejpam-5509	121	6	are	be	AUX
ejpam-5509	121	7	in	in	ADP
ejpam-5509	121	8	the	the	DET
ejpam-5509	121	9	infectious	infectious	ADJ
ejpam-5509	121	10	acute	acute	ADJ
ejpam-5509	121	11	stage	stage	NOUN
ejpam-5509	121	12	of	of	ADP
ejpam-5509	121	13	hb	hb	PROPN
ejpam-5509	121	14	,	,	PUNCT
ejpam-5509	121	15	which	which	PRON
ejpam-5509	121	16	typically	typically	ADV
ejpam-5509	121	17	spans	span	VERB
ejpam-5509	121	18	the	the	DET
ejpam-5509	121	19	first	first	ADJ
ejpam-5509	121	20	six	six	NUM
ejpam-5509	121	21	months	month	NOUN
ejpam-5509	121	22	following	follow	VERB
ejpam-5509	121	23	infection	infection	NOUN
ejpam-5509	121	24	.	.	PUNCT
ejpam-5509	122	1	c(t	c(t	PROPN
ejpam-5509	122	2	)	)	PUNCT
ejpam-5509	122	3	represents	represent	VERB
ejpam-5509	122	4	individuals	individual	NOUN
ejpam-5509	122	5	in	in	ADP
ejpam-5509	122	6	the	the	DET
ejpam-5509	122	7	chronic	chronic	ADJ
ejpam-5509	122	8	infectious	infectious	ADJ
ejpam-5509	122	9	stage	stage	NOUN
ejpam-5509	122	10	,	,	PUNCT
ejpam-5509	122	11	and	and	CCONJ
ejpam-5509	122	12	r(t	r(t	NOUN
ejpam-5509	122	13	)	)	PUNCT
ejpam-5509	122	14	designates	designate	VERB
ejpam-5509	122	15	those	those	PRON
ejpam-5509	122	16	who	who	PRON
ejpam-5509	122	17	have	have	AUX
ejpam-5509	122	18	successfully	successfully	ADV
ejpam-5509	122	19	recovered	recover	VERB
ejpam-5509	122	20	from	from	ADP
ejpam-5509	122	21	hepatitis	hepatitis	PROPN
ejpam-5509	122	22	b.	b.	PROPN
ejpam-5509	122	23	i.	i.	PROPN
ejpam-5509	122	24	ahmad	ahmad	PROPN
ejpam-5509	122	25	et	et	PROPN
ejpam-5509	122	26	al	al	PROPN
ejpam-5509	122	27	.	.	PUNCT
ejpam-5509	122	28	/	/	SYM
ejpam-5509	122	29	eur	eur	PROPN
ejpam-5509	122	30	.	.	PUNCT
ejpam-5509	123	1	j.	j.	PROPN
ejpam-5509	123	2	pure	pure	PROPN
ejpam-5509	123	3	appl	appl	PROPN
ejpam-5509	123	4	.	.	PROPN
ejpam-5509	123	5	math	math	PROPN
ejpam-5509	123	6	,	,	PUNCT
ejpam-5509	123	7	18	18	NUM
ejpam-5509	123	8	(	(	PUNCT
ejpam-5509	123	9	1	1	NUM
ejpam-5509	123	10	)	)	PUNCT
ejpam-5509	123	11	(	(	PUNCT
ejpam-5509	123	12	2025	2025	NUM
ejpam-5509	123	13	)	)	PUNCT
ejpam-5509	123	14	,	,	PUNCT
ejpam-5509	123	15	5509	5509	NUM
ejpam-5509	123	16	6	6	NUM
ejpam-5509	123	17	of	of	ADP
ejpam-5509	123	18	27	27	NUM
ejpam-5509	123	19	the	the	DET
ejpam-5509	123	20	underlying	underlying	ADJ
ejpam-5509	123	21	assumptions	assumption	NOUN
ejpam-5509	123	22	of	of	ADP
ejpam-5509	123	23	this	this	DET
ejpam-5509	123	24	model	model	NOUN
ejpam-5509	123	25	include	include	VERB
ejpam-5509	123	26	the	the	DET
ejpam-5509	123	27	transmission	transmission	NOUN
ejpam-5509	123	28	of	of	ADP
ejpam-5509	123	29	hb	hb	PROPN
ejpam-5509	123	30	via	via	ADP
ejpam-5509	123	31	both	both	CCONJ
ejpam-5509	123	32	vertical	vertical	ADJ
ejpam-5509	123	33	and	and	CCONJ
ejpam-5509	123	34	horizontal	horizontal	ADJ
ejpam-5509	123	35	methods	method	NOUN
ejpam-5509	123	36	.	.	PUNCT
ejpam-5509	124	1	additionally	additionally	ADV
ejpam-5509	124	2	,	,	PUNCT
ejpam-5509	124	3	the	the	DET
ejpam-5509	124	4	model	model	NOUN
ejpam-5509	124	5	disregards	disregard	VERB
ejpam-5509	124	6	infection	infection	NOUN
ejpam-5509	124	7	from	from	ADP
ejpam-5509	124	8	acutely	acutely	ADV
ejpam-5509	124	9	infected	infect	VERB
ejpam-5509	124	10	mothers	mother	NOUN
ejpam-5509	124	11	,	,	PUNCT
ejpam-5509	124	12	as	as	SCONJ
ejpam-5509	124	13	the	the	DET
ejpam-5509	124	14	acute	acute	ADJ
ejpam-5509	124	15	infection	infection	NOUN
ejpam-5509	124	16	stage	stage	NOUN
ejpam-5509	124	17	is	be	AUX
ejpam-5509	124	18	relatively	relatively	ADV
ejpam-5509	124	19	short	short	ADJ
ejpam-5509	124	20	compared	compare	VERB
ejpam-5509	124	21	to	to	ADP
ejpam-5509	124	22	the	the	DET
ejpam-5509	124	23	duration	duration	NOUN
ejpam-5509	124	24	of	of	ADP
ejpam-5509	124	25	pregnancy	pregnancy	NOUN
ejpam-5509	124	26	.	.	PUNCT
ejpam-5509	125	1	the	the	DET
ejpam-5509	125	2	model	model	NOUN
ejpam-5509	125	3	accounts	account	VERB
ejpam-5509	125	4	for	for	ADP
ejpam-5509	125	5	disease	disease	NOUN
ejpam-5509	125	6	-	-	PUNCT
ejpam-5509	125	7	induced	induce	VERB
ejpam-5509	125	8	mortality	mortality	NOUN
ejpam-5509	125	9	within	within	ADP
ejpam-5509	125	10	the	the	DET
ejpam-5509	125	11	chronic	chronic	ADJ
ejpam-5509	125	12	class	class	NOUN
ejpam-5509	125	13	and	and	CCONJ
ejpam-5509	125	14	incorporates	incorporate	VERB
ejpam-5509	125	15	a	a	DET
ejpam-5509	125	16	natural	natural	ADJ
ejpam-5509	125	17	mortality	mortality	NOUN
ejpam-5509	125	18	rate	rate	NOUN
ejpam-5509	125	19	for	for	ADP
ejpam-5509	125	20	each	each	DET
ejpam-5509	125	21	compartment	compartment	NOUN
ejpam-5509	125	22	.	.	PUNCT
ejpam-5509	126	1	furthermore	furthermore	ADV
ejpam-5509	126	2	,	,	PUNCT
ejpam-5509	126	3	it	it	PRON
ejpam-5509	126	4	postulates	postulate	VERB
ejpam-5509	126	5	a	a	DET
ejpam-5509	126	6	constant	constant	ADJ
ejpam-5509	126	7	generation	generation	NOUN
ejpam-5509	126	8	of	of	ADP
ejpam-5509	126	9	new	new	ADJ
ejpam-5509	126	10	susceptible	susceptible	ADJ
ejpam-5509	126	11	individuals	individual	NOUN
ejpam-5509	126	12	,	,	PUNCT
ejpam-5509	126	13	represented	represent	VERB
ejpam-5509	126	14	by	by	ADP
ejpam-5509	126	15	the	the	DET
ejpam-5509	126	16	symbol	symbol	NOUN
ejpam-5509	126	17	π	π	X
ejpam-5509	126	18	.	.	PUNCT
ejpam-5509	127	1	all	all	DET
ejpam-5509	127	2	parameters	parameter	NOUN
ejpam-5509	127	3	involved	involve	VERB
ejpam-5509	127	4	in	in	ADP
ejpam-5509	127	5	the	the	DET
ejpam-5509	127	6	model	model	NOUN
ejpam-5509	127	7	are	be	AUX
ejpam-5509	127	8	nonnegative	nonnegative	ADJ
ejpam-5509	127	9	.	.	PUNCT
ejpam-5509	128	1	individuals	individual	NOUN
ejpam-5509	128	2	at	at	ADP
ejpam-5509	128	3	risk	risk	NOUN
ejpam-5509	128	4	can	can	AUX
ejpam-5509	128	5	contract	contract	VERB
ejpam-5509	128	6	the	the	DET
ejpam-5509	128	7	infection	infection	NOUN
ejpam-5509	128	8	through	through	ADP
ejpam-5509	128	9	horizontal	horizontal	ADJ
ejpam-5509	128	10	transmission	transmission	NOUN
ejpam-5509	128	11	,	,	PUNCT
ejpam-5509	128	12	driven	drive	VERB
ejpam-5509	128	13	by	by	ADP
ejpam-5509	128	14	the	the	DET
ejpam-5509	128	15	force	force	NOUN
ejpam-5509	128	16	of	of	ADP
ejpam-5509	128	17	infection	infection	NOUN
ejpam-5509	128	18	represented	represent	VERB
ejpam-5509	128	19	as	as	ADP
ejpam-5509	128	20	λ	λ	X
ejpam-5509	128	21	=	=	SYM
ejpam-5509	128	22	ξ(κa	ξ(κa	PROPN
ejpam-5509	128	23	+	+	SYM
ejpam-5509	128	24	c	c	NOUN
ejpam-5509	128	25	)	)	PUNCT
ejpam-5509	128	26	.	.	PUNCT
ejpam-5509	129	1	here	here	ADV
ejpam-5509	129	2	,	,	PUNCT
ejpam-5509	129	3	the	the	DET
ejpam-5509	129	4	effective	effective	ADJ
ejpam-5509	129	5	contact	contact	NOUN
ejpam-5509	129	6	rate	rate	NOUN
ejpam-5509	129	7	is	be	AUX
ejpam-5509	129	8	denoted	denote	VERB
ejpam-5509	129	9	by	by	ADP
ejpam-5509	129	10	ξ	ξ	NOUN
ejpam-5509	129	11	,	,	PUNCT
ejpam-5509	129	12	while	while	SCONJ
ejpam-5509	129	13	the	the	DET
ejpam-5509	129	14	relative	relative	ADJ
ejpam-5509	129	15	infectiousness	infectiousness	NOUN
ejpam-5509	129	16	of	of	ADP
ejpam-5509	129	17	acute	acute	ADJ
ejpam-5509	129	18	infections	infection	NOUN
ejpam-5509	129	19	versus	versus	ADP
ejpam-5509	129	20	chronic	chronic	ADJ
ejpam-5509	129	21	ones	one	NOUN
ejpam-5509	129	22	is	be	AUX
ejpam-5509	129	23	represented	represent	VERB
ejpam-5509	129	24	by	by	ADP
ejpam-5509	129	25	κ	κ	X
ejpam-5509	129	26	.	.	PUNCT
ejpam-5509	130	1	when	when	SCONJ
ejpam-5509	130	2	κ	κ	X
ejpam-5509	130	3	>	>	X
ejpam-5509	130	4	1	1	NUM
ejpam-5509	130	5	,	,	PUNCT
ejpam-5509	130	6	it	it	PRON
ejpam-5509	130	7	indicates	indicate	VERB
ejpam-5509	130	8	that	that	SCONJ
ejpam-5509	130	9	acute	acute	ADJ
ejpam-5509	130	10	infections	infection	NOUN
ejpam-5509	130	11	have	have	VERB
ejpam-5509	130	12	a	a	DET
ejpam-5509	130	13	higher	high	ADJ
ejpam-5509	130	14	likelihood	likelihood	NOUN
ejpam-5509	130	15	of	of	ADP
ejpam-5509	130	16	transmission	transmission	NOUN
ejpam-5509	130	17	to	to	ADP
ejpam-5509	130	18	susceptible	susceptible	ADJ
ejpam-5509	130	19	individuals	individual	NOUN
ejpam-5509	130	20	than	than	ADP
ejpam-5509	130	21	chronic	chronic	ADJ
ejpam-5509	130	22	infections	infection	NOUN
ejpam-5509	130	23	.	.	PUNCT
ejpam-5509	131	1	both	both	CCONJ
ejpam-5509	131	2	acute	acute	ADJ
ejpam-5509	131	3	and	and	CCONJ
ejpam-5509	131	4	chronic	chronic	ADJ
ejpam-5509	131	5	infections	infection	NOUN
ejpam-5509	131	6	have	have	VERB
ejpam-5509	131	7	an	an	DET
ejpam-5509	131	8	identical	identical	ADJ
ejpam-5509	131	9	chance	chance	NOUN
ejpam-5509	131	10	of	of	ADP
ejpam-5509	131	11	spreading	spread	VERB
ejpam-5509	131	12	to	to	ADP
ejpam-5509	131	13	individuals	individual	NOUN
ejpam-5509	131	14	who	who	PRON
ejpam-5509	131	15	are	be	AUX
ejpam-5509	131	16	susceptible	susceptible	ADJ
ejpam-5509	131	17	when	when	SCONJ
ejpam-5509	131	18	κ	κ	X
ejpam-5509	131	19	=	=	NOUN
ejpam-5509	131	20	1	1	X
ejpam-5509	131	21	.	.	PUNCT
ejpam-5509	132	1	in	in	ADP
ejpam-5509	132	2	contrast	contrast	NOUN
ejpam-5509	132	3	,	,	PUNCT
ejpam-5509	132	4	if	if	SCONJ
ejpam-5509	132	5	κ	κ	PRON
ejpam-5509	132	6	<	<	X
ejpam-5509	132	7	1	1	NUM
ejpam-5509	132	8	,	,	PUNCT
ejpam-5509	132	9	it	it	PRON
ejpam-5509	132	10	means	mean	VERB
ejpam-5509	132	11	that	that	SCONJ
ejpam-5509	132	12	chronic	chronic	ADJ
ejpam-5509	132	13	infections	infection	NOUN
ejpam-5509	132	14	are	be	AUX
ejpam-5509	132	15	more	more	ADV
ejpam-5509	132	16	probable	probable	ADJ
ejpam-5509	132	17	than	than	ADP
ejpam-5509	132	18	acute	acute	ADJ
ejpam-5509	132	19	infections	infection	NOUN
ejpam-5509	132	20	to	to	PART
ejpam-5509	132	21	spread	spread	VERB
ejpam-5509	132	22	to	to	ADP
ejpam-5509	132	23	individuals	individual	NOUN
ejpam-5509	132	24	who	who	PRON
ejpam-5509	132	25	are	be	AUX
ejpam-5509	132	26	susceptible	susceptible	ADJ
ejpam-5509	132	27	.	.	PUNCT
ejpam-5509	133	1	in	in	ADP
ejpam-5509	133	2	the	the	DET
ejpam-5509	133	3	scenario	scenario	NOUN
ejpam-5509	133	4	of	of	ADP
ejpam-5509	133	5	vertical	vertical	ADJ
ejpam-5509	133	6	transmission	transmission	NOUN
ejpam-5509	133	7	,	,	PUNCT
ejpam-5509	133	8	we	we	PRON
ejpam-5509	133	9	make	make	VERB
ejpam-5509	133	10	the	the	DET
ejpam-5509	133	11	assumption	assumption	NOUN
ejpam-5509	133	12	that	that	SCONJ
ejpam-5509	133	13	newborn	newborn	ADJ
ejpam-5509	133	14	infants	infant	NOUN
ejpam-5509	133	15	receive	receive	VERB
ejpam-5509	133	16	successful	successful	ADJ
ejpam-5509	133	17	vaccination	vaccination	NOUN
ejpam-5509	133	18	at	at	ADP
ejpam-5509	133	19	a	a	DET
ejpam-5509	133	20	rate	rate	NOUN
ejpam-5509	133	21	represented	represent	VERB
ejpam-5509	133	22	by	by	ADP
ejpam-5509	133	23	πω	πω	PROPN
ejpam-5509	133	24	,	,	PUNCT
ejpam-5509	133	25	or	or	CCONJ
ejpam-5509	133	26	unsuccessful	unsuccessful	ADJ
ejpam-5509	133	27	vaccination	vaccination	NOUN
ejpam-5509	133	28	at	at	ADP
ejpam-5509	133	29	a	a	DET
ejpam-5509	133	30	rate	rate	NOUN
ejpam-5509	133	31	represented	represent	VERB
ejpam-5509	133	32	by	by	ADP
ejpam-5509	133	33	π(1−	π(1−	PROPN
ejpam-5509	133	34	ω	ω	PROPN
ejpam-5509	133	35	)	)	PUNCT
ejpam-5509	133	36	.	.	PUNCT
ejpam-5509	134	1	here	here	ADV
ejpam-5509	134	2	,	,	PUNCT
ejpam-5509	134	3	the	the	DET
ejpam-5509	134	4	birth	birth	NOUN
ejpam-5509	134	5	rate	rate	NOUN
ejpam-5509	134	6	is	be	AUX
ejpam-5509	134	7	denoted	denote	VERB
ejpam-5509	134	8	by	by	ADP
ejpam-5509	134	9	π	π	PROPN
ejpam-5509	134	10	,	,	PUNCT
ejpam-5509	134	11	and	and	CCONJ
ejpam-5509	134	12	the	the	DET
ejpam-5509	134	13	proportion	proportion	NOUN
ejpam-5509	134	14	of	of	ADP
ejpam-5509	134	15	effectively	effectively	ADV
ejpam-5509	134	16	immunized	immunize	VERB
ejpam-5509	134	17	individuals	individual	NOUN
ejpam-5509	134	18	is	be	AUX
ejpam-5509	134	19	denoted	denote	VERB
ejpam-5509	134	20	by	by	ADP
ejpam-5509	134	21	ω	ω	PROPN
ejpam-5509	134	22	,	,	PUNCT
ejpam-5509	134	23	where	where	SCONJ
ejpam-5509	134	24	0	0	NUM
ejpam-5509	134	25	<	<	X
ejpam-5509	134	26	ω	ω	X
ejpam-5509	134	27	<	<	X
ejpam-5509	134	28	1	1	NUM
ejpam-5509	134	29	.	.	PUNCT
ejpam-5509	135	1	consequently	consequently	ADV
ejpam-5509	135	2	,	,	PUNCT
ejpam-5509	135	3	πω	πω	PRON
ejpam-5509	135	4	individuals	individual	NOUN
ejpam-5509	135	5	transition	transition	VERB
ejpam-5509	135	6	to	to	ADP
ejpam-5509	135	7	the	the	DET
ejpam-5509	135	8	vaccinated	vaccinated	ADJ
ejpam-5509	135	9	first	first	ADJ
ejpam-5509	135	10	dose	dose	NOUN
ejpam-5509	135	11	class	class	NOUN
ejpam-5509	135	12	,	,	PUNCT
ejpam-5509	135	13	while	while	SCONJ
ejpam-5509	135	14	π(1	π(1	PROPN
ejpam-5509	135	15	−	−	PROPN
ejpam-5509	135	16	ω)τc	ω)τc	PROPN
ejpam-5509	135	17	move	move	NOUN
ejpam-5509	135	18	into	into	ADP
ejpam-5509	135	19	the	the	DET
ejpam-5509	135	20	chronic	chronic	ADJ
ejpam-5509	135	21	class	class	NOUN
ejpam-5509	135	22	.	.	PUNCT
ejpam-5509	136	1	the	the	DET
ejpam-5509	136	2	remaining	remain	VERB
ejpam-5509	136	3	fraction	fraction	NOUN
ejpam-5509	136	4	,	,	PUNCT
ejpam-5509	136	5	π(1−	π(1−	NOUN
ejpam-5509	136	6	ω)(1−	ω)(1−	NUM
ejpam-5509	136	7	τc	τc	PRON
ejpam-5509	136	8	)	)	PUNCT
ejpam-5509	136	9	,	,	PUNCT
ejpam-5509	136	10	enters	enter	VERB
ejpam-5509	136	11	the	the	DET
ejpam-5509	136	12	susceptible	susceptible	ADJ
ejpam-5509	136	13	class	class	NOUN
ejpam-5509	136	14	.	.	PUNCT
ejpam-5509	137	1	in	in	ADP
ejpam-5509	137	2	this	this	DET
ejpam-5509	137	3	context	context	NOUN
ejpam-5509	137	4	,	,	PUNCT
ejpam-5509	137	5	the	the	DET
ejpam-5509	137	6	symbol	symbol	NOUN
ejpam-5509	137	7	τ	τ	PROPN
ejpam-5509	137	8	denotes	denote	VERB
ejpam-5509	137	9	the	the	DET
ejpam-5509	137	10	fraction	fraction	NOUN
ejpam-5509	137	11	of	of	ADP
ejpam-5509	137	12	infants	infant	NOUN
ejpam-5509	137	13	born	bear	VERB
ejpam-5509	137	14	to	to	ADP
ejpam-5509	137	15	carrier	carrier	NOUN
ejpam-5509	137	16	mothers	mother	NOUN
ejpam-5509	137	17	who	who	PRON
ejpam-5509	137	18	remain	remain	VERB
ejpam-5509	137	19	unvaccinated	unvaccinated	ADJ
ejpam-5509	137	20	and	and	CCONJ
ejpam-5509	137	21	subsequently	subsequently	ADV
ejpam-5509	137	22	develop	develop	VERB
ejpam-5509	137	23	a	a	DET
ejpam-5509	137	24	chronic	chronic	ADJ
ejpam-5509	137	25	condition	condition	NOUN
ejpam-5509	137	26	.	.	PUNCT
ejpam-5509	138	1	furthermore	furthermore	ADV
ejpam-5509	138	2	,	,	PUNCT
ejpam-5509	138	3	we	we	PRON
ejpam-5509	138	4	have	have	AUX
ejpam-5509	138	5	taken	take	VERB
ejpam-5509	138	6	into	into	ADP
ejpam-5509	138	7	account	account	NOUN
ejpam-5509	138	8	that	that	SCONJ
ejpam-5509	138	9	the	the	DET
ejpam-5509	138	10	percentage	percentage	NOUN
ejpam-5509	138	11	of	of	ADP
ejpam-5509	138	12	unvaccinated	unvaccinated	ADJ
ejpam-5509	138	13	newborns	newborn	NOUN
ejpam-5509	138	14	moving	move	VERB
ejpam-5509	138	15	into	into	ADP
ejpam-5509	138	16	a	a	DET
ejpam-5509	138	17	chronic	chronic	ADJ
ejpam-5509	138	18	state	state	NOUN
ejpam-5509	138	19	is	be	AUX
ejpam-5509	138	20	lower	low	ADJ
ejpam-5509	138	21	than	than	ADP
ejpam-5509	138	22	the	the	DET
ejpam-5509	138	23	sum	sum	NOUN
ejpam-5509	138	24	of	of	ADP
ejpam-5509	138	25	the	the	DET
ejpam-5509	138	26	mortality	mortality	NOUN
ejpam-5509	138	27	rates	rate	NOUN
ejpam-5509	138	28	from	from	ADP
ejpam-5509	138	29	hepatitis	hepatitis	PROPN
ejpam-5509	138	30	b	b	PROPN
ejpam-5509	138	31	and	and	CCONJ
ejpam-5509	138	32	the	the	DET
ejpam-5509	138	33	percentage	percentage	NOUN
ejpam-5509	138	34	of	of	ADP
ejpam-5509	138	35	patients	patient	NOUN
ejpam-5509	138	36	who	who	PRON
ejpam-5509	138	37	recover	recover	VERB
ejpam-5509	138	38	from	from	ADP
ejpam-5509	138	39	the	the	DET
ejpam-5509	138	40	chronic	chronic	ADJ
ejpam-5509	138	41	category	category	NOUN
ejpam-5509	138	42	.	.	PUNCT
ejpam-5509	139	1	furthermore	furthermore	ADV
ejpam-5509	139	2	,	,	PUNCT
ejpam-5509	139	3	the	the	DET
ejpam-5509	139	4	model	model	NOUN
ejpam-5509	139	5	encompasses	encompass	VERB
ejpam-5509	139	6	a	a	DET
ejpam-5509	139	7	range	range	NOUN
ejpam-5509	139	8	of	of	ADP
ejpam-5509	139	9	parameters	parameter	NOUN
ejpam-5509	139	10	,	,	PUNCT
ejpam-5509	139	11	each	each	PRON
ejpam-5509	139	12	with	with	ADP
ejpam-5509	139	13	specific	specific	ADJ
ejpam-5509	139	14	interpretations	interpretation	NOUN
ejpam-5509	139	15	:	:	PUNCT
ejpam-5509	139	16	π	π	NOUN
ejpam-5509	139	17	represents	represent	VERB
ejpam-5509	139	18	the	the	DET
ejpam-5509	139	19	birth	birth	NOUN
ejpam-5509	139	20	rate	rate	NOUN
ejpam-5509	139	21	,	,	PUNCT
ejpam-5509	139	22	µ	µ	PRON
ejpam-5509	139	23	signifies	signify	VERB
ejpam-5509	139	24	the	the	DET
ejpam-5509	139	25	natural	natural	ADJ
ejpam-5509	139	26	death	death	NOUN
ejpam-5509	139	27	rate	rate	NOUN
ejpam-5509	139	28	,	,	PUNCT
ejpam-5509	139	29	σ	σ	PROPN
ejpam-5509	139	30	denotes	denote	VERB
ejpam-5509	139	31	the	the	DET
ejpam-5509	139	32	natural	natural	ADJ
ejpam-5509	139	33	recovery	recovery	NOUN
ejpam-5509	139	34	rate	rate	NOUN
ejpam-5509	139	35	from	from	ADP
ejpam-5509	139	36	the	the	DET
ejpam-5509	139	37	acute	acute	ADJ
ejpam-5509	139	38	class	class	NOUN
ejpam-5509	139	39	,	,	PUNCT
ejpam-5509	139	40	ϑ	ϑ	X
ejpam-5509	139	41	characterizes	characterize	VERB
ejpam-5509	139	42	the	the	DET
ejpam-5509	139	43	rate	rate	NOUN
ejpam-5509	139	44	of	of	ADP
ejpam-5509	139	45	recovery	recovery	NOUN
ejpam-5509	139	46	from	from	ADP
ejpam-5509	139	47	the	the	DET
ejpam-5509	139	48	chronic	chronic	ADJ
ejpam-5509	139	49	class	class	NOUN
ejpam-5509	139	50	due	due	ADP
ejpam-5509	139	51	to	to	ADP
ejpam-5509	139	52	treatment	treatment	NOUN
ejpam-5509	139	53	,	,	PUNCT
ejpam-5509	139	54	δ	δ	PROPN
ejpam-5509	139	55	represents	represent	VERB
ejpam-5509	139	56	the	the	DET
ejpam-5509	139	57	speed	speed	NOUN
ejpam-5509	139	58	at	at	ADP
ejpam-5509	139	59	which	which	PRON
ejpam-5509	139	60	individuals	individual	NOUN
ejpam-5509	139	61	move	move	VERB
ejpam-5509	139	62	from	from	ADP
ejpam-5509	139	63	the	the	DET
ejpam-5509	139	64	acute	acute	ADJ
ejpam-5509	139	65	class	class	NOUN
ejpam-5509	139	66	to	to	ADP
ejpam-5509	139	67	the	the	DET
ejpam-5509	139	68	chronic	chronic	ADJ
ejpam-5509	139	69	class	class	NOUN
ejpam-5509	139	70	once	once	SCONJ
ejpam-5509	139	71	they	they	PRON
ejpam-5509	139	72	exhibit	exhibit	VERB
ejpam-5509	139	73	symptoms	symptom	NOUN
ejpam-5509	139	74	,	,	PUNCT
ejpam-5509	139	75	α	α	PRON
ejpam-5509	139	76	represents	represent	VERB
ejpam-5509	139	77	the	the	DET
ejpam-5509	139	78	rate	rate	NOUN
ejpam-5509	139	79	at	at	ADP
ejpam-5509	139	80	which	which	PRON
ejpam-5509	139	81	individuals	individual	NOUN
ejpam-5509	139	82	in	in	ADP
ejpam-5509	139	83	the	the	DET
ejpam-5509	139	84	initially	initially	ADV
ejpam-5509	139	85	vaccinated	vaccinate	VERB
ejpam-5509	139	86	first	first	ADJ
ejpam-5509	139	87	dose	dose	NOUN
ejpam-5509	139	88	class	class	NOUN
ejpam-5509	139	89	receive	receive	VERB
ejpam-5509	139	90	their	their	PRON
ejpam-5509	139	91	second	second	ADJ
ejpam-5509	139	92	vaccine	vaccine	NOUN
ejpam-5509	139	93	dose	dose	VERB
ejpam-5509	139	94	whereas	whereas	SCONJ
ejpam-5509	139	95	the	the	DET
ejpam-5509	139	96	rate	rate	NOUN
ejpam-5509	139	97	of	of	ADP
ejpam-5509	139	98	recovery	recovery	NOUN
ejpam-5509	139	99	from	from	ADP
ejpam-5509	139	100	the	the	DET
ejpam-5509	139	101	second	second	ADJ
ejpam-5509	139	102	dose	dose	NOUN
ejpam-5509	139	103	class	class	NOUN
ejpam-5509	139	104	of	of	ADP
ejpam-5509	139	105	vaccination	vaccination	NOUN
ejpam-5509	139	106	is	be	AUX
ejpam-5509	139	107	represented	represent	VERB
ejpam-5509	139	108	by	by	ADP
ejpam-5509	139	109	ϵ.	ϵ.	NOUN
ejpam-5509	139	110	ψ	ψ	PROPN
ejpam-5509	139	111	represents	represent	VERB
ejpam-5509	139	112	the	the	DET
ejpam-5509	139	113	disease	disease	NOUN
ejpam-5509	139	114	-	-	PUNCT
ejpam-5509	139	115	related	relate	VERB
ejpam-5509	139	116	death	death	NOUN
ejpam-5509	139	117	rate	rate	NOUN
ejpam-5509	139	118	in	in	ADP
ejpam-5509	139	119	the	the	DET
ejpam-5509	139	120	chronic	chronic	ADJ
ejpam-5509	139	121	class	class	NOUN
ejpam-5509	139	122	,	,	PUNCT
ejpam-5509	139	123	φ1	φ1	PROPN
ejpam-5509	139	124	designates	designate	VERB
ejpam-5509	139	125	the	the	DET
ejpam-5509	139	126	rate	rate	NOUN
ejpam-5509	139	127	at	at	ADP
ejpam-5509	139	128	which	which	PRON
ejpam-5509	139	129	members	member	NOUN
ejpam-5509	139	130	of	of	ADP
ejpam-5509	139	131	the	the	DET
ejpam-5509	139	132	susceptible	susceptible	ADJ
ejpam-5509	139	133	population	population	NOUN
ejpam-5509	139	134	receive	receive	VERB
ejpam-5509	139	135	their	their	PRON
ejpam-5509	139	136	first	first	ADJ
ejpam-5509	139	137	dosage	dosage	NOUN
ejpam-5509	139	138	of	of	ADP
ejpam-5509	139	139	the	the	DET
ejpam-5509	139	140	vaccine	vaccine	NOUN
ejpam-5509	139	141	,	,	PUNCT
ejpam-5509	139	142	and	and	CCONJ
ejpam-5509	139	143	φ2	φ2	PROPN
ejpam-5509	139	144	signifies	signify	VERB
ejpam-5509	139	145	the	the	DET
ejpam-5509	139	146	rate	rate	NOUN
ejpam-5509	139	147	at	at	ADP
ejpam-5509	139	148	which	which	PRON
ejpam-5509	139	149	vaccine	vaccine	NOUN
ejpam-5509	139	150	immunity	immunity	NOUN
ejpam-5509	139	151	diminishes	diminish	VERB
ejpam-5509	139	152	in	in	ADP
ejpam-5509	139	153	the	the	DET
ejpam-5509	139	154	vaccinated	vaccinated	ADJ
ejpam-5509	139	155	first	first	ADJ
ejpam-5509	139	156	dose	dose	PROPN
ejpam-5509	139	157	i.	i.	PROPN
ejpam-5509	139	158	ahmad	ahmad	PROPN
ejpam-5509	139	159	et	et	PROPN
ejpam-5509	139	160	al	al	PROPN
ejpam-5509	139	161	.	.	PUNCT
ejpam-5509	139	162	/	/	SYM
ejpam-5509	139	163	eur	eur	PROPN
ejpam-5509	139	164	.	.	PUNCT
ejpam-5509	140	1	j.	j.	PROPN
ejpam-5509	140	2	pure	pure	PROPN
ejpam-5509	140	3	appl	appl	PROPN
ejpam-5509	140	4	.	.	PROPN
ejpam-5509	140	5	math	math	PROPN
ejpam-5509	140	6	,	,	PUNCT
ejpam-5509	140	7	18	18	NUM
ejpam-5509	140	8	(	(	PUNCT
ejpam-5509	140	9	1	1	NUM
ejpam-5509	140	10	)	)	PUNCT
ejpam-5509	140	11	(	(	PUNCT
ejpam-5509	140	12	2025	2025	NUM
ejpam-5509	140	13	)	)	PUNCT
ejpam-5509	140	14	,	,	PUNCT
ejpam-5509	140	15	5509	5509	NUM
ejpam-5509	140	16	7	7	NUM
ejpam-5509	140	17	of	of	ADP
ejpam-5509	140	18	27	27	NUM
ejpam-5509	140	19	class	class	NOUN
ejpam-5509	140	20	.	.	PUNCT
ejpam-5509	141	1	the	the	DET
ejpam-5509	141	2	system	system	NOUN
ejpam-5509	141	3	of	of	ADP
ejpam-5509	141	4	odes	ode	NOUN
ejpam-5509	141	5	,	,	PUNCT
ejpam-5509	141	6	under	under	ADP
ejpam-5509	141	7	the	the	DET
ejpam-5509	141	8	specified	specified	ADJ
ejpam-5509	141	9	assumptions	assumption	NOUN
ejpam-5509	141	10	,	,	PUNCT
ejpam-5509	141	11	is	be	AUX
ejpam-5509	141	12	expressed	express	VERB
ejpam-5509	141	13	as	as	SCONJ
ejpam-5509	141	14	follows	follow	VERB
ejpam-5509	141	15	[	[	X
ejpam-5509	141	16	13]:	13]:	NUM
ejpam-5509	141	17	ds	ds	NOUN
ejpam-5509	141	18	dt	dt	NOUN
ejpam-5509	141	19	=	=	PUNCT
ejpam-5509	141	20	π(1−	π(1−	PROPN
ejpam-5509	141	21	ω)(1−	ω)(1−	NUM
ejpam-5509	141	22	τc	τc	PRON
ejpam-5509	141	23	)	)	PUNCT
ejpam-5509	142	1	+	+	CCONJ
ejpam-5509	143	1	φ2v1	φ2v1	NUM
ejpam-5509	143	2	−	−	PROPN
ejpam-5509	143	3	(	(	PUNCT
ejpam-5509	143	4	λ+	λ+	X
ejpam-5509	143	5	µ+	µ+	X
ejpam-5509	143	6	φ1)s	φ1)s	NOUN
ejpam-5509	143	7	,	,	PUNCT
ejpam-5509	143	8	dv1	dv1	NOUN
ejpam-5509	143	9	dt	dt	NOUN
ejpam-5509	143	10	=	=	SYM
ejpam-5509	143	11	φ1s	φ1s	PROPN
ejpam-5509	143	12	+	+	PROPN
ejpam-5509	143	13	πω	πω	ADP
ejpam-5509	143	14	−	−	PROPN
ejpam-5509	143	15	(	(	PUNCT
ejpam-5509	143	16	α+	α+	X
ejpam-5509	143	17	µ+	µ+	PRON
ejpam-5509	143	18	φ2)v1	φ2)v1	PROPN
ejpam-5509	143	19	,	,	PUNCT
ejpam-5509	143	20	dv2	dv2	NOUN
ejpam-5509	143	21	dt	dt	NOUN
ejpam-5509	143	22	=	=	PUNCT
ejpam-5509	143	23	αv1	αv1	PROPN
ejpam-5509	144	1	−	−	PROPN
ejpam-5509	144	2	(	(	PUNCT
ejpam-5509	144	3	ϵ+	ϵ+	X
ejpam-5509	144	4	µ)v2	µ)v2	PROPN
ejpam-5509	144	5	,	,	PUNCT
ejpam-5509	144	6	da	da	ADJ
ejpam-5509	144	7	dt	dt	NOUN
ejpam-5509	145	1	=	=	PUNCT
ejpam-5509	145	2	λs	λs	PROPN
ejpam-5509	145	3	−	−	PROPN
ejpam-5509	146	1	(	(	PUNCT
ejpam-5509	146	2	δ	δ	PROPN
ejpam-5509	146	3	+	+	CCONJ
ejpam-5509	146	4	σ	σ	PROPN
ejpam-5509	146	5	+	+	CCONJ
ejpam-5509	146	6	µ)a	µ)a	NOUN
ejpam-5509	146	7	,	,	PUNCT
ejpam-5509	146	8	dc	dc	PROPN
ejpam-5509	146	9	dt	dt	X
ejpam-5509	146	10	=	=	SYM
ejpam-5509	146	11	δa+π(1−	δa+π(1−	PROPN
ejpam-5509	147	1	ω)τc	ω)τc	PROPN
ejpam-5509	147	2	−	−	PROPN
ejpam-5509	147	3	(	(	PUNCT
ejpam-5509	147	4	ϑ+	ϑ+	X
ejpam-5509	147	5	µ+	µ+	VERB
ejpam-5509	147	6	ψ)c	ψ)c	NOUN
ejpam-5509	147	7	,	,	PUNCT
ejpam-5509	147	8	dr	dr	PROPN
ejpam-5509	147	9	dt	dt	PROPN
ejpam-5509	147	10	=	=	PUNCT
ejpam-5509	147	11	σa+	σa+	ADP
ejpam-5509	147	12	ϑc	ϑc	NOUN
ejpam-5509	147	13	+	+	CCONJ
ejpam-5509	147	14	ϵv2	ϵv2	NOUN
ejpam-5509	147	15	−	−	NOUN
ejpam-5509	147	16	µr	µr	ADP
ejpam-5509	147	17	,	,	PUNCT
ejpam-5509	147	18	(	(	PUNCT
ejpam-5509	147	19	9	9	NUM
ejpam-5509	147	20	)	)	PUNCT
ejpam-5509	147	21	with	with	ADP
ejpam-5509	147	22	the	the	DET
ejpam-5509	147	23	following	follow	VERB
ejpam-5509	147	24	values	value	NOUN
ejpam-5509	147	25	0	0	NUM
ejpam-5509	147	26	≤	≤	NUM
ejpam-5509	147	27	s(0	s(0	PROPN
ejpam-5509	147	28	)	)	PUNCT
ejpam-5509	147	29	,	,	PUNCT
ejpam-5509	147	30	0	0	NUM
ejpam-5509	147	31	≤	≤	NUM
ejpam-5509	147	32	v1(0	v1(0	NOUN
ejpam-5509	147	33	)	)	PUNCT
ejpam-5509	147	34	,	,	PUNCT
ejpam-5509	147	35	0	0	NUM
ejpam-5509	147	36	≤	≤	NUM
ejpam-5509	147	37	v2(0	v2(0	NOUN
ejpam-5509	147	38	)	)	PUNCT
ejpam-5509	147	39	0	0	NUM
ejpam-5509	148	1	≤	≤	NUM
ejpam-5509	148	2	a(0	a(0	PROPN
ejpam-5509	148	3	)	)	PUNCT
ejpam-5509	148	4	,	,	PUNCT
ejpam-5509	148	5	0	0	NUM
ejpam-5509	148	6	≤	≤	NUM
ejpam-5509	148	7	c(0	c(0	NOUN
ejpam-5509	148	8	)	)	PUNCT
ejpam-5509	148	9	,	,	PUNCT
ejpam-5509	148	10	0	0	NUM
ejpam-5509	148	11	≤	≤	NUM
ejpam-5509	148	12	r(0	r(0	PROPN
ejpam-5509	148	13	)	)	PUNCT
ejpam-5509	148	14	.	.	PUNCT
ejpam-5509	149	1	this	this	DET
ejpam-5509	149	2	incorporation	incorporation	NOUN
ejpam-5509	149	3	facilitates	facilitate	VERB
ejpam-5509	149	4	a	a	DET
ejpam-5509	149	5	comprehensive	comprehensive	ADJ
ejpam-5509	149	6	examination	examination	NOUN
ejpam-5509	149	7	of	of	ADP
ejpam-5509	149	8	epidemic	epidemic	NOUN
ejpam-5509	149	9	dissemination	dissemination	NOUN
ejpam-5509	149	10	in	in	ADP
ejpam-5509	149	11	complex	complex	ADJ
ejpam-5509	149	12	scenarios	scenario	NOUN
ejpam-5509	149	13	featuring	feature	VERB
ejpam-5509	149	14	memory	memory	NOUN
ejpam-5509	149	15	effects	effect	NOUN
ejpam-5509	149	16	and	and	CCONJ
ejpam-5509	149	17	long	long	ADJ
ejpam-5509	149	18	-	-	PUNCT
ejpam-5509	149	19	range	range	NOUN
ejpam-5509	149	20	interactions	interaction	NOUN
ejpam-5509	149	21	,	,	PUNCT
ejpam-5509	149	22	which	which	PRON
ejpam-5509	149	23	enhances	enhance	VERB
ejpam-5509	149	24	our	our	PRON
ejpam-5509	149	25	understanding	understanding	NOUN
ejpam-5509	149	26	of	of	ADP
ejpam-5509	149	27	the	the	DET
ejpam-5509	149	28	underlying	underlie	VERB
ejpam-5509	149	29	mechanisms	mechanism	NOUN
ejpam-5509	149	30	.	.	PUNCT
ejpam-5509	150	1	consequently	consequently	ADV
ejpam-5509	150	2	,	,	PUNCT
ejpam-5509	150	3	we	we	PRON
ejpam-5509	150	4	have	have	AUX
ejpam-5509	150	5	applied	apply	VERB
ejpam-5509	150	6	a	a	DET
ejpam-5509	150	7	fractional	fractional	ADJ
ejpam-5509	150	8	framework	framework	NOUN
ejpam-5509	150	9	to	to	PART
ejpam-5509	150	10	describe	describe	VERB
ejpam-5509	150	11	the	the	DET
ejpam-5509	150	12	dynamics	dynamic	NOUN
ejpam-5509	150	13	of	of	ADP
ejpam-5509	150	14	hb	hb	PROPN
ejpam-5509	150	15	disease	disease	NOUN
ejpam-5509	150	16	.	.	PUNCT
ejpam-5509	151	1	in	in	ADP
ejpam-5509	151	2	our	our	PRON
ejpam-5509	151	3	proposed	propose	VERB
ejpam-5509	151	4	model	model	NOUN
ejpam-5509	151	5	,	,	PUNCT
ejpam-5509	151	6	we	we	PRON
ejpam-5509	151	7	have	have	AUX
ejpam-5509	151	8	employed	employ	VERB
ejpam-5509	151	9	the	the	DET
ejpam-5509	151	10	cf	cf	NOUN
ejpam-5509	151	11	fractional	fractional	ADJ
ejpam-5509	151	12	operator	operator	NOUN
ejpam-5509	151	13	in	in	ADP
ejpam-5509	151	14	the	the	DET
ejpam-5509	151	15	following	follow	VERB
ejpam-5509	151	16	manner.	manner.	PROPN
ejpam-5509	151	17	cf	cf	NOUN
ejpam-5509	151	18	0	0	NUM
ejpam-5509	151	19	dς	dς	NOUN
ejpam-5509	151	20	ts	ts	X
ejpam-5509	151	21	=	=	PUNCT
ejpam-5509	151	22	π(1−	π(1−	PROPN
ejpam-5509	151	23	ω)(1−	ω)(1−	NUM
ejpam-5509	151	24	τc	τc	PRON
ejpam-5509	151	25	)	)	PUNCT
ejpam-5509	152	1	+	+	CCONJ
ejpam-5509	153	1	φ2v1	φ2v1	NUM
ejpam-5509	153	2	−	−	PROPN
ejpam-5509	153	3	(	(	PUNCT
ejpam-5509	153	4	λ+	λ+	X
ejpam-5509	153	5	µ+	µ+	X
ejpam-5509	153	6	φ1)s	φ1)s	NOUN
ejpam-5509	153	7	,	,	PUNCT
ejpam-5509	153	8	cf	cf	NOUN
ejpam-5509	153	9	0	0	NUM
ejpam-5509	153	10	dς	dς	PROPN
ejpam-5509	153	11	tv1	tv1	PROPN
ejpam-5509	153	12	=	=	PROPN
ejpam-5509	153	13	φ1s	φ1s	PROPN
ejpam-5509	153	14	+	+	PROPN
ejpam-5509	153	15	πω	πω	ADP
ejpam-5509	153	16	−	−	PROPN
ejpam-5509	153	17	(	(	PUNCT
ejpam-5509	153	18	α+	α+	X
ejpam-5509	153	19	µ+	µ+	PRON
ejpam-5509	153	20	φ2)v1	φ2)v1	PROPN
ejpam-5509	153	21	,	,	PUNCT
ejpam-5509	153	22	cf	cf	NOUN
ejpam-5509	153	23	0	0	NUM
ejpam-5509	153	24	dς	dς	NOUN
ejpam-5509	153	25	tv2	tv2	NOUN
ejpam-5509	153	26	=	=	SYM
ejpam-5509	153	27	αv1	αv1	PROPN
ejpam-5509	154	1	−	−	PROPN
ejpam-5509	154	2	(	(	PUNCT
ejpam-5509	154	3	ϵ+	ϵ+	X
ejpam-5509	154	4	µ)v2	µ)v2	ADJ
ejpam-5509	154	5	,	,	PUNCT
ejpam-5509	154	6	cf	cf	NOUN
ejpam-5509	154	7	0	0	NUM
ejpam-5509	154	8	dς	dς	NOUN
ejpam-5509	154	9	ta	ta	ADP
ejpam-5509	154	10	=	=	PUNCT
ejpam-5509	154	11	λs	λs	PROPN
ejpam-5509	154	12	−	−	PROPN
ejpam-5509	154	13	(	(	PUNCT
ejpam-5509	154	14	δ	δ	PROPN
ejpam-5509	154	15	+	+	CCONJ
ejpam-5509	154	16	σ	σ	PROPN
ejpam-5509	154	17	+	+	CCONJ
ejpam-5509	154	18	µ)a	µ)a	NOUN
ejpam-5509	154	19	,	,	PUNCT
ejpam-5509	154	20	cf	cf	NOUN
ejpam-5509	154	21	0	0	NUM
ejpam-5509	154	22	dς	dς	NOUN
ejpam-5509	154	23	tc	tc	NOUN
ejpam-5509	154	24	=	=	SYM
ejpam-5509	154	25	δa+π(1−	δa+π(1−	PROPN
ejpam-5509	154	26	ω)τc	ω)τc	PROPN
ejpam-5509	154	27	−	−	PROPN
ejpam-5509	154	28	(	(	PUNCT
ejpam-5509	154	29	ϑ+	ϑ+	X
ejpam-5509	154	30	µ+	µ+	VERB
ejpam-5509	154	31	ψ)c	ψ)c	NOUN
ejpam-5509	154	32	,	,	PUNCT
ejpam-5509	154	33	cf	cf	NOUN
ejpam-5509	154	34	0	0	NUM
ejpam-5509	154	35	dς	dς	NOUN
ejpam-5509	154	36	tr	tr	NOUN
ejpam-5509	154	37	=	=	SYM
ejpam-5509	154	38	σa+	σa+	NOUN
ejpam-5509	154	39	ϑc	ϑc	NOUN
ejpam-5509	154	40	+	+	CCONJ
ejpam-5509	154	41	ϵv2	ϵv2	NOUN
ejpam-5509	154	42	−	−	NOUN
ejpam-5509	154	43	µr	µr	ADP
ejpam-5509	154	44	,	,	PUNCT
ejpam-5509	154	45	(	(	PUNCT
ejpam-5509	154	46	10	10	NUM
ejpam-5509	154	47	)	)	PUNCT
ejpam-5509	154	48	with	with	ADP
ejpam-5509	154	49	positive	positive	ADJ
ejpam-5509	154	50	initial	initial	ADJ
ejpam-5509	154	51	conditions	condition	NOUN
ejpam-5509	154	52	.	.	PUNCT
ejpam-5509	155	1	3.1	3.1	NUM
ejpam-5509	155	2	.	.	PUNCT
ejpam-5509	155	3	analysis	analysis	NOUN
ejpam-5509	155	4	of	of	ADP
ejpam-5509	155	5	disease	disease	NOUN
ejpam-5509	155	6	-	-	PUNCT
ejpam-5509	155	7	free	free	ADJ
ejpam-5509	155	8	equilibrium	equilibrium	NOUN
ejpam-5509	155	9	the	the	DET
ejpam-5509	155	10	system	system	NOUN
ejpam-5509	155	11	(	(	PUNCT
ejpam-5509	155	12	10	10	NUM
ejpam-5509	155	13	)	)	PUNCT
ejpam-5509	155	14	reaches	reach	VERB
ejpam-5509	155	15	a	a	DET
ejpam-5509	155	16	disease	disease	NOUN
ejpam-5509	155	17	-	-	PUNCT
ejpam-5509	155	18	free	free	ADJ
ejpam-5509	155	19	equilibrium	equilibrium	NOUN
ejpam-5509	155	20	(	(	PUNCT
ejpam-5509	155	21	dfe	dfe	PROPN
ejpam-5509	155	22	)	)	PUNCT
ejpam-5509	155	23	in	in	ADP
ejpam-5509	155	24	the	the	DET
ejpam-5509	155	25	absence	absence	NOUN
ejpam-5509	155	26	of	of	ADP
ejpam-5509	155	27	infections	infection	NOUN
ejpam-5509	155	28	.	.	PUNCT
ejpam-5509	156	1	to	to	PART
ejpam-5509	156	2	find	find	VERB
ejpam-5509	156	3	the	the	DET
ejpam-5509	156	4	dfe	dfe	PROPN
ejpam-5509	156	5	,	,	PUNCT
ejpam-5509	156	6	one	one	PRON
ejpam-5509	156	7	must	must	AUX
ejpam-5509	156	8	solve	solve	VERB
ejpam-5509	156	9	the	the	DET
ejpam-5509	156	10	system	system	NOUN
ejpam-5509	156	11	by	by	ADP
ejpam-5509	156	12	setting	set	VERB
ejpam-5509	156	13	the	the	DET
ejpam-5509	156	14	left	left	ADJ
ejpam-5509	156	15	-	-	PUNCT
ejpam-5509	156	16	hand	hand	NOUN
ejpam-5509	156	17	side	side	NOUN
ejpam-5509	156	18	of	of	ADP
ejpam-5509	156	19	equation	equation	NOUN
ejpam-5509	156	20	(	(	PUNCT
ejpam-5509	156	21	10	10	NUM
ejpam-5509	156	22	)	)	PUNCT
ejpam-5509	156	23	to	to	ADP
ejpam-5509	156	24	zero	zero	NUM
ejpam-5509	156	25	.	.	PUNCT
ejpam-5509	157	1	at	at	ADP
ejpam-5509	157	2	the	the	DET
ejpam-5509	157	3	dfe	dfe	PROPN
ejpam-5509	157	4	,	,	PUNCT
ejpam-5509	157	5	both	both	PRON
ejpam-5509	157	6	a	a	PRON
ejpam-5509	157	7	and	and	CCONJ
ejpam-5509	157	8	c	c	NOUN
ejpam-5509	157	9	are	be	AUX
ejpam-5509	157	10	equal	equal	ADJ
ejpam-5509	157	11	to	to	ADP
ejpam-5509	157	12	zero	zero	NUM
ejpam-5509	157	13	,	,	PUNCT
ejpam-5509	157	14	causing	cause	VERB
ejpam-5509	157	15	system	system	NOUN
ejpam-5509	157	16	(	(	PUNCT
ejpam-5509	157	17	10	10	NUM
ejpam-5509	157	18	)	)	PUNCT
ejpam-5509	157	19	to	to	PART
ejpam-5509	157	20	simplify	simplify	VERB
ejpam-5509	157	21	to	to	PROPN
ejpam-5509	157	22	0	0	PUNCT
ejpam-5509	157	23	=	=	SYM
ejpam-5509	157	24	π(1−	π(1−	PROPN
ejpam-5509	157	25	ω	ω	X
ejpam-5509	157	26	)	)	PUNCT
ejpam-5509	158	1	+	+	NUM
ejpam-5509	159	1	φ2v1	φ2v1	NUM
ejpam-5509	159	2	−	−	PROPN
ejpam-5509	159	3	(	(	PUNCT
ejpam-5509	159	4	λ+	λ+	X
ejpam-5509	159	5	µ+	µ+	X
ejpam-5509	159	6	φ1)s	φ1)s	NOUN
ejpam-5509	159	7	,	,	PUNCT
ejpam-5509	159	8	0	0	NUM
ejpam-5509	159	9	=	=	NOUN
ejpam-5509	159	10	φ1s	φ1s	PROPN
ejpam-5509	159	11	+	+	PROPN
ejpam-5509	159	12	πω	πω	ADP
ejpam-5509	159	13	−	−	PROPN
ejpam-5509	159	14	(	(	PUNCT
ejpam-5509	159	15	α+	α+	X
ejpam-5509	159	16	µ+	µ+	PRON
ejpam-5509	159	17	φ2)v1	φ2)v1	PROPN
ejpam-5509	159	18	,	,	PUNCT
ejpam-5509	159	19	0	0	NUM
ejpam-5509	159	20	=	=	SYM
ejpam-5509	159	21	αv1	αv1	PROPN
ejpam-5509	159	22	−	−	NOUN
ejpam-5509	159	23	(	(	PUNCT
ejpam-5509	159	24	ϵ+	ϵ+	X
ejpam-5509	159	25	µ)v2	µ)v2	PROPN
ejpam-5509	159	26	,	,	PUNCT
ejpam-5509	159	27	0	0	NUM
ejpam-5509	159	28	=	=	SYM
ejpam-5509	159	29	ϵv2	ϵv2	NOUN
ejpam-5509	159	30	−	−	NOUN
ejpam-5509	159	31	µr	µr	ADP
ejpam-5509	159	32	,	,	PUNCT
ejpam-5509	159	33	(	(	PUNCT
ejpam-5509	159	34	11	11	NUM
ejpam-5509	159	35	)	)	PUNCT
ejpam-5509	159	36	therefore	therefore	ADV
ejpam-5509	159	37	,	,	PUNCT
ejpam-5509	159	38	based	base	VERB
ejpam-5509	159	39	on	on	ADP
ejpam-5509	159	40	(	(	PUNCT
ejpam-5509	159	41	11	11	NUM
ejpam-5509	159	42	)	)	PUNCT
ejpam-5509	159	43	,	,	PUNCT
ejpam-5509	159	44	the	the	DET
ejpam-5509	159	45	dfe	dfe	PROPN
ejpam-5509	159	46	for	for	ADP
ejpam-5509	159	47	model	model	NOUN
ejpam-5509	159	48	(	(	PUNCT
ejpam-5509	159	49	10	10	NUM
ejpam-5509	159	50	)	)	PUNCT
ejpam-5509	159	51	can	can	AUX
ejpam-5509	159	52	be	be	AUX
ejpam-5509	159	53	expressed	express	VERB
ejpam-5509	159	54	as	as	ADP
ejpam-5509	159	55	e0	e0	PROPN
ejpam-5509	159	56	=	=	SYM
ejpam-5509	159	57	(	(	PUNCT
ejpam-5509	159	58	s0	s0	PROPN
ejpam-5509	159	59	,	,	PUNCT
ejpam-5509	159	60	v	v	NOUN
ejpam-5509	159	61	0	0	NUM
ejpam-5509	159	62	1	1	NUM
ejpam-5509	159	63	,	,	PUNCT
ejpam-5509	159	64	v	v	NOUN
ejpam-5509	159	65	0	0	NUM
ejpam-5509	159	66	2	2	NUM
ejpam-5509	159	67	,	,	PUNCT
ejpam-5509	159	68	a	a	DET
ejpam-5509	159	69	0	0	NUM
ejpam-5509	159	70	,	,	PUNCT
ejpam-5509	159	71	c0	c0	NOUN
ejpam-5509	159	72	,	,	PUNCT
ejpam-5509	159	73	r0	r0	NOUN
ejpam-5509	159	74	)	)	PUNCT
ejpam-5509	159	75	,	,	PUNCT
ejpam-5509	160	1	=	=	PRON
ejpam-5509	160	2	(	(	PUNCT
ejpam-5509	160	3	π(l−ωv	π(l−ωv	PROPN
ejpam-5509	160	4	)	)	PUNCT
ejpam-5509	160	5	µl+φ1v	µl+φ1v	NOUN
ejpam-5509	160	6	,	,	PUNCT
ejpam-5509	160	7	π(φ1+ωµ	π(φ1+ωµ	NUM
ejpam-5509	160	8	)	)	PUNCT
ejpam-5509	160	9	µl+φ1v	µl+φ1v	NOUN
ejpam-5509	160	10	,	,	PUNCT
ejpam-5509	160	11	πα(φ1+ωµ	πα(φ1+ωµ	PROPN
ejpam-5509	160	12	)	)	PUNCT
ejpam-5509	160	13	(	(	PUNCT
ejpam-5509	160	14	ϵ+µ)(µl+φ1v	ϵ+µ)(µl+φ1v	PROPN
ejpam-5509	160	15	)	)	PUNCT
ejpam-5509	160	16	,	,	PUNCT
ejpam-5509	160	17	0	0	NUM
ejpam-5509	160	18	,	,	PUNCT
ejpam-5509	160	19	0	0	NUM
ejpam-5509	160	20	,	,	PUNCT
ejpam-5509	160	21	πεα(φ1+ωµ	πεα(φ1+ωµ	X
ejpam-5509	160	22	)	)	PUNCT
ejpam-5509	160	23	(	(	PUNCT
ejpam-5509	160	24	ε+µ)(µl+φ1v	ε+µ)(µl+φ1v	PROPN
ejpam-5509	160	25	)	)	PUNCT
ejpam-5509	160	26	)	)	PUNCT
ejpam-5509	160	27	,	,	PUNCT
ejpam-5509	160	28	(	(	PUNCT
ejpam-5509	160	29	12	12	NUM
ejpam-5509	160	30	)	)	PUNCT
ejpam-5509	160	31	where	where	SCONJ
ejpam-5509	160	32	l	l	NOUN
ejpam-5509	160	33	=	=	SYM
ejpam-5509	160	34	α+	α+	PUNCT
ejpam-5509	160	35	µ+	µ+	PROPN
ejpam-5509	160	36	φ2	φ2	PROPN
ejpam-5509	160	37	,	,	PUNCT
ejpam-5509	160	38	v	v	NOUN
ejpam-5509	160	39	=	=	SYM
ejpam-5509	160	40	α+	α+	X
ejpam-5509	160	41	µ	µ	NOUN
ejpam-5509	160	42	,	,	PUNCT
ejpam-5509	160	43	and	and	CCONJ
ejpam-5509	160	44	α+	α+	X
ejpam-5509	160	45	µ	µ	X
ejpam-5509	160	46	<	<	X
ejpam-5509	160	47	ω(α+	ω(α+	NUM
ejpam-5509	160	48	µ	µ	NUM
ejpam-5509	160	49	)	)	PUNCT
ejpam-5509	160	50	.	.	PUNCT
ejpam-5509	161	1	i.	i.	PROPN
ejpam-5509	161	2	ahmad	ahmad	PROPN
ejpam-5509	161	3	et	et	PROPN
ejpam-5509	161	4	al	al	PROPN
ejpam-5509	161	5	.	.	PUNCT
ejpam-5509	161	6	/	/	SYM
ejpam-5509	161	7	eur	eur	PROPN
ejpam-5509	161	8	.	.	PUNCT
ejpam-5509	162	1	j.	j.	PROPN
ejpam-5509	162	2	pure	pure	PROPN
ejpam-5509	162	3	appl	appl	PROPN
ejpam-5509	162	4	.	.	PROPN
ejpam-5509	162	5	math	math	PROPN
ejpam-5509	162	6	,	,	PUNCT
ejpam-5509	162	7	18	18	NUM
ejpam-5509	162	8	(	(	PUNCT
ejpam-5509	162	9	1	1	NUM
ejpam-5509	162	10	)	)	PUNCT
ejpam-5509	162	11	(	(	PUNCT
ejpam-5509	162	12	2025	2025	NUM
ejpam-5509	162	13	)	)	PUNCT
ejpam-5509	162	14	,	,	PUNCT
ejpam-5509	162	15	5509	5509	NUM
ejpam-5509	162	16	8	8	NUM
ejpam-5509	162	17	of	of	ADP
ejpam-5509	162	18	27	27	NUM
ejpam-5509	162	19	the	the	DET
ejpam-5509	162	20	basic	basic	ADJ
ejpam-5509	162	21	reproduction	reproduction	NOUN
ejpam-5509	162	22	number	number	NOUN
ejpam-5509	162	23	,	,	PUNCT
ejpam-5509	162	24	r0	r0	NOUN
ejpam-5509	162	25	,	,	PUNCT
ejpam-5509	162	26	for	for	ADP
ejpam-5509	162	27	the	the	DET
ejpam-5509	162	28	system	system	NOUN
ejpam-5509	162	29	described	describe	VERB
ejpam-5509	162	30	in	in	ADP
ejpam-5509	162	31	(	(	PUNCT
ejpam-5509	162	32	10	10	NUM
ejpam-5509	162	33	)	)	PUNCT
ejpam-5509	162	34	is	be	AUX
ejpam-5509	162	35	calculated	calculate	VERB
ejpam-5509	162	36	using	use	VERB
ejpam-5509	162	37	the	the	DET
ejpam-5509	162	38	approach	approach	NOUN
ejpam-5509	162	39	outlined	outline	VERB
ejpam-5509	162	40	in	in	ADP
ejpam-5509	162	41	[	[	X
ejpam-5509	162	42	38	38	NUM
ejpam-5509	162	43	]	]	PUNCT
ejpam-5509	162	44	.	.	PUNCT
ejpam-5509	163	1	this	this	DET
ejpam-5509	163	2	parameter	parameter	NOUN
ejpam-5509	163	3	is	be	AUX
ejpam-5509	163	4	defined	define	VERB
ejpam-5509	163	5	as	as	ADP
ejpam-5509	163	6	r0	r0	NOUN
ejpam-5509	163	7	=	=	NOUN
ejpam-5509	163	8	ρ(fv	ρ(fv	NOUN
ejpam-5509	163	9	−1	−1	NOUN
ejpam-5509	163	10	)	)	PUNCT
ejpam-5509	163	11	,	,	PUNCT
ejpam-5509	163	12	where	where	SCONJ
ejpam-5509	163	13	ρ(fv	ρ(fv	PROPN
ejpam-5509	163	14	−1	−1	NOUN
ejpam-5509	163	15	)	)	PUNCT
ejpam-5509	163	16	represents	represent	VERB
ejpam-5509	163	17	the	the	DET
ejpam-5509	163	18	spectral	spectral	ADJ
ejpam-5509	163	19	radius	radius	NOUN
ejpam-5509	163	20	of	of	ADP
ejpam-5509	163	21	the	the	DET
ejpam-5509	163	22	matrix	matrix	NOUN
ejpam-5509	163	23	fv	fv	X
ejpam-5509	163	24	−1	−1	NOUN
ejpam-5509	163	25	.	.	PUNCT
ejpam-5509	164	1	in	in	ADP
ejpam-5509	164	2	our	our	PRON
ejpam-5509	164	3	analysis	analysis	NOUN
ejpam-5509	164	4	,	,	PUNCT
ejpam-5509	164	5	we	we	PRON
ejpam-5509	164	6	focus	focus	VERB
ejpam-5509	164	7	only	only	ADV
ejpam-5509	164	8	on	on	ADP
ejpam-5509	164	9	the	the	DET
ejpam-5509	164	10	infectious	infectious	ADJ
ejpam-5509	164	11	classes	class	NOUN
ejpam-5509	164	12	within	within	ADP
ejpam-5509	164	13	the	the	DET
ejpam-5509	164	14	differential	differential	ADJ
ejpam-5509	164	15	equation	equation	NOUN
ejpam-5509	164	16	system	system	NOUN
ejpam-5509	164	17	(	(	PUNCT
ejpam-5509	164	18	10	10	NUM
ejpam-5509	164	19	)	)	PUNCT
ejpam-5509	164	20	,	,	PUNCT
ejpam-5509	164	21	which	which	PRON
ejpam-5509	164	22	can	can	AUX
ejpam-5509	164	23	be	be	AUX
ejpam-5509	164	24	expressed	express	VERB
ejpam-5509	164	25	as	as	ADP
ejpam-5509	164	26	:	:	PUNCT
ejpam-5509	164	27	da	da	NOUN
ejpam-5509	164	28	dt	dt	NOUN
ejpam-5509	165	1	=	=	PUNCT
ejpam-5509	165	2	λs	λs	PROPN
ejpam-5509	165	3	−	−	PROPN
ejpam-5509	166	1	(	(	PUNCT
ejpam-5509	166	2	δ	δ	PROPN
ejpam-5509	166	3	+	+	CCONJ
ejpam-5509	166	4	σ	σ	PROPN
ejpam-5509	166	5	+	+	CCONJ
ejpam-5509	166	6	µ)a	µ)a	NOUN
ejpam-5509	166	7	,	,	PUNCT
ejpam-5509	166	8	dc	dc	PROPN
ejpam-5509	166	9	dt	dt	X
ejpam-5509	166	10	=	=	SYM
ejpam-5509	166	11	δa+π(1−	δa+π(1−	PROPN
ejpam-5509	167	1	ω)τc	ω)τc	PROPN
ejpam-5509	167	2	−	−	PROPN
ejpam-5509	167	3	(	(	PUNCT
ejpam-5509	167	4	ϑ+	ϑ+	X
ejpam-5509	167	5	µ+	µ+	VERB
ejpam-5509	167	6	ψ)c	ψ)c	NOUN
ejpam-5509	167	7	.	.	PUNCT
ejpam-5509	168	1	(	(	PUNCT
ejpam-5509	168	2	13	13	NUM
ejpam-5509	168	3	)	)	PUNCT
ejpam-5509	168	4	consider	consider	VERB
ejpam-5509	168	5	f	f	NOUN
ejpam-5509	168	6	to	to	PART
ejpam-5509	168	7	represent	represent	VERB
ejpam-5509	168	8	the	the	DET
ejpam-5509	168	9	rate	rate	NOUN
ejpam-5509	168	10	at	at	ADP
ejpam-5509	168	11	which	which	PRON
ejpam-5509	168	12	new	new	ADJ
ejpam-5509	168	13	infections	infection	NOUN
ejpam-5509	168	14	enter	enter	VERB
ejpam-5509	168	15	the	the	DET
ejpam-5509	168	16	system	system	NOUN
ejpam-5509	168	17	,	,	PUNCT
ejpam-5509	168	18	and	and	CCONJ
ejpam-5509	168	19	let	let	VERB
ejpam-5509	168	20	v	v	PRON
ejpam-5509	168	21	quantify	quantify	VERB
ejpam-5509	168	22	the	the	DET
ejpam-5509	168	23	disparity	disparity	NOUN
ejpam-5509	168	24	between	between	ADP
ejpam-5509	168	25	the	the	DET
ejpam-5509	168	26	immigration	immigration	NOUN
ejpam-5509	168	27	rate	rate	NOUN
ejpam-5509	168	28	into	into	ADP
ejpam-5509	168	29	the	the	DET
ejpam-5509	168	30	compartments	compartment	NOUN
ejpam-5509	168	31	and	and	CCONJ
ejpam-5509	168	32	the	the	DET
ejpam-5509	168	33	rate	rate	NOUN
ejpam-5509	168	34	of	of	ADP
ejpam-5509	168	35	inter	inter	ADJ
ejpam-5509	168	36	-	-	ADJ
ejpam-5509	168	37	compartmental	compartmental	ADJ
ejpam-5509	168	38	transfer	transfer	NOUN
ejpam-5509	168	39	.	.	PUNCT
ejpam-5509	169	1	f	f	X
ejpam-5509	170	1	=	=	PUNCT
ejpam-5509	170	2	[	[	PUNCT
ejpam-5509	170	3	λs	λs	NOUN
ejpam-5509	170	4	0	0	NUM
ejpam-5509	170	5	]	]	PUNCT
ejpam-5509	170	6	,	,	PUNCT
ejpam-5509	170	7	and	and	CCONJ
ejpam-5509	170	8	v	v	X
ejpam-5509	170	9	=	=	X
ejpam-5509	170	10	[	[	PUNCT
ejpam-5509	170	11	(	(	PUNCT
ejpam-5509	170	12	δ	δ	PROPN
ejpam-5509	170	13	+	+	PROPN
ejpam-5509	170	14	σ	σ	PROPN
ejpam-5509	170	15	+	+	CCONJ
ejpam-5509	170	16	µ)a	µ)a	NOUN
ejpam-5509	170	17	(	(	PUNCT
ejpam-5509	170	18	ϑ+	ϑ+	X
ejpam-5509	170	19	µ+	µ+	VERB
ejpam-5509	170	20	ψ)c	ψ)c	NOUN
ejpam-5509	170	21	−π(1−	−π(1−	ADJ
ejpam-5509	170	22	ω)τc	ω)τc	PROPN
ejpam-5509	170	23	−	−	NOUN
ejpam-5509	170	24	δa	δa	NOUN
ejpam-5509	170	25	]	]	PUNCT
ejpam-5509	170	26	,	,	PUNCT
ejpam-5509	170	27	where	where	SCONJ
ejpam-5509	170	28	λ	λ	PROPN
ejpam-5509	170	29	=	=	SYM
ejpam-5509	170	30	ξ(κa	ξ(κa	PROPN
ejpam-5509	170	31	+	+	SYM
ejpam-5509	170	32	c	c	NOUN
ejpam-5509	170	33	)	)	PUNCT
ejpam-5509	170	34	.	.	PUNCT
ejpam-5509	171	1	next	next	ADV
ejpam-5509	171	2	,	,	PUNCT
ejpam-5509	171	3	calculate	calculate	VERB
ejpam-5509	171	4	the	the	DET
ejpam-5509	171	5	jacobian	jacobian	ADJ
ejpam-5509	171	6	matrix	matrix	NOUN
ejpam-5509	171	7	for	for	ADP
ejpam-5509	171	8	both	both	DET
ejpam-5509	171	9	f	f	PROPN
ejpam-5509	171	10	and	and	CCONJ
ejpam-5509	171	11	v	v	ADP
ejpam-5509	171	12	concerning	concern	VERB
ejpam-5509	171	13	the	the	DET
ejpam-5509	171	14	variables	variable	NOUN
ejpam-5509	171	15	a	a	PRON
ejpam-5509	171	16	and	and	CCONJ
ejpam-5509	171	17	c	c	NOUN
ejpam-5509	171	18	at	at	ADP
ejpam-5509	171	19	the	the	DET
ejpam-5509	171	20	dfe	dfe	PROPN
ejpam-5509	171	21	denoted	denote	VERB
ejpam-5509	171	22	as	as	ADP
ejpam-5509	171	23	e0	e0	PROPN
ejpam-5509	171	24	.	.	PUNCT
ejpam-5509	172	1	f	f	X
ejpam-5509	173	1	=	=	PUNCT
ejpam-5509	173	2	[	[	PUNCT
ejpam-5509	173	3	κ	κ	NOUN
ejpam-5509	173	4	1	1	NUM
ejpam-5509	173	5	0	0	NUM
ejpam-5509	173	6	0	0	NUM
ejpam-5509	173	7	]	]	PUNCT
ejpam-5509	173	8	,	,	PUNCT
ejpam-5509	173	9	and	and	CCONJ
ejpam-5509	173	10	v	v	X
ejpam-5509	173	11	=	=	X
ejpam-5509	173	12	[	[	PUNCT
ejpam-5509	173	13	δ	δ	PROPN
ejpam-5509	173	14	+	+	CCONJ
ejpam-5509	173	15	σ	σ	PROPN
ejpam-5509	173	16	+	+	X
ejpam-5509	173	17	µ	µ	X
ejpam-5509	173	18	0	0	NUM
ejpam-5509	173	19	−δ	−δ	NOUN
ejpam-5509	173	20	(	(	PUNCT
ejpam-5509	173	21	ϑ+	ϑ+	X
ejpam-5509	173	22	µ+	µ+	X
ejpam-5509	173	23	ψ)−π(1−	ψ)−π(1−	NOUN
ejpam-5509	173	24	ω)τ	ω)τ	PRON
ejpam-5509	173	25	]	]	PUNCT
ejpam-5509	173	26	.	.	PUNCT
ejpam-5509	174	1	next	next	ADV
ejpam-5509	174	2	,	,	PUNCT
ejpam-5509	174	3	by	by	ADP
ejpam-5509	174	4	calculating	calculate	VERB
ejpam-5509	174	5	the	the	DET
ejpam-5509	174	6	matrix	matrix	NOUN
ejpam-5509	174	7	v	v	ADP
ejpam-5509	174	8	inverse	inverse	NOUN
ejpam-5509	174	9	,	,	PUNCT
ejpam-5509	174	10	we	we	PRON
ejpam-5509	174	11	obtain	obtain	VERB
ejpam-5509	174	12	the	the	DET
ejpam-5509	174	13	following	follow	VERB
ejpam-5509	174	14	result	result	NOUN
ejpam-5509	174	15	.	.	PUNCT
ejpam-5509	175	1	v	v	X
ejpam-5509	175	2	−1	−1	NOUN
ejpam-5509	175	3	=	=	SYM
ejpam-5509	175	4	1	1	NUM
ejpam-5509	175	5	(	(	PUNCT
ejpam-5509	175	6	δ	δ	PROPN
ejpam-5509	175	7	+	+	PROPN
ejpam-5509	175	8	σ	σ	PROPN
ejpam-5509	175	9	+	+	CCONJ
ejpam-5509	175	10	µ)((ϑ+	µ)((ϑ+	PROPN
ejpam-5509	175	11	µ+	µ+	X
ejpam-5509	175	12	ψ)−π(1−	ψ)−π(1−	NOUN
ejpam-5509	175	13	ω)τ	ω)τ	NOUN
ejpam-5509	175	14	)	)	PUNCT
ejpam-5509	175	15	[	[	PUNCT
ejpam-5509	175	16	(	(	PUNCT
ejpam-5509	175	17	ϑ+	ϑ+	X
ejpam-5509	175	18	µ+	µ+	X
ejpam-5509	175	19	ψ)−π(1−	ψ)−π(1−	NOUN
ejpam-5509	175	20	ω)τ	ω)τ	NOUN
ejpam-5509	175	21	0	0	NUM
ejpam-5509	175	22	δ	δ	PROPN
ejpam-5509	175	23	δ	δ	PROPN
ejpam-5509	175	24	+	+	CCONJ
ejpam-5509	175	25	σ	σ	PROPN
ejpam-5509	175	26	+	+	X
ejpam-5509	175	27	µ	µ	X
ejpam-5509	175	28	]	]	PUNCT
ejpam-5509	175	29	,	,	PUNCT
ejpam-5509	175	30	then	then	ADV
ejpam-5509	175	31	fv	fv	PROPN
ejpam-5509	175	32	−1	−1	NOUN
ejpam-5509	175	33	is	be	AUX
ejpam-5509	175	34	given	give	VERB
ejpam-5509	175	35	by	by	ADP
ejpam-5509	175	36	fv	fv	NUM
ejpam-5509	175	37	−1	−1	NOUN
ejpam-5509	175	38	=	=	PUNCT
ejpam-5509	175	39	[	[	PUNCT
ejpam-5509	175	40	κξs0	κξs0	NOUN
ejpam-5509	175	41	δ+σ+µ	δ+σ+µ	NOUN
ejpam-5509	175	42	+	+	CCONJ
ejpam-5509	175	43	ξδs0	ξδs0	NOUN
ejpam-5509	175	44	(	(	PUNCT
ejpam-5509	175	45	δ+σ)((ϑ+µ+ψ)−π(1−ω)τ	δ+σ)((ϑ+µ+ψ)−π(1−ω)τ	NOUN
ejpam-5509	175	46	)	)	PUNCT
ejpam-5509	175	47	ξs0	ξs0	PROPN
ejpam-5509	175	48	(	(	PUNCT
ejpam-5509	175	49	ϑ+µ+ψ)−π(1−ω)τ	ϑ+µ+ψ)−π(1−ω)τ	X
ejpam-5509	175	50	0	0	NUM
ejpam-5509	175	51	0	0	NUM
ejpam-5509	175	52	]	]	PUNCT
ejpam-5509	175	53	.	.	PUNCT
ejpam-5509	176	1	the	the	DET
ejpam-5509	176	2	endemic	endemic	ADJ
ejpam-5509	176	3	indicator	indicator	NOUN
ejpam-5509	176	4	r0	r0	NOUN
ejpam-5509	176	5	corresponds	correspond	VERB
ejpam-5509	176	6	to	to	ADP
ejpam-5509	176	7	the	the	DET
ejpam-5509	176	8	highest	high	ADJ
ejpam-5509	176	9	eigenvalue	eigenvalue	NOUN
ejpam-5509	176	10	of	of	ADP
ejpam-5509	176	11	the	the	DET
ejpam-5509	176	12	matrix	matrix	NOUN
ejpam-5509	176	13	mentioned	mention	VERB
ejpam-5509	176	14	above	above	ADV
ejpam-5509	176	15	.	.	PUNCT
ejpam-5509	177	1	r0	r0	NOUN
ejpam-5509	177	2	=	=	PUNCT
ejpam-5509	177	3	ξs0	ξs0	PROPN
ejpam-5509	177	4	(	(	PUNCT
ejpam-5509	177	5	κ	κ	NOUN
ejpam-5509	177	6	δ+σ+µ	δ+σ+µ	NOUN
ejpam-5509	177	7	+	+	CCONJ
ejpam-5509	177	8	δ	δ	PROPN
ejpam-5509	177	9	(	(	PUNCT
ejpam-5509	177	10	δ+σ+µ)((ϑ+µ+ψ)−π(1−ω)τ	δ+σ+µ)((ϑ+µ+ψ)−π(1−ω)τ	PROPN
ejpam-5509	177	11	)	)	PUNCT
ejpam-5509	177	12	)	)	PUNCT
ejpam-5509	177	13	.	.	PUNCT
ejpam-5509	178	1	(	(	PUNCT
ejpam-5509	178	2	14	14	NUM
ejpam-5509	178	3	)	)	PUNCT
ejpam-5509	178	4	theorem	theorem	NOUN
ejpam-5509	178	5	1	1	NUM
ejpam-5509	178	6	.	.	PUNCT
ejpam-5509	179	1	the	the	DET
ejpam-5509	179	2	state	state	NOUN
ejpam-5509	179	3	of	of	ADP
ejpam-5509	179	4	dfe	dfe	PROPN
ejpam-5509	179	5	exhibits	exhibit	VERB
ejpam-5509	179	6	local	local	ADJ
ejpam-5509	179	7	asymptotic	asymptotic	ADJ
ejpam-5509	179	8	stability	stability	NOUN
ejpam-5509	179	9	when	when	SCONJ
ejpam-5509	179	10	r0	r0	NOUN
ejpam-5509	179	11	<	<	X
ejpam-5509	179	12	1	1	NUM
ejpam-5509	179	13	,	,	PUNCT
ejpam-5509	179	14	and	and	CCONJ
ejpam-5509	179	15	it	it	PRON
ejpam-5509	179	16	becomes	become	VERB
ejpam-5509	179	17	unstable	unstable	ADJ
ejpam-5509	179	18	when	when	SCONJ
ejpam-5509	179	19	r0	r0	NOUN
ejpam-5509	179	20	exceeds	exceed	VERB
ejpam-5509	179	21	1	1	NUM
ejpam-5509	179	22	.	.	PUNCT
ejpam-5509	180	1	proof	proof	NOUN
ejpam-5509	180	2	.	.	PUNCT
ejpam-5509	181	1	the	the	DET
ejpam-5509	181	2	jacobian	jacobian	ADJ
ejpam-5509	181	3	matrix	matrix	NOUN
ejpam-5509	181	4	of	of	ADP
ejpam-5509	181	5	the	the	DET
ejpam-5509	181	6	system	system	NOUN
ejpam-5509	181	7	described	describe	VERB
ejpam-5509	181	8	in	in	ADP
ejpam-5509	181	9	(	(	PUNCT
ejpam-5509	181	10	10	10	NUM
ejpam-5509	181	11	)	)	PUNCT
ejpam-5509	181	12	at	at	ADP
ejpam-5509	181	13	the	the	DET
ejpam-5509	181	14	equilibrium	equilibrium	NOUN
ejpam-5509	181	15	point	point	NOUN
ejpam-5509	181	16	denoted	denote	VERB
ejpam-5509	181	17	as	as	SCONJ
ejpam-5509	181	18	e0	e0	PROPN
ejpam-5509	181	19	is	be	AUX
ejpam-5509	181	20	given	give	VERB
ejpam-5509	181	21	by	by	ADP
ejpam-5509	181	22	j(e0	j(e0	ADJ
ejpam-5509	181	23	)	)	PUNCT
ejpam-5509	181	24	=	=	SYM
ejpam-5509	181	25			NOUN
ejpam-5509	181	26	−(µ+	−(µ+	PROPN
ejpam-5509	181	27	φ1	φ1	PROPN
ejpam-5509	181	28	)	)	PUNCT
ejpam-5509	181	29	φ2	φ2	NOUN
ejpam-5509	181	30	0	0	PUNCT
ejpam-5509	182	1	−ξκs0	−ξκs0	PRON
ejpam-5509	182	2	−π(1−	−π(1−	ADJ
ejpam-5509	182	3	ω)τ	ω)τ	NOUN
ejpam-5509	182	4	−	−	NOUN
ejpam-5509	182	5	ξs0	ξs0	ADJ
ejpam-5509	182	6	0	0	NUM
ejpam-5509	183	1	φ1	φ1	PROPN
ejpam-5509	183	2	−(α+	−(α+	NUM
ejpam-5509	183	3	µ+	µ+	DET
ejpam-5509	183	4	φ2	φ2	PROPN
ejpam-5509	183	5	)	)	PUNCT
ejpam-5509	183	6	0	0	NUM
ejpam-5509	184	1	0	0	NUM
ejpam-5509	184	2	0	0	NUM
ejpam-5509	184	3	0	0	NUM
ejpam-5509	184	4	0	0	NUM
ejpam-5509	184	5	α	α	NOUN
ejpam-5509	184	6	−(µ+	−(µ+	PROPN
ejpam-5509	184	7	ϵ	ϵ	NOUN
ejpam-5509	184	8	)	)	PUNCT
ejpam-5509	184	9	0	0	NUM
ejpam-5509	184	10	0	0	NUM
ejpam-5509	184	11	0	0	NUM
ejpam-5509	184	12	0	0	NUM
ejpam-5509	184	13	0	0	NUM
ejpam-5509	184	14	0	0	NUM
ejpam-5509	184	15	ξκs0	ξκs0	PROPN
ejpam-5509	184	16	−	−	PROPN
ejpam-5509	184	17	(	(	PUNCT
ejpam-5509	184	18	δ	δ	PROPN
ejpam-5509	184	19	+	+	PROPN
ejpam-5509	184	20	σ	σ	PROPN
ejpam-5509	184	21	+	+	X
ejpam-5509	184	22	µ	µ	X
ejpam-5509	184	23	)	)	PUNCT
ejpam-5509	184	24	ξs0	ξs0	NOUN
ejpam-5509	184	25	0	0	NUM
ejpam-5509	184	26	0	0	NUM
ejpam-5509	184	27	0	0	NUM
ejpam-5509	184	28	0	0	NUM
ejpam-5509	184	29	δ	δ	PROPN
ejpam-5509	184	30	π(1−	π(1−	ADJ
ejpam-5509	184	31	ω)τ	ω)τ	X
ejpam-5509	184	32	−	−	PROPN
ejpam-5509	184	33	(	(	PUNCT
ejpam-5509	184	34	ϑ+	ϑ+	X
ejpam-5509	184	35	µ+	µ+	X
ejpam-5509	184	36	ψ	ψ	SYM
ejpam-5509	184	37	)	)	PUNCT
ejpam-5509	184	38	0	0	NUM
ejpam-5509	184	39	0	0	NUM
ejpam-5509	184	40	0	0	NUM
ejpam-5509	185	1	ϵ	ϵ	X
ejpam-5509	185	2	σ	σ	PROPN
ejpam-5509	185	3	ϑ	ϑ	PROPN
ejpam-5509	185	4	−µ	−µ	NOUN
ejpam-5509	185	5			NUM
ejpam-5509	185	6	,	,	PUNCT
ejpam-5509	185	7	i.	i.	PROPN
ejpam-5509	185	8	ahmad	ahmad	PROPN
ejpam-5509	185	9	et	et	PROPN
ejpam-5509	185	10	al	al	PROPN
ejpam-5509	185	11	.	.	PUNCT
ejpam-5509	185	12	/	/	SYM
ejpam-5509	185	13	eur	eur	PROPN
ejpam-5509	185	14	.	.	PUNCT
ejpam-5509	186	1	j.	j.	PROPN
ejpam-5509	186	2	pure	pure	PROPN
ejpam-5509	186	3	appl	appl	PROPN
ejpam-5509	186	4	.	.	PROPN
ejpam-5509	186	5	math	math	PROPN
ejpam-5509	186	6	,	,	PUNCT
ejpam-5509	186	7	18	18	NUM
ejpam-5509	186	8	(	(	PUNCT
ejpam-5509	186	9	1	1	NUM
ejpam-5509	186	10	)	)	PUNCT
ejpam-5509	186	11	(	(	PUNCT
ejpam-5509	186	12	2025	2025	NUM
ejpam-5509	186	13	)	)	PUNCT
ejpam-5509	186	14	,	,	PUNCT
ejpam-5509	186	15	5509	5509	NUM
ejpam-5509	186	16	9	9	NUM
ejpam-5509	186	17	of	of	ADP
ejpam-5509	186	18	27	27	NUM
ejpam-5509	186	19	then	then	ADV
ejpam-5509	186	20	the	the	DET
ejpam-5509	186	21	characteristic	characteristic	ADJ
ejpam-5509	186	22	equation	equation	NOUN
ejpam-5509	186	23	of	of	ADP
ejpam-5509	186	24	the	the	DET
ejpam-5509	186	25	above	above	ADJ
ejpam-5509	186	26	is	be	AUX
ejpam-5509	186	27	|j(e0)−	|j(e0)−	PROPN
ejpam-5509	186	28	λ|	λ|	PROPN
ejpam-5509	186	29	=	=	SYM
ejpam-5509	186	30	0	0	PROPN
ejpam-5509	186	31	.	.	PUNCT
ejpam-5509	187	1	from	from	ADP
ejpam-5509	187	2	which	which	PRON
ejpam-5509	187	3	,	,	PUNCT
ejpam-5509	187	4	we	we	PRON
ejpam-5509	187	5	derived	derive	VERB
ejpam-5509	187	6	λ1	λ1	NOUN
ejpam-5509	187	7	=	=	SYM
ejpam-5509	187	8	−µ	−µ	NOUN
ejpam-5509	187	9	<	<	X
ejpam-5509	187	10	0	0	NUM
ejpam-5509	187	11	,	,	PUNCT
ejpam-5509	187	12	λ2	λ2	NOUN
ejpam-5509	187	13	=	=	SYM
ejpam-5509	187	14	−(µ+	−(µ+	NUM
ejpam-5509	187	15	ϵ	ϵ	NUM
ejpam-5509	187	16	)	)	PUNCT
ejpam-5509	187	17	<	<	X
ejpam-5509	187	18	0	0	X
ejpam-5509	187	19	.	.	PUNCT
ejpam-5509	188	1	furthermore	furthermore	ADV
ejpam-5509	188	2	,	,	PUNCT
ejpam-5509	188	3	employing	employ	VERB
ejpam-5509	188	4	the	the	DET
ejpam-5509	188	5	routh	routh	PROPN
ejpam-5509	188	6	-	-	PUNCT
ejpam-5509	188	7	hurwitz	hurwitz	PROPN
ejpam-5509	188	8	criteria	criterion	NOUN
ejpam-5509	188	9	,	,	PUNCT
ejpam-5509	188	10	we	we	PRON
ejpam-5509	188	11	established	establish	VERB
ejpam-5509	188	12	that	that	SCONJ
ejpam-5509	188	13	both	both	DET
ejpam-5509	188	14	λ3	λ3	PROPN
ejpam-5509	188	15	and	and	CCONJ
ejpam-5509	188	16	λ4	λ4	PROPN
ejpam-5509	188	17	are	be	AUX
ejpam-5509	188	18	negative	negative	ADJ
ejpam-5509	188	19	.	.	PUNCT
ejpam-5509	189	1	as	as	ADP
ejpam-5509	189	2	for	for	ADP
ejpam-5509	189	3	the	the	DET
ejpam-5509	189	4	remaining	remain	VERB
ejpam-5509	189	5	two	two	NUM
ejpam-5509	189	6	eigenvalues	eigenvalue	NOUN
ejpam-5509	189	7	,	,	PUNCT
ejpam-5509	189	8	they	they	PRON
ejpam-5509	189	9	constitute	constitute	VERB
ejpam-5509	189	10	the	the	DET
ejpam-5509	189	11	eigenvalues	eigenvalue	NOUN
ejpam-5509	189	12	of	of	ADP
ejpam-5509	189	13	the	the	DET
ejpam-5509	189	14	given	give	VERB
ejpam-5509	189	15	system	system	NOUN
ejpam-5509	189	16	.	.	PUNCT
ejpam-5509	190	1	j1	j1	PROPN
ejpam-5509	190	2	=	=	PUNCT
ejpam-5509	191	1	[	[	PUNCT
ejpam-5509	191	2	ξκs0	ξκs0	PROPN
ejpam-5509	191	3	−	−	PROPN
ejpam-5509	192	1	(	(	PUNCT
ejpam-5509	192	2	δ	δ	PROPN
ejpam-5509	192	3	+	+	PROPN
ejpam-5509	192	4	σ	σ	PROPN
ejpam-5509	192	5	+	+	X
ejpam-5509	192	6	µ	µ	X
ejpam-5509	192	7	)	)	PUNCT
ejpam-5509	192	8	ξs0	ξs0	NUM
ejpam-5509	192	9	δ	δ	PROPN
ejpam-5509	192	10	π(1−	π(1−	ADJ
ejpam-5509	192	11	ω)τ	ω)τ	X
ejpam-5509	192	12	−	−	PROPN
ejpam-5509	192	13	(	(	PUNCT
ejpam-5509	192	14	ϑ+	ϑ+	X
ejpam-5509	192	15	µ+	µ+	X
ejpam-5509	192	16	ψ	ψ	NOUN
ejpam-5509	192	17	)	)	PUNCT
ejpam-5509	192	18	]	]	PUNCT
ejpam-5509	192	19	.	.	PUNCT
ejpam-5509	193	1	we	we	PRON
ejpam-5509	193	2	can	can	AUX
ejpam-5509	193	3	now	now	ADV
ejpam-5509	193	4	employ	employ	VERB
ejpam-5509	193	5	the	the	DET
ejpam-5509	193	6	standard	standard	ADJ
ejpam-5509	193	7	criteria	criterion	NOUN
ejpam-5509	193	8	to	to	PART
ejpam-5509	193	9	guarantee	guarantee	VERB
ejpam-5509	193	10	that	that	SCONJ
ejpam-5509	193	11	the	the	DET
ejpam-5509	193	12	eigenvalues	eigenvalue	NOUN
ejpam-5509	193	13	of	of	ADP
ejpam-5509	193	14	j1	j1	PROPN
ejpam-5509	193	15	exhibit	exhibit	VERB
ejpam-5509	193	16	a	a	DET
ejpam-5509	193	17	negative	negative	ADJ
ejpam-5509	193	18	real	real	ADJ
ejpam-5509	193	19	component	component	NOUN
ejpam-5509	193	20	.	.	PUNCT
ejpam-5509	194	1	specifically	specifically	ADV
ejpam-5509	194	2	,	,	PUNCT
ejpam-5509	194	3	we	we	PRON
ejpam-5509	194	4	seek	seek	VERB
ejpam-5509	194	5	a	a	DET
ejpam-5509	194	6	condition	condition	NOUN
ejpam-5509	194	7	where	where	SCONJ
ejpam-5509	194	8	both	both	CCONJ
ejpam-5509	194	9	the	the	DET
ejpam-5509	194	10	trace	trace	NOUN
ejpam-5509	194	11	of	of	ADP
ejpam-5509	194	12	j1	j1	PROPN
ejpam-5509	194	13	<	<	X
ejpam-5509	194	14	0	0	NUM
ejpam-5509	194	15	,	,	PUNCT
ejpam-5509	194	16	and	and	CCONJ
ejpam-5509	194	17	the	the	DET
ejpam-5509	194	18	determinant	determinant	NOUN
ejpam-5509	194	19	of	of	ADP
ejpam-5509	194	20	j1	j1	PROPN
ejpam-5509	194	21	>	>	X
ejpam-5509	194	22	0	0	X
ejpam-5509	194	23	.	.	PUNCT
ejpam-5509	195	1	from	from	ADP
ejpam-5509	195	2	the	the	DET
ejpam-5509	195	3	second	second	ADJ
ejpam-5509	195	4	set	set	NOUN
ejpam-5509	195	5	of	of	ADP
ejpam-5509	195	6	inequalities	inequality	NOUN
ejpam-5509	195	7	,	,	PUNCT
ejpam-5509	195	8	the	the	DET
ejpam-5509	195	9	following	follow	VERB
ejpam-5509	195	10	condition	condition	NOUN
ejpam-5509	195	11	has	have	AUX
ejpam-5509	195	12	been	be	AUX
ejpam-5509	195	13	derived	derive	VERB
ejpam-5509	195	14	:	:	PUNCT
ejpam-5509	195	15	(	(	PUNCT
ejpam-5509	195	16	ξκs0	ξκs0	PROPN
ejpam-5509	195	17	−	−	PROPN
ejpam-5509	195	18	(	(	PUNCT
ejpam-5509	195	19	δ	δ	PROPN
ejpam-5509	195	20	+	+	PROPN
ejpam-5509	195	21	σ	σ	PROPN
ejpam-5509	195	22	+	+	CCONJ
ejpam-5509	196	1	µ))(π(1−	µ))(π(1−	NOUN
ejpam-5509	196	2	ω)τ	ω)τ	ADJ
ejpam-5509	196	3	−	−	PROPN
ejpam-5509	196	4	(	(	PUNCT
ejpam-5509	196	5	ϑ+	ϑ+	X
ejpam-5509	196	6	µ+	µ+	X
ejpam-5509	196	7	ψ))−	ψ))−	VERB
ejpam-5509	196	8	δξs0	δξs0	PROPN
ejpam-5509	196	9	>	>	X
ejpam-5509	196	10	0	0	NUM
ejpam-5509	196	11	,	,	PUNCT
ejpam-5509	196	12	−(δ	−(δ	PROPN
ejpam-5509	196	13	+	+	CCONJ
ejpam-5509	196	14	σ	σ	PROPN
ejpam-5509	196	15	+	+	CCONJ
ejpam-5509	196	16	µ)(π(1−	µ)(π(1−	NOUN
ejpam-5509	196	17	ω)τ	ω)τ	NUM
ejpam-5509	196	18	−	−	PROPN
ejpam-5509	196	19	(	(	PUNCT
ejpam-5509	196	20	ϑ+	ϑ+	X
ejpam-5509	196	21	µ+	µ+	ADJ
ejpam-5509	196	22	ψ	ψ	NOUN
ejpam-5509	196	23	)	)	PUNCT
ejpam-5509	196	24	)	)	PUNCT
ejpam-5509	196	25	>	>	X
ejpam-5509	196	26	(	(	PUNCT
ejpam-5509	196	27	ϑ+	ϑ+	X
ejpam-5509	196	28	µ+	µ+	X
ejpam-5509	196	29	ψ	ψ	X
ejpam-5509	196	30	−π(1−	−π(1−	ADJ
ejpam-5509	196	31	ω)τ)ξκs0	ω)τ)ξκs0	NOUN
ejpam-5509	196	32	+	+	CCONJ
ejpam-5509	196	33	δξs0	δξs0	PROPN
ejpam-5509	196	34	,	,	PUNCT
ejpam-5509	196	35	1	1	NUM
ejpam-5509	196	36	>	>	X
ejpam-5509	196	37	ξs0	ξs0	PROPN
ejpam-5509	196	38	(	(	PUNCT
ejpam-5509	196	39	κ	κ	NOUN
ejpam-5509	196	40	δ+σ+µ	δ+σ+µ	NOUN
ejpam-5509	196	41	+	+	CCONJ
ejpam-5509	196	42	δ	δ	PROPN
ejpam-5509	196	43	(	(	PUNCT
ejpam-5509	196	44	δ+σ+µ)(ϑ+µ+ψ−π(1−ω)τ	δ+σ+µ)(ϑ+µ+ψ−π(1−ω)τ	NOUN
ejpam-5509	196	45	)	)	PUNCT
ejpam-5509	196	46	)	)	PUNCT
ejpam-5509	197	1	=	=	SYM
ejpam-5509	197	2	r0	r0	NOUN
ejpam-5509	197	3	.	.	PUNCT
ejpam-5509	198	1	(	(	PUNCT
ejpam-5509	198	2	15	15	X
ejpam-5509	198	3	)	)	PUNCT
ejpam-5509	198	4	observing	observe	VERB
ejpam-5509	198	5	the	the	DET
ejpam-5509	198	6	condition	condition	NOUN
ejpam-5509	198	7	r0	r0	NOUN
ejpam-5509	198	8	<	<	X
ejpam-5509	198	9	1	1	NUM
ejpam-5509	198	10	,	,	PUNCT
ejpam-5509	198	11	we	we	PRON
ejpam-5509	198	12	can	can	AUX
ejpam-5509	198	13	determine	determine	VERB
ejpam-5509	198	14	that	that	SCONJ
ejpam-5509	198	15	the	the	DET
ejpam-5509	198	16	trace	trace	NOUN
ejpam-5509	198	17	of	of	ADP
ejpam-5509	198	18	j1	j1	PROPN
ejpam-5509	198	19	is	be	AUX
ejpam-5509	198	20	negative	negative	ADJ
ejpam-5509	198	21	(	(	PUNCT
ejpam-5509	198	22	j1	j1	X
ejpam-5509	198	23	<	<	X
ejpam-5509	198	24	0	0	NUM
ejpam-5509	198	25	)	)	PUNCT
ejpam-5509	198	26	,	,	PUNCT
ejpam-5509	198	27	and	and	CCONJ
ejpam-5509	198	28	the	the	DET
ejpam-5509	198	29	determinant	determinant	NOUN
ejpam-5509	198	30	of	of	ADP
ejpam-5509	198	31	j1	j1	PROPN
ejpam-5509	198	32	is	be	AUX
ejpam-5509	198	33	positive	positive	ADJ
ejpam-5509	198	34	(	(	PUNCT
ejpam-5509	198	35	j1	j1	PROPN
ejpam-5509	198	36	>	>	X
ejpam-5509	198	37	0	0	NUM
ejpam-5509	198	38	)	)	PUNCT
ejpam-5509	198	39	.	.	PUNCT
ejpam-5509	199	1	these	these	DET
ejpam-5509	199	2	indications	indication	NOUN
ejpam-5509	199	3	imply	imply	VERB
ejpam-5509	199	4	that	that	SCONJ
ejpam-5509	199	5	the	the	DET
ejpam-5509	199	6	remaining	remain	VERB
ejpam-5509	199	7	two	two	NUM
ejpam-5509	199	8	eigenvalues	eigenvalue	NOUN
ejpam-5509	199	9	have	have	VERB
ejpam-5509	199	10	negative	negative	ADJ
ejpam-5509	199	11	real	real	ADJ
ejpam-5509	199	12	parts	part	NOUN
ejpam-5509	199	13	.	.	PUNCT
ejpam-5509	200	1	consequently	consequently	ADV
ejpam-5509	200	2	,	,	PUNCT
ejpam-5509	200	3	when	when	SCONJ
ejpam-5509	200	4	r0	r0	NOUN
ejpam-5509	200	5	<	<	X
ejpam-5509	200	6	1	1	NUM
ejpam-5509	200	7	,	,	PUNCT
ejpam-5509	200	8	the	the	DET
ejpam-5509	200	9	dfe	dfe	PROPN
ejpam-5509	200	10	point	point	NOUN
ejpam-5509	200	11	exhibits	exhibit	VERB
ejpam-5509	200	12	local	local	ADJ
ejpam-5509	200	13	asymptotic	asymptotic	ADJ
ejpam-5509	200	14	stability	stability	NOUN
ejpam-5509	200	15	,	,	PUNCT
ejpam-5509	200	16	while	while	SCONJ
ejpam-5509	200	17	for	for	ADP
ejpam-5509	200	18	r0	r0	NOUN
ejpam-5509	200	19	>	>	X
ejpam-5509	200	20	1	1	NUM
ejpam-5509	200	21	,	,	PUNCT
ejpam-5509	200	22	the	the	DET
ejpam-5509	200	23	dfe	dfe	PROPN
ejpam-5509	200	24	point	point	NOUN
ejpam-5509	200	25	becomes	become	VERB
ejpam-5509	200	26	unstable	unstable	ADJ
ejpam-5509	200	27	.	.	PUNCT
ejpam-5509	201	1	3.2	3.2	NUM
ejpam-5509	201	2	.	.	PUNCT
ejpam-5509	202	1	existence	existence	NOUN
ejpam-5509	202	2	theory	theory	NOUN
ejpam-5509	202	3	our	our	PRON
ejpam-5509	202	4	focus	focus	NOUN
ejpam-5509	202	5	is	be	AUX
ejpam-5509	202	6	on	on	ADP
ejpam-5509	202	7	analyzing	analyze	VERB
ejpam-5509	202	8	the	the	DET
ejpam-5509	202	9	solutions	solution	NOUN
ejpam-5509	202	10	of	of	ADP
ejpam-5509	202	11	the	the	DET
ejpam-5509	202	12	proposed	propose	VERB
ejpam-5509	202	13	fractional	fractional	ADJ
ejpam-5509	202	14	hbv	hbv	NOUN
ejpam-5509	202	15	system	system	NOUN
ejpam-5509	202	16	.	.	PUNCT
ejpam-5509	203	1	the	the	DET
ejpam-5509	203	2	existence	existence	NOUN
ejpam-5509	203	3	of	of	ADP
ejpam-5509	203	4	the	the	DET
ejpam-5509	203	5	solution	solution	NOUN
ejpam-5509	203	6	(	(	PUNCT
ejpam-5509	203	7	10	10	NUM
ejpam-5509	203	8	)	)	PUNCT
ejpam-5509	203	9	is	be	AUX
ejpam-5509	203	10	investigated	investigate	VERB
ejpam-5509	203	11	using	use	VERB
ejpam-5509	203	12	fixed	fix	VERB
ejpam-5509	203	13	point	point	NOUN
ejpam-5509	203	14	theory	theory	NOUN
ejpam-5509	203	15	.	.	PUNCT
ejpam-5509	204	1	the	the	DET
ejpam-5509	204	2	procedure	procedure	NOUN
ejpam-5509	204	3	is	be	AUX
ejpam-5509	204	4	as	as	ADP
ejpam-5509	204	5	follows:	follows:	ADJ
ejpam-5509	204	6	s(t)−	s(t)−	PROPN
ejpam-5509	204	7	s(0	s(0	PROPN
ejpam-5509	204	8	)	)	PUNCT
ejpam-5509	204	9	=	=	PUNCT
ejpam-5509	204	10	cf	cf	NOUN
ejpam-5509	204	11	0	0	NUM
ejpam-5509	204	12	iςt	iςt	PROPN
ejpam-5509	204	13	{	{	PUNCT
ejpam-5509	204	14	π(1−	π(1−	PROPN
ejpam-5509	204	15	ω)(1−	ω)(1−	NUM
ejpam-5509	204	16	τc	τc	PRON
ejpam-5509	204	17	)	)	PUNCT
ejpam-5509	205	1	+	+	CCONJ
ejpam-5509	206	1	φ2v1	φ2v1	NUM
ejpam-5509	206	2	−	−	PROPN
ejpam-5509	206	3	(	(	PUNCT
ejpam-5509	206	4	λ+	λ+	X
ejpam-5509	206	5	µ+	µ+	X
ejpam-5509	206	6	φ1)s	φ1)s	NOUN
ejpam-5509	206	7	}	}	PUNCT
ejpam-5509	206	8	,	,	PUNCT
ejpam-5509	206	9	v1(t)−	v1(t)−	PROPN
ejpam-5509	206	10	v1(0	v1(0	NOUN
ejpam-5509	206	11	)	)	PUNCT
ejpam-5509	206	12	=	=	PUNCT
ejpam-5509	207	1	cf	cf	NOUN
ejpam-5509	207	2	0	0	NUM
ejpam-5509	207	3	iςt	iςt	PROPN
ejpam-5509	207	4	{	{	PUNCT
ejpam-5509	207	5	φ1s	φ1s	PROPN
ejpam-5509	207	6	+	+	PROPN
ejpam-5509	207	7	πω	πω	ADP
ejpam-5509	207	8	−	−	PROPN
ejpam-5509	207	9	(	(	PUNCT
ejpam-5509	207	10	α+	α+	X
ejpam-5509	207	11	µ+	µ+	X
ejpam-5509	207	12	φ2)v1	φ2)v1	PROPN
ejpam-5509	207	13	}	}	PUNCT
ejpam-5509	207	14	,	,	PUNCT
ejpam-5509	207	15	v2(t)−	v2(t)−	PUNCT
ejpam-5509	207	16	v2(0	v2(0	NOUN
ejpam-5509	207	17	)	)	PUNCT
ejpam-5509	207	18	=	=	PUNCT
ejpam-5509	208	1	cf	cf	NOUN
ejpam-5509	208	2	0	0	NUM
ejpam-5509	208	3	iςt	iςt	PROPN
ejpam-5509	208	4	{	{	PUNCT
ejpam-5509	208	5	αv1	αv1	PROPN
ejpam-5509	208	6	−	−	PROPN
ejpam-5509	208	7	(	(	PUNCT
ejpam-5509	208	8	ϵ+	ϵ+	PUNCT
ejpam-5509	208	9	µ)v2	µ)v2	PROPN
ejpam-5509	208	10	}	}	PUNCT
ejpam-5509	208	11	,	,	PUNCT
ejpam-5509	208	12	a(t)−a(0	a(t)−a(0	PUNCT
ejpam-5509	208	13	)	)	PUNCT
ejpam-5509	208	14	=	=	SYM
ejpam-5509	209	1	cf	cf	NOUN
ejpam-5509	209	2	0	0	NUM
ejpam-5509	209	3	iςt	iςt	PROPN
ejpam-5509	209	4	{	{	PUNCT
ejpam-5509	209	5	λs	λs	X
ejpam-5509	209	6	−	−	PROPN
ejpam-5509	209	7	(	(	PUNCT
ejpam-5509	209	8	δ	δ	PROPN
ejpam-5509	209	9	+	+	CCONJ
ejpam-5509	209	10	σ	σ	PROPN
ejpam-5509	209	11	+	+	CCONJ
ejpam-5509	209	12	µ)a	µ)a	NOUN
ejpam-5509	209	13	}	}	PUNCT
ejpam-5509	209	14	,	,	PUNCT
ejpam-5509	209	15	c(t)−	c(t)−	PROPN
ejpam-5509	209	16	c(0	c(0	PROPN
ejpam-5509	209	17	)	)	PUNCT
ejpam-5509	209	18	=	=	PUNCT
ejpam-5509	210	1	cf	cf	NOUN
ejpam-5509	210	2	0	0	NUM
ejpam-5509	210	3	iςt	iςt	PROPN
ejpam-5509	210	4	{	{	PUNCT
ejpam-5509	210	5	δa+π(1−	δa+π(1−	PUNCT
ejpam-5509	210	6	ω)τc	ω)τc	PROPN
ejpam-5509	210	7	−	−	PROPN
ejpam-5509	210	8	(	(	PUNCT
ejpam-5509	210	9	ϑ+	ϑ+	X
ejpam-5509	210	10	µ+	µ+	VERB
ejpam-5509	210	11	ψ)c	ψ)c	NOUN
ejpam-5509	210	12	}	}	PUNCT
ejpam-5509	210	13	,	,	PUNCT
ejpam-5509	210	14	r(t)−r(0	r(t)−r(0	ADJ
ejpam-5509	210	15	)	)	PUNCT
ejpam-5509	210	16	=	=	PUNCT
ejpam-5509	211	1	cf	cf	NOUN
ejpam-5509	211	2	0	0	NUM
ejpam-5509	211	3	iςt	iςt	PROPN
ejpam-5509	211	4	{	{	PUNCT
ejpam-5509	211	5	σa+	σa+	NOUN
ejpam-5509	211	6	ϑc	ϑc	NOUN
ejpam-5509	211	7	+	+	CCONJ
ejpam-5509	211	8	ϵv2	ϵv2	NOUN
ejpam-5509	211	9	−	−	NOUN
ejpam-5509	211	10	µr	µr	ADP
ejpam-5509	211	11	}	}	PUNCT
ejpam-5509	211	12	.	.	PUNCT
ejpam-5509	212	1	(	(	PUNCT
ejpam-5509	212	2	16	16	NUM
ejpam-5509	212	3	)	)	PUNCT
ejpam-5509	212	4	after	after	ADP
ejpam-5509	212	5	that	that	PRON
ejpam-5509	212	6	,	,	PUNCT
ejpam-5509	212	7	we	we	PRON
ejpam-5509	212	8	have	have	VERB
ejpam-5509	212	9	s(t)−	s(t)−	PROPN
ejpam-5509	212	10	s(0	s(0	PROPN
ejpam-5509	212	11	)	)	PUNCT
ejpam-5509	212	12	=	=	PUNCT
ejpam-5509	213	1	2(1−	2(1−	NUM
ejpam-5509	213	2	ς	ς	NOUN
ejpam-5509	213	3	)	)	PUNCT
ejpam-5509	213	4	(	(	PUNCT
ejpam-5509	213	5	2−	2−	NUM
ejpam-5509	213	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	213	7	)	)	PUNCT
ejpam-5509	213	8	{	{	PUNCT
ejpam-5509	214	1	π(1−	π(1−	PROPN
ejpam-5509	214	2	ω)(1−	ω)(1−	NUM
ejpam-5509	214	3	τc	τc	PRON
ejpam-5509	214	4	)	)	PUNCT
ejpam-5509	215	1	+	+	CCONJ
ejpam-5509	216	1	φ2v1	φ2v1	NUM
ejpam-5509	216	2	−	−	PROPN
ejpam-5509	216	3	(	(	PUNCT
ejpam-5509	216	4	λ+	λ+	X
ejpam-5509	216	5	µ+	µ+	X
ejpam-5509	216	6	φ1)s	φ1)s	ADJ
ejpam-5509	216	7	}	}	PUNCT
ejpam-5509	216	8	i.	i.	PROPN
ejpam-5509	216	9	ahmad	ahmad	PROPN
ejpam-5509	216	10	et	et	PROPN
ejpam-5509	216	11	al	al	PROPN
ejpam-5509	216	12	.	.	PUNCT
ejpam-5509	216	13	/	/	SYM
ejpam-5509	216	14	eur	eur	PROPN
ejpam-5509	216	15	.	.	PUNCT
ejpam-5509	217	1	j.	j.	PROPN
ejpam-5509	217	2	pure	pure	PROPN
ejpam-5509	217	3	appl	appl	PROPN
ejpam-5509	217	4	.	.	PROPN
ejpam-5509	217	5	math	math	PROPN
ejpam-5509	217	6	,	,	PUNCT
ejpam-5509	217	7	18	18	NUM
ejpam-5509	217	8	(	(	PUNCT
ejpam-5509	217	9	1	1	NUM
ejpam-5509	217	10	)	)	PUNCT
ejpam-5509	217	11	(	(	PUNCT
ejpam-5509	217	12	2025	2025	NUM
ejpam-5509	217	13	)	)	PUNCT
ejpam-5509	217	14	,	,	PUNCT
ejpam-5509	217	15	5509	5509	NUM
ejpam-5509	217	16	10	10	NUM
ejpam-5509	217	17	of	of	ADP
ejpam-5509	217	18	27	27	NUM
ejpam-5509	217	19	+	+	NUM
ejpam-5509	217	20	2ς	2ς	NUM
ejpam-5509	217	21	(	(	PUNCT
ejpam-5509	217	22	2−	2−	NUM
ejpam-5509	217	23	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	217	24	)	)	PUNCT
ejpam-5509	218	1	∫	∫	PROPN
ejpam-5509	218	2	t	t	PROPN
ejpam-5509	218	3	0	0	NUM
ejpam-5509	218	4	{	{	PUNCT
ejpam-5509	218	5	π(1−	π(1−	PROPN
ejpam-5509	218	6	ω)(1−	ω)(1−	NUM
ejpam-5509	218	7	τc	τc	PRON
ejpam-5509	218	8	)	)	PUNCT
ejpam-5509	219	1	+	+	CCONJ
ejpam-5509	220	1	φ2v1	φ2v1	NUM
ejpam-5509	220	2	−	−	PROPN
ejpam-5509	220	3	(	(	PUNCT
ejpam-5509	220	4	λ+	λ+	X
ejpam-5509	220	5	µ+	µ+	X
ejpam-5509	220	6	φ1)s	φ1)s	NOUN
ejpam-5509	220	7	}	}	PUNCT
ejpam-5509	220	8	dy	dy	PROPN
ejpam-5509	220	9	,	,	PUNCT
ejpam-5509	220	10	v1(t)−	v1(t)−	PROPN
ejpam-5509	220	11	v1(0	v1(0	NOUN
ejpam-5509	220	12	)	)	PUNCT
ejpam-5509	220	13	=	=	PUNCT
ejpam-5509	221	1	2(1−	2(1−	NUM
ejpam-5509	221	2	ς	ς	NOUN
ejpam-5509	221	3	)	)	PUNCT
ejpam-5509	221	4	(	(	PUNCT
ejpam-5509	221	5	2−	2−	NUM
ejpam-5509	221	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	221	7	)	)	PUNCT
ejpam-5509	221	8	{	{	PUNCT
ejpam-5509	221	9	φ1s	φ1s	PROPN
ejpam-5509	221	10	+	+	PROPN
ejpam-5509	221	11	πω	πω	ADP
ejpam-5509	221	12	−	−	PROPN
ejpam-5509	221	13	(	(	PUNCT
ejpam-5509	221	14	α+	α+	X
ejpam-5509	221	15	µ+	µ+	X
ejpam-5509	221	16	φ2)v1	φ2)v1	PROPN
ejpam-5509	221	17	}	}	PUNCT
ejpam-5509	221	18	+	+	NUM
ejpam-5509	221	19	2ς	2ς	NUM
ejpam-5509	221	20	(	(	PUNCT
ejpam-5509	221	21	2−	2−	NUM
ejpam-5509	221	22	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	221	23	)	)	PUNCT
ejpam-5509	222	1	∫	∫	PROPN
ejpam-5509	222	2	t	t	PROPN
ejpam-5509	222	3	0	0	NUM
ejpam-5509	222	4	{	{	PUNCT
ejpam-5509	222	5	φ1s	φ1s	PROPN
ejpam-5509	222	6	+	+	PROPN
ejpam-5509	222	7	πω	πω	ADP
ejpam-5509	222	8	−	−	PROPN
ejpam-5509	222	9	(	(	PUNCT
ejpam-5509	222	10	α+	α+	X
ejpam-5509	222	11	µ+	µ+	X
ejpam-5509	222	12	φ2)v1	φ2)v1	PROPN
ejpam-5509	222	13	}	}	PUNCT
ejpam-5509	222	14	dy	dy	PROPN
ejpam-5509	222	15	,	,	PUNCT
ejpam-5509	222	16	v2(t)−	v2(t)−	PROPN
ejpam-5509	222	17	v2(0	v2(0	NOUN
ejpam-5509	222	18	)	)	PUNCT
ejpam-5509	222	19	=	=	PUNCT
ejpam-5509	223	1	2(1−	2(1−	NUM
ejpam-5509	223	2	ς	ς	NOUN
ejpam-5509	223	3	)	)	PUNCT
ejpam-5509	223	4	(	(	PUNCT
ejpam-5509	223	5	2−	2−	NUM
ejpam-5509	223	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	223	7	)	)	PUNCT
ejpam-5509	223	8	{	{	PUNCT
ejpam-5509	223	9	αv1	αv1	NOUN
ejpam-5509	223	10	−	−	PROPN
ejpam-5509	223	11	(	(	PUNCT
ejpam-5509	223	12	ϵ+	ϵ+	PUNCT
ejpam-5509	223	13	µ)v2	µ)v2	PROPN
ejpam-5509	223	14	}	}	PUNCT
ejpam-5509	223	15	+	+	NUM
ejpam-5509	223	16	2ς	2ς	NUM
ejpam-5509	223	17	(	(	PUNCT
ejpam-5509	223	18	2−	2−	NUM
ejpam-5509	223	19	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	223	20	)	)	PUNCT
ejpam-5509	224	1	∫	∫	PROPN
ejpam-5509	224	2	t	t	PROPN
ejpam-5509	224	3	0	0	NUM
ejpam-5509	224	4	{	{	PUNCT
ejpam-5509	224	5	αv1	αv1	PROPN
ejpam-5509	224	6	−	−	PROPN
ejpam-5509	224	7	(	(	PUNCT
ejpam-5509	224	8	ϵ+	ϵ+	PUNCT
ejpam-5509	224	9	µ)v2	µ)v2	PROPN
ejpam-5509	224	10	}	}	PUNCT
ejpam-5509	224	11	dy	dy	NOUN
ejpam-5509	224	12	,	,	PUNCT
ejpam-5509	224	13	a(t)−a(0	a(t)−a(0	PUNCT
ejpam-5509	224	14	)	)	PUNCT
ejpam-5509	224	15	=	=	SYM
ejpam-5509	225	1	2(1−	2(1−	NUM
ejpam-5509	225	2	ς	ς	NOUN
ejpam-5509	225	3	)	)	PUNCT
ejpam-5509	225	4	(	(	PUNCT
ejpam-5509	225	5	2−	2−	NUM
ejpam-5509	225	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	225	7	)	)	PUNCT
ejpam-5509	225	8	{	{	PUNCT
ejpam-5509	225	9	λs	λs	ADP
ejpam-5509	225	10	−	−	PROPN
ejpam-5509	225	11	(	(	PUNCT
ejpam-5509	225	12	δ	δ	PROPN
ejpam-5509	225	13	+	+	CCONJ
ejpam-5509	225	14	σ	σ	PROPN
ejpam-5509	225	15	+	+	CCONJ
ejpam-5509	225	16	µ)a	µ)a	NOUN
ejpam-5509	225	17	}	}	PUNCT
ejpam-5509	226	1	+	+	NUM
ejpam-5509	226	2	2ς	2ς	NUM
ejpam-5509	226	3	(	(	PUNCT
ejpam-5509	226	4	2−	2−	NUM
ejpam-5509	226	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	226	6	)	)	PUNCT
ejpam-5509	226	7	∫	∫	PROPN
ejpam-5509	226	8	t	t	PROPN
ejpam-5509	226	9	0	0	NUM
ejpam-5509	226	10	{	{	PUNCT
ejpam-5509	226	11	λs	λs	X
ejpam-5509	226	12	−	−	PROPN
ejpam-5509	226	13	(	(	PUNCT
ejpam-5509	226	14	δ	δ	PROPN
ejpam-5509	226	15	+	+	CCONJ
ejpam-5509	226	16	σ	σ	PROPN
ejpam-5509	226	17	+	+	CCONJ
ejpam-5509	226	18	µ)a	µ)a	NOUN
ejpam-5509	226	19	}	}	PUNCT
ejpam-5509	226	20	dy	dy	NOUN
ejpam-5509	226	21	,	,	PUNCT
ejpam-5509	226	22	c(t)−	c(t)−	PROPN
ejpam-5509	226	23	c(0	c(0	PROPN
ejpam-5509	226	24	)	)	PUNCT
ejpam-5509	226	25	=	=	PUNCT
ejpam-5509	227	1	2(1−	2(1−	NUM
ejpam-5509	227	2	ς	ς	NOUN
ejpam-5509	227	3	)	)	PUNCT
ejpam-5509	227	4	(	(	PUNCT
ejpam-5509	227	5	2−	2−	NUM
ejpam-5509	227	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	227	7	)	)	PUNCT
ejpam-5509	227	8	{	{	PUNCT
ejpam-5509	228	1	δa+π(1−	δa+π(1−	PUNCT
ejpam-5509	228	2	ω)τc	ω)τc	PROPN
ejpam-5509	228	3	−	−	PROPN
ejpam-5509	228	4	(	(	PUNCT
ejpam-5509	228	5	ϑ+	ϑ+	X
ejpam-5509	228	6	µ+	µ+	VERB
ejpam-5509	228	7	ψ)c	ψ)c	ADJ
ejpam-5509	228	8	}	}	PUNCT
ejpam-5509	229	1	+	+	CCONJ
ejpam-5509	229	2	2ς	2ς	NUM
ejpam-5509	229	3	(	(	PUNCT
ejpam-5509	229	4	2−	2−	NUM
ejpam-5509	229	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	229	6	)	)	PUNCT
ejpam-5509	229	7	∫	∫	PROPN
ejpam-5509	230	1	t	t	PROPN
ejpam-5509	230	2	0	0	NUM
ejpam-5509	230	3	{	{	PUNCT
ejpam-5509	230	4	δa+π(1−	δa+π(1−	PROPN
ejpam-5509	230	5	ω)τc	ω)τc	PROPN
ejpam-5509	230	6	−	−	PROPN
ejpam-5509	230	7	(	(	PUNCT
ejpam-5509	230	8	ϑ+	ϑ+	X
ejpam-5509	230	9	µ+	µ+	VERB
ejpam-5509	230	10	ψ)c	ψ)c	NOUN
ejpam-5509	230	11	}	}	PUNCT
ejpam-5509	230	12	dy	dy	NOUN
ejpam-5509	230	13	,	,	PUNCT
ejpam-5509	230	14	r(t)−r(0	r(t)−r(0	NUM
ejpam-5509	230	15	)	)	PUNCT
ejpam-5509	230	16	=	=	PUNCT
ejpam-5509	231	1	2(1−	2(1−	NUM
ejpam-5509	231	2	ς	ς	NOUN
ejpam-5509	231	3	)	)	PUNCT
ejpam-5509	231	4	(	(	PUNCT
ejpam-5509	231	5	2−	2−	NUM
ejpam-5509	231	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	231	7	)	)	PUNCT
ejpam-5509	231	8	{	{	PUNCT
ejpam-5509	231	9	σa+	σa+	NOUN
ejpam-5509	231	10	ϑc	ϑc	NOUN
ejpam-5509	231	11	+	+	CCONJ
ejpam-5509	231	12	ϵv2	ϵv2	NOUN
ejpam-5509	231	13	−	−	NOUN
ejpam-5509	231	14	µr	µr	ADP
ejpam-5509	231	15	}	}	PUNCT
ejpam-5509	231	16	+	+	NUM
ejpam-5509	231	17	2ς	2ς	NUM
ejpam-5509	231	18	(	(	PUNCT
ejpam-5509	231	19	2−	2−	NUM
ejpam-5509	231	20	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	231	21	)	)	PUNCT
ejpam-5509	231	22	∫	∫	PROPN
ejpam-5509	232	1	t	t	PROPN
ejpam-5509	232	2	0	0	NUM
ejpam-5509	232	3	{	{	PUNCT
ejpam-5509	232	4	σa+	σa+	NOUN
ejpam-5509	232	5	ϑc	ϑc	NOUN
ejpam-5509	232	6	+	+	CCONJ
ejpam-5509	232	7	ϵv2	ϵv2	NOUN
ejpam-5509	232	8	−	−	NOUN
ejpam-5509	232	9	µr	µr	ADP
ejpam-5509	232	10	}	}	PUNCT
ejpam-5509	232	11	.	.	PUNCT
ejpam-5509	233	1	(	(	PUNCT
ejpam-5509	233	2	17	17	NUM
ejpam-5509	233	3	)	)	PUNCT
ejpam-5509	233	4	moreover	moreover	ADV
ejpam-5509	233	5	,	,	PUNCT
ejpam-5509	233	6			X
ejpam-5509	233	7	l1(t	l1(t	PROPN
ejpam-5509	233	8	,	,	PUNCT
ejpam-5509	233	9	s	s	PART
ejpam-5509	233	10	)	)	PUNCT
ejpam-5509	233	11	=	=	PUNCT
ejpam-5509	234	1	π(1−	π(1−	PROPN
ejpam-5509	234	2	ω)(1−	ω)(1−	NUM
ejpam-5509	234	3	τc	τc	PRON
ejpam-5509	234	4	)	)	PUNCT
ejpam-5509	234	5	+	+	CCONJ
ejpam-5509	235	1	φ2v1	φ2v1	NUM
ejpam-5509	235	2	−	−	PROPN
ejpam-5509	235	3	(	(	PUNCT
ejpam-5509	235	4	λ+	λ+	X
ejpam-5509	235	5	µ+	µ+	X
ejpam-5509	235	6	φ1)s	φ1)s	NOUN
ejpam-5509	235	7	,	,	PUNCT
ejpam-5509	235	8	l2(t	l2(t	PROPN
ejpam-5509	235	9	,	,	PUNCT
ejpam-5509	235	10	v1	v1	NOUN
ejpam-5509	235	11	)	)	PUNCT
ejpam-5509	235	12	=	=	SYM
ejpam-5509	235	13	φ1s	φ1s	ADP
ejpam-5509	235	14	+	+	PROPN
ejpam-5509	235	15	πω	πω	ADP
ejpam-5509	235	16	−	−	PROPN
ejpam-5509	235	17	(	(	PUNCT
ejpam-5509	235	18	α+	α+	X
ejpam-5509	235	19	µ+	µ+	PRON
ejpam-5509	235	20	φ2)v1	φ2)v1	PROPN
ejpam-5509	235	21	,	,	PUNCT
ejpam-5509	235	22	l3(t	l3(t	NUM
ejpam-5509	235	23	,	,	PUNCT
ejpam-5509	235	24	v2	v2	NOUN
ejpam-5509	235	25	)	)	PUNCT
ejpam-5509	235	26	=	=	SYM
ejpam-5509	236	1	αv1	αv1	NUM
ejpam-5509	236	2	−	−	NOUN
ejpam-5509	237	1	(	(	PUNCT
ejpam-5509	237	2	ϵ+	ϵ+	X
ejpam-5509	237	3	µ)v2	µ)v2	PROPN
ejpam-5509	237	4	,	,	PUNCT
ejpam-5509	237	5	l4(t	l4(t	PROPN
ejpam-5509	237	6	,	,	PUNCT
ejpam-5509	237	7	a	a	PRON
ejpam-5509	237	8	)	)	PUNCT
ejpam-5509	238	1	=	=	SYM
ejpam-5509	238	2	βc	βc	PROPN
ejpam-5509	239	1	+	+	NOUN
ejpam-5509	239	2	γi	γi	INTJ
ejpam-5509	239	3	−	−	PROPN
ejpam-5509	239	4	(	(	PUNCT
ejpam-5509	239	5	d+	d+	NOUN
ejpam-5509	239	6	τ)r	τ)r	NOUN
ejpam-5509	239	7	,	,	PUNCT
ejpam-5509	239	8	l5(t	l5(t	NOUN
ejpam-5509	239	9	,	,	PUNCT
ejpam-5509	239	10	c	c	NOUN
ejpam-5509	239	11	)	)	PUNCT
ejpam-5509	239	12	=	=	PUNCT
ejpam-5509	240	1	δa+π(1−	δa+π(1−	PUNCT
ejpam-5509	240	2	ω)τc	ω)τc	PROPN
ejpam-5509	240	3	−	−	PROPN
ejpam-5509	240	4	(	(	PUNCT
ejpam-5509	240	5	ϑ+	ϑ+	X
ejpam-5509	240	6	µ+	µ+	VERB
ejpam-5509	240	7	ψ)c	ψ)c	NOUN
ejpam-5509	240	8	,	,	PUNCT
ejpam-5509	240	9	l6(t	l6(t	PROPN
ejpam-5509	240	10	,	,	PUNCT
ejpam-5509	240	11	r	r	NOUN
ejpam-5509	240	12	)	)	PUNCT
ejpam-5509	240	13	=	=	NOUN
ejpam-5509	240	14	σa+	σa+	NOUN
ejpam-5509	240	15	ϑc	ϑc	NOUN
ejpam-5509	240	16	+	+	CCONJ
ejpam-5509	240	17	ϵv2	ϵv2	NOUN
ejpam-5509	240	18	−	−	NOUN
ejpam-5509	240	19	µr	µr	ADP
ejpam-5509	240	20	.	.	PUNCT
ejpam-5509	241	1	(	(	PUNCT
ejpam-5509	241	2	18	18	NUM
ejpam-5509	241	3	)	)	PUNCT
ejpam-5509	241	4	theorem	theorem	NOUN
ejpam-5509	241	5	2	2	NUM
ejpam-5509	241	6	.	.	PUNCT
ejpam-5509	242	1	the	the	DET
ejpam-5509	242	2	kernels	kernel	NOUN
ejpam-5509	242	3	l1,l2,l3,l4,l5	l1,l2,l3,l4,l5	PROPN
ejpam-5509	242	4	,	,	PUNCT
ejpam-5509	242	5	and	and	CCONJ
ejpam-5509	242	6	l6	l6	PROPN
ejpam-5509	242	7	satisfy	satisfy	VERB
ejpam-5509	242	8	the	the	DET
ejpam-5509	242	9	conditions	condition	NOUN
ejpam-5509	242	10	of	of	ADP
ejpam-5509	242	11	lipschitz	lipschitz	NOUN
ejpam-5509	242	12	and	and	CCONJ
ejpam-5509	242	13	contraction	contraction	NOUN
ejpam-5509	242	14	if	if	SCONJ
ejpam-5509	242	15	the	the	DET
ejpam-5509	242	16	following	follow	VERB
ejpam-5509	242	17	criteria	criterion	NOUN
ejpam-5509	242	18	are	be	AUX
ejpam-5509	242	19	met	meet	VERB
ejpam-5509	242	20	.	.	PUNCT
ejpam-5509	242	21	0	0	NUM
ejpam-5509	243	1	≤	≤	NUM
ejpam-5509	243	2	(	(	PUNCT
ejpam-5509	243	3	ξ(κm	ξ(κm	ADV
ejpam-5509	243	4	+	+	NOUN
ejpam-5509	243	5	m	m	NOUN
ejpam-5509	243	6	)	)	PUNCT
ejpam-5509	244	1	+	+	CCONJ
ejpam-5509	244	2	µ+	µ+	DET
ejpam-5509	244	3	φ1	φ1	PROPN
ejpam-5509	244	4	)	)	PUNCT
ejpam-5509	244	5	<	<	X
ejpam-5509	245	1	1	1	X
ejpam-5509	245	2	.	.	PUNCT
ejpam-5509	245	3	proof	proof	NOUN
ejpam-5509	245	4	.	.	PUNCT
ejpam-5509	246	1	to	to	PART
ejpam-5509	246	2	achieve	achieve	VERB
ejpam-5509	246	3	the	the	DET
ejpam-5509	246	4	specified	specified	ADJ
ejpam-5509	246	5	outcomes	outcome	NOUN
ejpam-5509	246	6	,	,	PUNCT
ejpam-5509	246	7	we	we	PRON
ejpam-5509	246	8	consider	consider	VERB
ejpam-5509	246	9	the	the	DET
ejpam-5509	246	10	variables	variable	NOUN
ejpam-5509	246	11	denoted	denote	VERB
ejpam-5509	246	12	as	as	ADP
ejpam-5509	246	13	s	s	NOUN
ejpam-5509	246	14	and	and	CCONJ
ejpam-5509	246	15	s1	s1	NOUN
ejpam-5509	246	16	,	,	PUNCT
ejpam-5509	246	17	initiating	initiate	VERB
ejpam-5509	246	18	the	the	DET
ejpam-5509	246	19	process	process	NOUN
ejpam-5509	246	20	from	from	ADP
ejpam-5509	246	21	the	the	DET
ejpam-5509	246	22	initial	initial	ADJ
ejpam-5509	246	23	state	state	NOUN
ejpam-5509	246	24	l1	l1	PROPN
ejpam-5509	246	25	is	be	AUX
ejpam-5509	246	26	as	as	SCONJ
ejpam-5509	246	27	follows	follow	VERB
ejpam-5509	246	28	:	:	PUNCT
ejpam-5509	246	29	l1(t	l1(t	PROPN
ejpam-5509	246	30	,	,	PUNCT
ejpam-5509	246	31	s)−	s)−	PROPN
ejpam-5509	246	32	l1(t	l1(t	PROPN
ejpam-5509	246	33	,	,	PUNCT
ejpam-5509	246	34	s1	s1	NOUN
ejpam-5509	246	35	)	)	PUNCT
ejpam-5509	246	36	=	=	SYM
ejpam-5509	246	37	−λ{s(t)−	−λ{s(t)−	PROPN
ejpam-5509	246	38	s(t1	s(t1	VERB
ejpam-5509	246	39	)	)	PUNCT
ejpam-5509	246	40	}	}	PUNCT
ejpam-5509	247	1	−	−	PROPN
ejpam-5509	247	2	µ{s(t)−	µ{s(t)−	PROPN
ejpam-5509	247	3	s(t1	s(t1	VERB
ejpam-5509	247	4	)	)	PUNCT
ejpam-5509	247	5	}	}	PUNCT
ejpam-5509	248	1	i.	i.	PROPN
ejpam-5509	248	2	ahmad	ahmad	PROPN
ejpam-5509	248	3	et	et	PROPN
ejpam-5509	248	4	al	al	PROPN
ejpam-5509	248	5	.	.	PUNCT
ejpam-5509	248	6	/	/	SYM
ejpam-5509	248	7	eur	eur	PROPN
ejpam-5509	248	8	.	.	PUNCT
ejpam-5509	249	1	j.	j.	PROPN
ejpam-5509	249	2	pure	pure	PROPN
ejpam-5509	249	3	appl	appl	PROPN
ejpam-5509	249	4	.	.	PROPN
ejpam-5509	249	5	math	math	PROPN
ejpam-5509	249	6	,	,	PUNCT
ejpam-5509	249	7	18	18	NUM
ejpam-5509	249	8	(	(	PUNCT
ejpam-5509	249	9	1	1	NUM
ejpam-5509	249	10	)	)	PUNCT
ejpam-5509	249	11	(	(	PUNCT
ejpam-5509	249	12	2025	2025	NUM
ejpam-5509	249	13	)	)	PUNCT
ejpam-5509	249	14	,	,	PUNCT
ejpam-5509	249	15	5509	5509	NUM
ejpam-5509	249	16	11	11	NUM
ejpam-5509	249	17	of	of	ADP
ejpam-5509	249	18	27	27	NUM
ejpam-5509	249	19	−φ1{s(t)−	−φ1{s(t)−	PROPN
ejpam-5509	249	20	s(t1	s(t1	PROPN
ejpam-5509	249	21	)	)	PUNCT
ejpam-5509	249	22	}	}	PUNCT
ejpam-5509	249	23	.	.	PUNCT
ejpam-5509	250	1	(	(	PUNCT
ejpam-5509	250	2	19	19	NUM
ejpam-5509	250	3	)	)	PUNCT
ejpam-5509	250	4	upon	upon	SCONJ
ejpam-5509	250	5	simplifying	simplify	VERB
ejpam-5509	250	6	equation	equation	NOUN
ejpam-5509	250	7	(	(	PUNCT
ejpam-5509	250	8	19	19	NUM
ejpam-5509	250	9	)	)	PUNCT
ejpam-5509	250	10	,	,	PUNCT
ejpam-5509	250	11	we	we	PRON
ejpam-5509	250	12	attain	attain	VERB
ejpam-5509	250	13	the	the	DET
ejpam-5509	250	14	below	below	NOUN
ejpam-5509	250	15	∥l1(t	∥l1(t	ADV
ejpam-5509	250	16	,	,	PUNCT
ejpam-5509	250	17	s)−	s)−	PROPN
ejpam-5509	250	18	l1(t	l1(t	PROPN
ejpam-5509	250	19	,	,	PUNCT
ejpam-5509	250	20	s1)∥	s1)∥	PROPN
ejpam-5509	250	21	≤	≤	PUNCT
ejpam-5509	250	22	∥λ{s(t)−	∥λ{s(t)−	PROPN
ejpam-5509	250	23	s(t1)}||+	s(t1)}||+	NOUN
ejpam-5509	250	24	µ∥{s(t)−	µ∥{s(t)−	PROPN
ejpam-5509	250	25	s(t1)}∥	s(t1)}∥	PROPN
ejpam-5509	250	26	+	+	NUM
ejpam-5509	250	27	φ1∥{s(t)−	φ1∥{s(t)−	PROPN
ejpam-5509	250	28	s(t1)}∥	s(t1)}∥	NOUN
ejpam-5509	250	29	≤	≤	PUNCT
ejpam-5509	250	30	∥ξ(κa+	∥ξ(κa+	PROPN
ejpam-5509	250	31	c)∥∥{s(t)−	c)∥∥{s(t)−	PROPN
ejpam-5509	250	32	s(t1)}||+	s(t1)}||+	PROPN
ejpam-5509	250	33	µ∥{s(t)−	µ∥{s(t)−	PROPN
ejpam-5509	250	34	s(t1)}∥	s(t1)}∥	PROPN
ejpam-5509	250	35	+	+	NUM
ejpam-5509	250	36	φ1∥{s(t)−	φ1∥{s(t)−	PROPN
ejpam-5509	250	37	s(t1)}∥	s(t1)}∥	NOUN
ejpam-5509	250	38	≤	≤	VERB
ejpam-5509	250	39	ξ(κm	ξ(κm	ADV
ejpam-5509	250	40	+	+	PROPN
ejpam-5509	250	41	m)∥{s(t)−	m)∥{s(t)−	PROPN
ejpam-5509	250	42	s(t1)}||+	s(t1)}||+	ADJ
ejpam-5509	250	43	µ∥{s(t)−	µ∥{s(t)−	PROPN
ejpam-5509	250	44	s(t1)}∥	s(t1)}∥	PROPN
ejpam-5509	250	45	+	+	NUM
ejpam-5509	250	46	φ1∥{s(t)−	φ1∥{s(t)−	PROPN
ejpam-5509	250	47	s(t1)}∥	s(t1)}∥	NOUN
ejpam-5509	250	48	≤	≤	NOUN
ejpam-5509	250	49	(	(	PUNCT
ejpam-5509	250	50	ξ(κm	ξ(κm	ADV
ejpam-5509	250	51	+	+	NOUN
ejpam-5509	250	52	m	m	NOUN
ejpam-5509	250	53	)	)	PUNCT
ejpam-5509	251	1	+	+	CCONJ
ejpam-5509	251	2	µ+	µ+	PUNCT
ejpam-5509	251	3	φ1)∥{s(t)−	φ1)∥{s(t)−	PROPN
ejpam-5509	251	4	s(t1)}∥.	s(t1)}∥.	PROPN
ejpam-5509	251	5	taking	take	VERB
ejpam-5509	251	6	ϖ1	ϖ1	VERB
ejpam-5509	251	7	=	=	PUNCT
ejpam-5509	251	8	(	(	PUNCT
ejpam-5509	251	9	ξ(κm	ξ(κm	ADV
ejpam-5509	251	10	+	+	ADV
ejpam-5509	251	11	m)+µ+φ1	m)+µ+φ1	ADJ
ejpam-5509	251	12	)	)	PUNCT
ejpam-5509	251	13	,	,	PUNCT
ejpam-5509	251	14	where	where	SCONJ
ejpam-5509	251	15	∥a∥	∥a∥	ADJ
ejpam-5509	251	16	≤m	≤m	NOUN
ejpam-5509	251	17	and	and	CCONJ
ejpam-5509	251	18	∥c∥	∥c∥	X
ejpam-5509	251	19	≤m	≤m	NOUN
ejpam-5509	251	20	due	due	ADP
ejpam-5509	251	21	to	to	ADP
ejpam-5509	251	22	boundedness	boundedness	NOUN
ejpam-5509	251	23	,	,	PUNCT
ejpam-5509	251	24	we	we	PRON
ejpam-5509	251	25	have	have	VERB
ejpam-5509	251	26	||l1(t	||l1(t	NUM
ejpam-5509	251	27	,	,	PUNCT
ejpam-5509	251	28	s)−	s)−	PROPN
ejpam-5509	251	29	l1(t	l1(t	PROPN
ejpam-5509	251	30	,	,	PUNCT
ejpam-5509	251	31	s1)||	s1)||	ADJ
ejpam-5509	251	32	≤	≤	NOUN
ejpam-5509	251	33	ϖ1||s(t)−	ϖ1||s(t)−	PUNCT
ejpam-5509	251	34	s(t1)||	s(t1)||	NOUN
ejpam-5509	251	35	.	.	PUNCT
ejpam-5509	252	1	(	(	PUNCT
ejpam-5509	252	2	20	20	NUM
ejpam-5509	252	3	)	)	PUNCT
ejpam-5509	252	4	therefore	therefore	ADV
ejpam-5509	252	5	,	,	PUNCT
ejpam-5509	252	6	we	we	PRON
ejpam-5509	252	7	have	have	AUX
ejpam-5509	252	8	established	establish	VERB
ejpam-5509	252	9	the	the	DET
ejpam-5509	252	10	lipschitz	lipschitz	NOUN
ejpam-5509	252	11	condition	condition	NOUN
ejpam-5509	252	12	for	for	ADP
ejpam-5509	252	13	l1	l1	PROPN
ejpam-5509	252	14	,	,	PUNCT
ejpam-5509	252	15	and	and	CCONJ
ejpam-5509	252	16	additionally	additionally	ADV
ejpam-5509	252	17	,	,	PUNCT
ejpam-5509	252	18	contraction	contraction	NOUN
ejpam-5509	252	19	is	be	AUX
ejpam-5509	252	20	derived	derive	VERB
ejpam-5509	252	21	from	from	ADP
ejpam-5509	252	22	the	the	DET
ejpam-5509	252	23	condition	condition	NOUN
ejpam-5509	252	24	0	0	NUM
ejpam-5509	252	25	≤	≤	NUM
ejpam-5509	252	26	(	(	PUNCT
ejpam-5509	252	27	m	m	VERB
ejpam-5509	252	28	+	+	NUM
ejpam-5509	252	29	d+	d+	NOUN
ejpam-5509	252	30	ν	ν	X
ejpam-5509	252	31	)	)	PUNCT
ejpam-5509	252	32	<	<	X
ejpam-5509	253	1	1	1	X
ejpam-5509	253	2	.	.	PUNCT
ejpam-5509	253	3	similarly	similarly	ADV
ejpam-5509	253	4	,	,	PUNCT
ejpam-5509	253	5	the	the	DET
ejpam-5509	253	6	lipschitz	lipschitz	NOUN
ejpam-5509	253	7	conditions	condition	NOUN
ejpam-5509	253	8	can	can	AUX
ejpam-5509	253	9	be	be	AUX
ejpam-5509	253	10	determined	determine	VERB
ejpam-5509	253	11	as	as	SCONJ
ejpam-5509	253	12	follows	follow	VERB
ejpam-5509	253	13	||l2(t	||l2(t	NOUN
ejpam-5509	253	14	,	,	PUNCT
ejpam-5509	253	15	v1)−	v1)−	PROPN
ejpam-5509	253	16	l2(t	l2(t	PROPN
ejpam-5509	253	17	,	,	PUNCT
ejpam-5509	253	18	v11)||	v11)||	NOUN
ejpam-5509	253	19	≤	≤	NUM
ejpam-5509	253	20	ϖ2||v1(t)−	ϖ2||v1(t)−	PUNCT
ejpam-5509	253	21	v1(t1)||	v1(t1)||	NOUN
ejpam-5509	253	22	,	,	PUNCT
ejpam-5509	253	23	||l3(t	||l3(t	NUM
ejpam-5509	253	24	,	,	PUNCT
ejpam-5509	253	25	v2)−	v2)−	PROPN
ejpam-5509	253	26	l3(t	l3(t	ADJ
ejpam-5509	253	27	,	,	PUNCT
ejpam-5509	253	28	v21)||	v21)||	PROPN
ejpam-5509	253	29	≤	≤	PUNCT
ejpam-5509	253	30	ϖ3||v2(t)−	ϖ3||v2(t)−	PROPN
ejpam-5509	253	31	v2(t1)||	v2(t1)||	PROPN
ejpam-5509	253	32	,	,	PUNCT
ejpam-5509	253	33	||l4(t	||l4(t	NUM
ejpam-5509	253	34	,	,	PUNCT
ejpam-5509	253	35	a)−	a)−	PROPN
ejpam-5509	253	36	l4(t	l4(t	PROPN
ejpam-5509	253	37	,	,	PUNCT
ejpam-5509	253	38	a1)||	a1)||	PROPN
ejpam-5509	253	39	≤	≤	PUNCT
ejpam-5509	253	40	ϖ4||a(t)−a(t1)||	ϖ4||a(t)−a(t1)||	PROPN
ejpam-5509	253	41	,	,	PUNCT
ejpam-5509	253	42	||l5(t	||l5(t	INTJ
ejpam-5509	253	43	,	,	PUNCT
ejpam-5509	253	44	c)−	c)−	PROPN
ejpam-5509	253	45	l5(t	l5(t	PROPN
ejpam-5509	253	46	,	,	PUNCT
ejpam-5509	253	47	c1)||	c1)||	PROPN
ejpam-5509	253	48	≤	≤	PROPN
ejpam-5509	253	49	ϖ5||c(t)−	ϖ5||c(t)−	PROPN
ejpam-5509	253	50	c(t1)||	c(t1)||	NOUN
ejpam-5509	253	51	,	,	PUNCT
ejpam-5509	253	52	||l6(t	||l6(t	NOUN
ejpam-5509	253	53	,	,	PUNCT
ejpam-5509	253	54	r)−	r)−	PROPN
ejpam-5509	253	55	l6(t	l6(t	PROPN
ejpam-5509	253	56	,	,	PUNCT
ejpam-5509	253	57	r1)||	r1)||	NOUN
ejpam-5509	253	58	≤	≤	NUM
ejpam-5509	254	1	ϖ6||r(t)−r(t1)||	ϖ6||r(t)−r(t1)||	NOUN
ejpam-5509	254	2	.	.	PUNCT
ejpam-5509	255	1	(	(	PUNCT
ejpam-5509	255	2	21	21	NUM
ejpam-5509	255	3	)	)	PUNCT
ejpam-5509	255	4	i.	i.	PROPN
ejpam-5509	255	5	ahmad	ahmad	PROPN
ejpam-5509	255	6	et	et	PROPN
ejpam-5509	255	7	al	al	PROPN
ejpam-5509	255	8	.	.	PUNCT
ejpam-5509	255	9	/	/	SYM
ejpam-5509	255	10	eur	eur	PROPN
ejpam-5509	255	11	.	.	PUNCT
ejpam-5509	256	1	j.	j.	PROPN
ejpam-5509	256	2	pure	pure	PROPN
ejpam-5509	256	3	appl	appl	PROPN
ejpam-5509	256	4	.	.	PROPN
ejpam-5509	256	5	math	math	PROPN
ejpam-5509	256	6	,	,	PUNCT
ejpam-5509	256	7	18	18	NUM
ejpam-5509	256	8	(	(	PUNCT
ejpam-5509	256	9	1	1	NUM
ejpam-5509	256	10	)	)	PUNCT
ejpam-5509	256	11	(	(	PUNCT
ejpam-5509	256	12	2025	2025	NUM
ejpam-5509	256	13	)	)	PUNCT
ejpam-5509	256	14	,	,	PUNCT
ejpam-5509	256	15	5509	5509	NUM
ejpam-5509	256	16	12	12	NUM
ejpam-5509	256	17	of	of	ADP
ejpam-5509	256	18	27	27	NUM
ejpam-5509	256	19	utilizing	utilizing	NOUN
ejpam-5509	256	20	(	(	PUNCT
ejpam-5509	256	21	17	17	NUM
ejpam-5509	256	22	)	)	PUNCT
ejpam-5509	256	23	,	,	PUNCT
ejpam-5509	256	24	the	the	DET
ejpam-5509	256	25	following	follow	VERB
ejpam-5509	256	26	can	can	AUX
ejpam-5509	256	27	be	be	AUX
ejpam-5509	256	28	derived:	derived:	ADJ
ejpam-5509	256	29	sm(t	sm(t	NOUN
ejpam-5509	256	30	)	)	PUNCT
ejpam-5509	256	31	=	=	SYM
ejpam-5509	256	32	2	2	NUM
ejpam-5509	256	33	(	(	PUNCT
ejpam-5509	256	34	1−ς	1−ς	NUM
ejpam-5509	256	35	)	)	PUNCT
ejpam-5509	256	36	(	(	PUNCT
ejpam-5509	256	37	2−ς)u(ς)l1(t	2−ς)u(ς)l1(t	NUM
ejpam-5509	256	38	,	,	PUNCT
ejpam-5509	256	39	s(m−1	s(m−1	PROPN
ejpam-5509	256	40	)	)	PUNCT
ejpam-5509	256	41	)	)	PUNCT
ejpam-5509	257	1	+	+	CCONJ
ejpam-5509	257	2	2	2	NUM
ejpam-5509	257	3	ς	ς	PROPN
ejpam-5509	257	4	(	(	PUNCT
ejpam-5509	257	5	2−ς)u(ς	2−ς)u(ς	NOUN
ejpam-5509	257	6	)	)	PUNCT
ejpam-5509	257	7	∫	∫	PROPN
ejpam-5509	257	8	t	t	PROPN
ejpam-5509	257	9	0(l1(z	0(l1(z	NUM
ejpam-5509	257	10	,	,	PUNCT
ejpam-5509	257	11	s(m−1)))dz	s(m−1)))dz	PROPN
ejpam-5509	257	12	,	,	PUNCT
ejpam-5509	257	13	v1m(t	v1m(t	NOUN
ejpam-5509	257	14	)	)	PUNCT
ejpam-5509	257	15	=	=	SYM
ejpam-5509	257	16	2	2	NUM
ejpam-5509	257	17	(	(	PUNCT
ejpam-5509	257	18	1−ς	1−ς	NUM
ejpam-5509	257	19	)	)	PUNCT
ejpam-5509	257	20	(	(	PUNCT
ejpam-5509	257	21	2−ς)u(ς)l2(t	2−ς)u(ς)l2(t	NUM
ejpam-5509	257	22	,	,	PUNCT
ejpam-5509	257	23	v1(m−1	v1(m−1	PROPN
ejpam-5509	257	24	)	)	PUNCT
ejpam-5509	257	25	)	)	PUNCT
ejpam-5509	258	1	+	+	CCONJ
ejpam-5509	258	2	2	2	NUM
ejpam-5509	258	3	ς	ς	PROPN
ejpam-5509	258	4	(	(	PUNCT
ejpam-5509	258	5	2−ς)u(ς	2−ς)u(ς	NOUN
ejpam-5509	258	6	)	)	PUNCT
ejpam-5509	258	7	∫	∫	PROPN
ejpam-5509	258	8	t	t	PROPN
ejpam-5509	258	9	0(l2(z	0(l2(z	NUM
ejpam-5509	258	10	,	,	PUNCT
ejpam-5509	258	11	v1(m−1)))dz	v1(m−1)))dz	PROPN
ejpam-5509	258	12	,	,	PUNCT
ejpam-5509	258	13	v2m(t	v2m(t	PROPN
ejpam-5509	258	14	)	)	PUNCT
ejpam-5509	258	15	=	=	SYM
ejpam-5509	259	1	2	2	NUM
ejpam-5509	259	2	(	(	PUNCT
ejpam-5509	259	3	1−ς	1−ς	NUM
ejpam-5509	259	4	)	)	PUNCT
ejpam-5509	259	5	(	(	PUNCT
ejpam-5509	259	6	2−ς)u(ς)l3(t	2−ς)u(ς)l3(t	NOUN
ejpam-5509	259	7	,	,	PUNCT
ejpam-5509	259	8	v2(m−1	v2(m−1	NOUN
ejpam-5509	259	9	)	)	PUNCT
ejpam-5509	259	10	)	)	PUNCT
ejpam-5509	260	1	+	+	CCONJ
ejpam-5509	260	2	2	2	NUM
ejpam-5509	260	3	ς	ς	PROPN
ejpam-5509	260	4	(	(	PUNCT
ejpam-5509	260	5	2−ς)u(ς	2−ς)u(ς	NOUN
ejpam-5509	260	6	)	)	PUNCT
ejpam-5509	260	7	∫	∫	PROPN
ejpam-5509	260	8	t	t	PROPN
ejpam-5509	260	9	0(l3(z	0(l3(z	NUM
ejpam-5509	260	10	,	,	PUNCT
ejpam-5509	260	11	v2(m−1)))dz	v2(m−1)))dz	X
ejpam-5509	260	12	,	,	PUNCT
ejpam-5509	260	13	am(t	am(t	NOUN
ejpam-5509	260	14	)	)	PUNCT
ejpam-5509	260	15	=	=	SYM
ejpam-5509	260	16	2	2	NUM
ejpam-5509	260	17	(	(	PUNCT
ejpam-5509	260	18	1−ς	1−ς	NUM
ejpam-5509	260	19	)	)	PUNCT
ejpam-5509	260	20	(	(	PUNCT
ejpam-5509	260	21	2−ς)u(ς)l4(t	2−ς)u(ς)l4(t	NOUN
ejpam-5509	260	22	,	,	PUNCT
ejpam-5509	260	23	a(m−1	a(m−1	PROPN
ejpam-5509	260	24	)	)	PUNCT
ejpam-5509	260	25	)	)	PUNCT
ejpam-5509	261	1	+	+	CCONJ
ejpam-5509	261	2	2	2	NUM
ejpam-5509	261	3	ς	ς	PROPN
ejpam-5509	261	4	(	(	PUNCT
ejpam-5509	261	5	2−ς)u(ς	2−ς)u(ς	NOUN
ejpam-5509	261	6	)	)	PUNCT
ejpam-5509	261	7	∫	∫	PROPN
ejpam-5509	261	8	t	t	PROPN
ejpam-5509	261	9	0(l4(z	0(l4(z	NUM
ejpam-5509	261	10	,	,	PUNCT
ejpam-5509	261	11	a(m−1)))dz	a(m−1)))dz	PROPN
ejpam-5509	261	12	,	,	PUNCT
ejpam-5509	261	13	cm(t	cm(t	NOUN
ejpam-5509	261	14	)	)	PUNCT
ejpam-5509	261	15	=	=	SYM
ejpam-5509	261	16	2	2	NUM
ejpam-5509	261	17	(	(	PUNCT
ejpam-5509	261	18	1−ς	1−ς	NUM
ejpam-5509	261	19	)	)	PUNCT
ejpam-5509	261	20	(	(	PUNCT
ejpam-5509	261	21	2−ς)u(ς)l5(t	2−ς)u(ς)l5(t	NUM
ejpam-5509	261	22	,	,	PUNCT
ejpam-5509	261	23	c(m−1	c(m−1	PROPN
ejpam-5509	261	24	)	)	PUNCT
ejpam-5509	261	25	)	)	PUNCT
ejpam-5509	262	1	+	+	CCONJ
ejpam-5509	262	2	2	2	NUM
ejpam-5509	262	3	ς	ς	PROPN
ejpam-5509	262	4	(	(	PUNCT
ejpam-5509	262	5	2−ς)u(ς	2−ς)u(ς	NOUN
ejpam-5509	262	6	)	)	PUNCT
ejpam-5509	262	7	∫	∫	PROPN
ejpam-5509	262	8	t	t	PROPN
ejpam-5509	262	9	0(l5(z	0(l5(z	NUM
ejpam-5509	262	10	,	,	PUNCT
ejpam-5509	262	11	c(m−1)))dz	c(m−1)))dz	PROPN
ejpam-5509	262	12	,	,	PUNCT
ejpam-5509	262	13	rm(t	rm(t	NOUN
ejpam-5509	262	14	)	)	PUNCT
ejpam-5509	262	15	=	=	SYM
ejpam-5509	262	16	2	2	NUM
ejpam-5509	262	17	(	(	PUNCT
ejpam-5509	262	18	1−ς	1−ς	NUM
ejpam-5509	262	19	)	)	PUNCT
ejpam-5509	262	20	(	(	PUNCT
ejpam-5509	262	21	2−ς)u(ς)l6(t	2−ς)u(ς)l6(t	NOUN
ejpam-5509	262	22	,	,	PUNCT
ejpam-5509	262	23	c(m−1	c(m−1	PROPN
ejpam-5509	262	24	)	)	PUNCT
ejpam-5509	262	25	)	)	PUNCT
ejpam-5509	263	1	+	+	CCONJ
ejpam-5509	263	2	2	2	NUM
ejpam-5509	263	3	ς	ς	PROPN
ejpam-5509	263	4	(	(	PUNCT
ejpam-5509	263	5	2−ς)u(ς	2−ς)u(ς	NOUN
ejpam-5509	263	6	)	)	PUNCT
ejpam-5509	263	7	∫	∫	PROPN
ejpam-5509	263	8	t	t	PROPN
ejpam-5509	263	9	0(l6(z	0(l6(z	NUM
ejpam-5509	263	10	,	,	PUNCT
ejpam-5509	263	11	r(m−1)))dz	r(m−1)))dz	PROPN
ejpam-5509	263	12	,	,	PUNCT
ejpam-5509	263	13	(	(	PUNCT
ejpam-5509	263	14	22	22	NUM
ejpam-5509	263	15	)	)	PUNCT
ejpam-5509	263	16	with	with	ADP
ejpam-5509	263	17	the	the	DET
ejpam-5509	263	18	below	below	ADJ
ejpam-5509	263	19	initial	initial	ADJ
ejpam-5509	263	20	values	value	NOUN
ejpam-5509	263	21	s0(t	s0(t	NOUN
ejpam-5509	263	22	)	)	PUNCT
ejpam-5509	263	23	=	=	SYM
ejpam-5509	263	24	s(0	s(0	PROPN
ejpam-5509	263	25	)	)	PUNCT
ejpam-5509	263	26	,	,	PUNCT
ejpam-5509	263	27	v	v	NOUN
ejpam-5509	263	28	0	0	NUM
ejpam-5509	263	29	1	1	NUM
ejpam-5509	263	30	(	(	PUNCT
ejpam-5509	263	31	t	t	NOUN
ejpam-5509	263	32	)	)	PUNCT
ejpam-5509	263	33	=	=	SYM
ejpam-5509	263	34	v1(0	v1(0	PROPN
ejpam-5509	263	35	)	)	PUNCT
ejpam-5509	263	36	,	,	PUNCT
ejpam-5509	263	37	v	v	NOUN
ejpam-5509	263	38	0	0	NUM
ejpam-5509	263	39	2	2	NUM
ejpam-5509	263	40	(	(	PUNCT
ejpam-5509	263	41	t	t	NOUN
ejpam-5509	263	42	)	)	PUNCT
ejpam-5509	263	43	=	=	SYM
ejpam-5509	263	44	v2(0	v2(0	NOUN
ejpam-5509	263	45	)	)	PUNCT
ejpam-5509	263	46	,	,	PUNCT
ejpam-5509	263	47	a	a	DET
ejpam-5509	263	48	0(t	0(t	NUM
ejpam-5509	263	49	)	)	PUNCT
ejpam-5509	263	50	=	=	PUNCT
ejpam-5509	263	51	a(0	a(0	PROPN
ejpam-5509	263	52	)	)	PUNCT
ejpam-5509	263	53	,	,	PUNCT
ejpam-5509	263	54	c0(t	c0(t	NOUN
ejpam-5509	263	55	)	)	PUNCT
ejpam-5509	263	56	=	=	SYM
ejpam-5509	263	57	c(0	c(0	NOUN
ejpam-5509	263	58	)	)	PUNCT
ejpam-5509	263	59	,	,	PUNCT
ejpam-5509	263	60	r0(t	r0(t	PROPN
ejpam-5509	263	61	)	)	PUNCT
ejpam-5509	263	62	=	=	SYM
ejpam-5509	263	63	r(0	r(0	PROPN
ejpam-5509	263	64	)	)	PUNCT
ejpam-5509	263	65	.	.	PUNCT
ejpam-5509	264	1	the	the	DET
ejpam-5509	264	2	difference	difference	NOUN
ejpam-5509	264	3	expressions	expression	NOUN
ejpam-5509	264	4	are	be	AUX
ejpam-5509	264	5	derived	derive	VERB
ejpam-5509	264	6	in	in	ADP
ejpam-5509	264	7	the	the	DET
ejpam-5509	264	8	following	following	ADJ
ejpam-5509	264	9	manner	manner	NOUN
ejpam-5509	264	10	.	.	PUNCT
ejpam-5509	265	1	κ1m(t	κ1m(t	NOUN
ejpam-5509	265	2	)	)	PUNCT
ejpam-5509	266	1	=	=	SYM
ejpam-5509	266	2	sm(t)−	sm(t)−	PROPN
ejpam-5509	266	3	s(m−1)(t	s(m−1)(t	PROPN
ejpam-5509	266	4	)	)	PUNCT
ejpam-5509	266	5	=	=	PUNCT
ejpam-5509	267	1	2(1−	2(1−	NUM
ejpam-5509	267	2	ς	ς	NOUN
ejpam-5509	267	3	)	)	PUNCT
ejpam-5509	267	4	(	(	PUNCT
ejpam-5509	267	5	2−	2−	NUM
ejpam-5509	267	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	267	7	)	)	PUNCT
ejpam-5509	267	8	(	(	PUNCT
ejpam-5509	267	9	l1(t	l1(t	PROPN
ejpam-5509	267	10	,	,	PUNCT
ejpam-5509	267	11	s(m−1))−	s(m−1))−	PROPN
ejpam-5509	267	12	l1(t	l1(t	PROPN
ejpam-5509	267	13	,	,	PUNCT
ejpam-5509	267	14	s(m−2	s(m−2	NOUN
ejpam-5509	267	15	)	)	PUNCT
ejpam-5509	267	16	)	)	PUNCT
ejpam-5509	267	17	)	)	PUNCT
ejpam-5509	268	1	+2	+2	PROPN
ejpam-5509	268	2	ς	ς	PROPN
ejpam-5509	268	3	(	(	PUNCT
ejpam-5509	268	4	2−	2−	NUM
ejpam-5509	268	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	268	6	)	)	PUNCT
ejpam-5509	268	7	∫	∫	PROPN
ejpam-5509	268	8	t	t	PROPN
ejpam-5509	268	9	0	0	NUM
ejpam-5509	268	10	(	(	PUNCT
ejpam-5509	268	11	l1(z	l1(z	PROPN
ejpam-5509	268	12	,	,	PUNCT
ejpam-5509	268	13	s(m−1))−	s(m−1))−	PROPN
ejpam-5509	268	14	l1(z	l1(z	PROPN
ejpam-5509	268	15	,	,	PUNCT
ejpam-5509	268	16	s(m−2)))dz	s(m−2)))dz	PROPN
ejpam-5509	268	17	,	,	PUNCT
ejpam-5509	268	18	κ2m(t	κ2m(t	PROPN
ejpam-5509	268	19	)	)	PUNCT
ejpam-5509	268	20	=	=	SYM
ejpam-5509	268	21	v1m(t)−	v1m(t)−	PUNCT
ejpam-5509	268	22	v1(m−1)(t	v1(m−1)(t	NOUN
ejpam-5509	268	23	)	)	PUNCT
ejpam-5509	268	24	=	=	SYM
ejpam-5509	269	1	2(1−	2(1−	NUM
ejpam-5509	269	2	ς	ς	NOUN
ejpam-5509	269	3	)	)	PUNCT
ejpam-5509	269	4	(	(	PUNCT
ejpam-5509	269	5	2−	2−	NUM
ejpam-5509	269	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	269	7	)	)	PUNCT
ejpam-5509	269	8	(	(	PUNCT
ejpam-5509	269	9	l2(t	l2(t	PROPN
ejpam-5509	269	10	,	,	PUNCT
ejpam-5509	269	11	v1(m−1))−	v1(m−1))−	NOUN
ejpam-5509	269	12	l2(t	l2(t	PROPN
ejpam-5509	269	13	,	,	PUNCT
ejpam-5509	269	14	v1(m−2	v1(m−2	NOUN
ejpam-5509	269	15	)	)	PUNCT
ejpam-5509	269	16	)	)	PUNCT
ejpam-5509	269	17	)	)	PUNCT
ejpam-5509	270	1	+2	+2	PROPN
ejpam-5509	270	2	ς	ς	PROPN
ejpam-5509	270	3	(	(	PUNCT
ejpam-5509	270	4	2−	2−	NUM
ejpam-5509	270	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	270	6	)	)	PUNCT
ejpam-5509	270	7	∫	∫	PROPN
ejpam-5509	270	8	t	t	PROPN
ejpam-5509	270	9	0	0	NUM
ejpam-5509	270	10	(	(	PUNCT
ejpam-5509	270	11	l2(z	l2(z	NOUN
ejpam-5509	270	12	,	,	PUNCT
ejpam-5509	270	13	v1(m−1))−	v1(m−1))−	NOUN
ejpam-5509	270	14	l2(z	l2(z	PROPN
ejpam-5509	270	15	,	,	PUNCT
ejpam-5509	270	16	v1(m−2)))dz	v1(m−2)))dz	PROPN
ejpam-5509	270	17	,	,	PUNCT
ejpam-5509	270	18	κ3m(t	κ3m(t	ADJ
ejpam-5509	270	19	)	)	PUNCT
ejpam-5509	270	20	=	=	SYM
ejpam-5509	271	1	v2m(t)−	v2m(t)−	X
ejpam-5509	271	2	v2(m−1)(t	v2(m−1)(t	ADJ
ejpam-5509	271	3	)	)	PUNCT
ejpam-5509	271	4	=	=	SYM
ejpam-5509	272	1	2(1−	2(1−	NUM
ejpam-5509	272	2	ς	ς	NOUN
ejpam-5509	272	3	)	)	PUNCT
ejpam-5509	272	4	(	(	PUNCT
ejpam-5509	272	5	2−	2−	NUM
ejpam-5509	272	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	272	7	)	)	PUNCT
ejpam-5509	272	8	(	(	PUNCT
ejpam-5509	272	9	l3(t	l3(t	X
ejpam-5509	272	10	,	,	PUNCT
ejpam-5509	272	11	v2(m−1))−	v2(m−1))−	PRON
ejpam-5509	272	12	l3(t	l3(t	VERB
ejpam-5509	272	13	,	,	PUNCT
ejpam-5509	272	14	v2(m−2	v2(m−2	NOUN
ejpam-5509	272	15	)	)	PUNCT
ejpam-5509	272	16	)	)	PUNCT
ejpam-5509	272	17	)	)	PUNCT
ejpam-5509	273	1	+2	+2	PROPN
ejpam-5509	273	2	ς	ς	PROPN
ejpam-5509	273	3	(	(	PUNCT
ejpam-5509	273	4	2−	2−	NUM
ejpam-5509	273	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	273	6	)	)	PUNCT
ejpam-5509	273	7	∫	∫	PROPN
ejpam-5509	273	8	t	t	PROPN
ejpam-5509	273	9	0	0	NUM
ejpam-5509	274	1	(	(	PUNCT
ejpam-5509	274	2	l3(z	l3(z	PROPN
ejpam-5509	274	3	,	,	PUNCT
ejpam-5509	274	4	v2(m−1))−	v2(m−1))−	PRON
ejpam-5509	274	5	l3(z	l3(z	PROPN
ejpam-5509	274	6	,	,	PUNCT
ejpam-5509	274	7	v2(m−2)))dz	v2(m−2)))dz	PROPN
ejpam-5509	274	8	,	,	PUNCT
ejpam-5509	274	9	κ4m(t	κ4m(t	PROPN
ejpam-5509	274	10	)	)	PUNCT
ejpam-5509	274	11	=	=	SYM
ejpam-5509	274	12	am(t)−a(m−1)(t	am(t)−a(m−1)(t	PROPN
ejpam-5509	274	13	)	)	PUNCT
ejpam-5509	274	14	=	=	PUNCT
ejpam-5509	275	1	2(1−	2(1−	NUM
ejpam-5509	275	2	ς	ς	NOUN
ejpam-5509	275	3	)	)	PUNCT
ejpam-5509	275	4	(	(	PUNCT
ejpam-5509	275	5	2−	2−	NUM
ejpam-5509	275	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	275	7	)	)	PUNCT
ejpam-5509	275	8	(	(	PUNCT
ejpam-5509	275	9	l4(t	l4(t	X
ejpam-5509	275	10	,	,	PUNCT
ejpam-5509	275	11	a(m−1))−	a(m−1))−	PROPN
ejpam-5509	275	12	l4(t	l4(t	PROPN
ejpam-5509	275	13	,	,	PUNCT
ejpam-5509	275	14	a(m−2	a(m−2	ADV
ejpam-5509	275	15	)	)	PUNCT
ejpam-5509	275	16	)	)	PUNCT
ejpam-5509	275	17	)	)	PUNCT
ejpam-5509	276	1	+2	+2	PROPN
ejpam-5509	276	2	ς	ς	PROPN
ejpam-5509	276	3	(	(	PUNCT
ejpam-5509	276	4	2−	2−	NUM
ejpam-5509	276	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	276	6	)	)	PUNCT
ejpam-5509	276	7	∫	∫	PROPN
ejpam-5509	276	8	t	t	PROPN
ejpam-5509	276	9	0	0	NUM
ejpam-5509	276	10	(	(	PUNCT
ejpam-5509	276	11	l4(z	l4(z	PROPN
ejpam-5509	276	12	,	,	PUNCT
ejpam-5509	276	13	a(m−1))−	a(m−1))−	PROPN
ejpam-5509	276	14	l4(z	l4(z	PROPN
ejpam-5509	276	15	,	,	PUNCT
ejpam-5509	276	16	a(m−2)))dz	a(m−2)))dz	PROPN
ejpam-5509	276	17	,	,	PUNCT
ejpam-5509	276	18	κ5m(t	κ5m(t	NOUN
ejpam-5509	276	19	)	)	PUNCT
ejpam-5509	276	20	=	=	PROPN
ejpam-5509	276	21	cm(t)−	cm(t)−	PROPN
ejpam-5509	276	22	c(m−1)(t	c(m−1)(t	PROPN
ejpam-5509	276	23	)	)	PUNCT
ejpam-5509	276	24	=	=	PUNCT
ejpam-5509	277	1	2(1−	2(1−	NUM
ejpam-5509	277	2	ς	ς	NOUN
ejpam-5509	277	3	)	)	PUNCT
ejpam-5509	277	4	(	(	PUNCT
ejpam-5509	277	5	2−	2−	NUM
ejpam-5509	277	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	277	7	)	)	PUNCT
ejpam-5509	277	8	(	(	PUNCT
ejpam-5509	277	9	l5(t	l5(t	PROPN
ejpam-5509	277	10	,	,	PUNCT
ejpam-5509	277	11	c(m−1))−	c(m−1))−	PROPN
ejpam-5509	277	12	l5(t	l5(t	PROPN
ejpam-5509	277	13	,	,	PUNCT
ejpam-5509	277	14	c(m−2	c(m−2	NOUN
ejpam-5509	277	15	)	)	PUNCT
ejpam-5509	277	16	)	)	PUNCT
ejpam-5509	277	17	)	)	PUNCT
ejpam-5509	278	1	+2	+2	PROPN
ejpam-5509	278	2	ς	ς	PROPN
ejpam-5509	278	3	(	(	PUNCT
ejpam-5509	278	4	2−	2−	NUM
ejpam-5509	278	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	278	6	)	)	PUNCT
ejpam-5509	278	7	∫	∫	PROPN
ejpam-5509	278	8	t	t	PROPN
ejpam-5509	278	9	0	0	NUM
ejpam-5509	278	10	(	(	PUNCT
ejpam-5509	278	11	l5(z	l5(z	PROPN
ejpam-5509	278	12	,	,	PUNCT
ejpam-5509	278	13	c(m−1))−	c(m−1))−	PROPN
ejpam-5509	278	14	l5(z	l5(z	PROPN
ejpam-5509	278	15	,	,	PUNCT
ejpam-5509	278	16	c(m−2)))dz	c(m−2)))dz	PROPN
ejpam-5509	278	17	,	,	PUNCT
ejpam-5509	278	18	κ6m(t	κ6m(t	NOUN
ejpam-5509	278	19	)	)	PUNCT
ejpam-5509	278	20	=	=	SYM
ejpam-5509	278	21	rm(t)−r(m−1)(t	rm(t)−r(m−1)(t	X
ejpam-5509	278	22	)	)	PUNCT
ejpam-5509	278	23	=	=	PUNCT
ejpam-5509	279	1	2(1−	2(1−	NUM
ejpam-5509	279	2	ς	ς	NOUN
ejpam-5509	279	3	)	)	PUNCT
ejpam-5509	279	4	(	(	PUNCT
ejpam-5509	279	5	2−	2−	NUM
ejpam-5509	279	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	279	7	)	)	PUNCT
ejpam-5509	279	8	(	(	PUNCT
ejpam-5509	279	9	l6(t	l6(t	PROPN
ejpam-5509	279	10	,	,	PUNCT
ejpam-5509	279	11	r(m−1))−	r(m−1))−	PROPN
ejpam-5509	279	12	l6(t	l6(t	PROPN
ejpam-5509	279	13	,	,	PUNCT
ejpam-5509	279	14	r(m−2	r(m−2	PROPN
ejpam-5509	279	15	)	)	PUNCT
ejpam-5509	279	16	)	)	PUNCT
ejpam-5509	279	17	)	)	PUNCT
ejpam-5509	280	1	+2	+2	PROPN
ejpam-5509	280	2	ς	ς	PROPN
ejpam-5509	280	3	(	(	PUNCT
ejpam-5509	280	4	2−	2−	NUM
ejpam-5509	280	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	280	6	)	)	PUNCT
ejpam-5509	280	7	∫	∫	PROPN
ejpam-5509	280	8	t	t	PROPN
ejpam-5509	280	9	0	0	NUM
ejpam-5509	280	10	(	(	PUNCT
ejpam-5509	280	11	l6(z	l6(z	NOUN
ejpam-5509	280	12	,	,	PUNCT
ejpam-5509	280	13	r(m−1))−	r(m−1))−	PROPN
ejpam-5509	280	14	l6(z	l6(z	NOUN
ejpam-5509	280	15	,	,	PUNCT
ejpam-5509	280	16	r(m−2)))dz	r(m−2)))dz	PROPN
ejpam-5509	280	17	.	.	PUNCT
ejpam-5509	281	1	(	(	PUNCT
ejpam-5509	281	2	23	23	NUM
ejpam-5509	281	3	)	)	PUNCT
ejpam-5509	281	4	i.	i.	PROPN
ejpam-5509	281	5	ahmad	ahmad	PROPN
ejpam-5509	281	6	et	et	PROPN
ejpam-5509	281	7	al	al	PROPN
ejpam-5509	281	8	.	.	PUNCT
ejpam-5509	281	9	/	/	SYM
ejpam-5509	281	10	eur	eur	PROPN
ejpam-5509	281	11	.	.	PUNCT
ejpam-5509	282	1	j.	j.	PROPN
ejpam-5509	282	2	pure	pure	PROPN
ejpam-5509	282	3	appl	appl	PROPN
ejpam-5509	282	4	.	.	PROPN
ejpam-5509	282	5	math	math	PROPN
ejpam-5509	282	6	,	,	PUNCT
ejpam-5509	282	7	18	18	NUM
ejpam-5509	282	8	(	(	PUNCT
ejpam-5509	282	9	1	1	NUM
ejpam-5509	282	10	)	)	PUNCT
ejpam-5509	282	11	(	(	PUNCT
ejpam-5509	282	12	2025	2025	NUM
ejpam-5509	282	13	)	)	PUNCT
ejpam-5509	282	14	,	,	PUNCT
ejpam-5509	282	15	5509	5509	NUM
ejpam-5509	282	16	13	13	NUM
ejpam-5509	282	17	of	of	ADP
ejpam-5509	282	18	27	27	NUM
ejpam-5509	282	19	noticing	noticing	NUM
ejpam-5509	282	20	sm(t	sm(t	NUM
ejpam-5509	282	21	)	)	PUNCT
ejpam-5509	283	1	=	=	PUNCT
ejpam-5509	283	2	∑m	∑m	PROPN
ejpam-5509	283	3	j=1	j=1	PROPN
ejpam-5509	283	4	κ1j(t	κ1j(t	PROPN
ejpam-5509	283	5	)	)	PUNCT
ejpam-5509	283	6	,	,	PUNCT
ejpam-5509	283	7	v1n(t	v1n(t	PROPN
ejpam-5509	283	8	)	)	PUNCT
ejpam-5509	283	9	=	=	PUNCT
ejpam-5509	284	1	∑m	∑m	ADJ
ejpam-5509	284	2	j=1	j=1	PROPN
ejpam-5509	284	3	κ2j(t	κ2j(t	PROPN
ejpam-5509	284	4	)	)	PUNCT
ejpam-5509	284	5	,	,	PUNCT
ejpam-5509	284	6	v2m(t	v2m(t	PROPN
ejpam-5509	284	7	)	)	PUNCT
ejpam-5509	285	1	=	=	PUNCT
ejpam-5509	286	1	∑m	∑m	PROPN
ejpam-5509	286	2	j=1	j=1	PROPN
ejpam-5509	286	3	κ3j(t	κ3j(t	PROPN
ejpam-5509	286	4	)	)	PUNCT
ejpam-5509	286	5	,	,	PUNCT
ejpam-5509	286	6	am(t	am(t	NOUN
ejpam-5509	286	7	)	)	PUNCT
ejpam-5509	287	1	=	=	PUNCT
ejpam-5509	287	2	∑m	∑m	PROPN
ejpam-5509	287	3	j=1	j=1	PROPN
ejpam-5509	287	4	κ4j(t	κ4j(t	PROPN
ejpam-5509	287	5	)	)	PUNCT
ejpam-5509	287	6	,	,	PUNCT
ejpam-5509	287	7	cm(t	cm(t	NOUN
ejpam-5509	287	8	)	)	PUNCT
ejpam-5509	288	1	=	=	PUNCT
ejpam-5509	288	2	∑m	∑m	PROPN
ejpam-5509	288	3	j=1	j=1	PROPN
ejpam-5509	288	4	κ5j(t	κ5j(t	PROPN
ejpam-5509	288	5	)	)	PUNCT
ejpam-5509	288	6	,	,	PUNCT
ejpam-5509	288	7	rm(t	rm(t	NOUN
ejpam-5509	288	8	)	)	PUNCT
ejpam-5509	289	1	=	=	PUNCT
ejpam-5509	289	2	∑m	∑m	PROPN
ejpam-5509	289	3	j=1	j=1	PROPN
ejpam-5509	289	4	κ6j(t	κ6j(t	PROPN
ejpam-5509	289	5	)	)	PUNCT
ejpam-5509	289	6	.	.	PUNCT
ejpam-5509	290	1	(	(	PUNCT
ejpam-5509	290	2	24	24	NUM
ejpam-5509	290	3	)	)	PUNCT
ejpam-5509	290	4	similarly	similarly	ADV
ejpam-5509	290	5	,	,	PUNCT
ejpam-5509	290	6	||κ1m(t)||	||κ1m(t)||	PROPN
ejpam-5509	290	7	=	=	PUNCT
ejpam-5509	291	1	||sm(t)−	||sm(t)−	PROPN
ejpam-5509	291	2	s(m−1)(t)||	s(m−1)(t)||	PROPN
ejpam-5509	291	3	=	=	SYM
ejpam-5509	291	4	∥∥∥∥2	∥∥∥∥2	PROPN
ejpam-5509	291	5	(	(	PUNCT
ejpam-5509	291	6	1−	1−	NUM
ejpam-5509	291	7	ς	ς	NOUN
ejpam-5509	291	8	)	)	PUNCT
ejpam-5509	291	9	(	(	PUNCT
ejpam-5509	291	10	2−	2−	NUM
ejpam-5509	291	11	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	291	12	)	)	PUNCT
ejpam-5509	291	13	(	(	PUNCT
ejpam-5509	291	14	l1(t	l1(t	PROPN
ejpam-5509	291	15	,	,	PUNCT
ejpam-5509	291	16	s(m−1))−	s(m−1))−	PROPN
ejpam-5509	291	17	l1(t	l1(t	PROPN
ejpam-5509	291	18	,	,	PUNCT
ejpam-5509	291	19	s(m−2	s(m−2	NOUN
ejpam-5509	291	20	)	)	PUNCT
ejpam-5509	291	21	)	)	PUNCT
ejpam-5509	291	22	)	)	PUNCT
ejpam-5509	292	1	+2	+2	PROPN
ejpam-5509	292	2	ς	ς	PROPN
ejpam-5509	292	3	(	(	PUNCT
ejpam-5509	292	4	2−	2−	NUM
ejpam-5509	292	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	292	6	)	)	PUNCT
ejpam-5509	292	7	∫	∫	PROPN
ejpam-5509	292	8	t	t	PROPN
ejpam-5509	292	9	0	0	NUM
ejpam-5509	292	10	(	(	PUNCT
ejpam-5509	292	11	l1(z	l1(z	PROPN
ejpam-5509	292	12	,	,	PUNCT
ejpam-5509	292	13	s(m−1))−	s(m−1))−	PROPN
ejpam-5509	292	14	l1(z	l1(z	PROPN
ejpam-5509	292	15	,	,	PUNCT
ejpam-5509	292	16	s(m−2)))dz	s(m−2)))dz	PROPN
ejpam-5509	292	17	∥∥∥∥.	∥∥∥∥.	PROPN
ejpam-5509	292	18	(	(	PUNCT
ejpam-5509	292	19	25	25	NUM
ejpam-5509	292	20	)	)	PUNCT
ejpam-5509	292	21	equation	equation	NOUN
ejpam-5509	292	22	(	(	PUNCT
ejpam-5509	292	23	25	25	NUM
ejpam-5509	292	24	)	)	PUNCT
ejpam-5509	292	25	suggests	suggest	VERB
ejpam-5509	292	26	that	that	SCONJ
ejpam-5509	292	27	∥sm(t)−	∥sm(t)−	PROPN
ejpam-5509	292	28	s(m−1)(t)∥	s(m−1)(t)∥	VERB
ejpam-5509	292	29	≤	≤	ADV
ejpam-5509	292	30	2	2	NUM
ejpam-5509	292	31	(	(	PUNCT
ejpam-5509	292	32	1−	1−	NUM
ejpam-5509	292	33	ς	ς	NOUN
ejpam-5509	292	34	)	)	PUNCT
ejpam-5509	292	35	(	(	PUNCT
ejpam-5509	292	36	2−	2−	NUM
ejpam-5509	292	37	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	292	38	)	)	PUNCT
ejpam-5509	292	39	∥(l1(t	∥(l1(t	PROPN
ejpam-5509	292	40	,	,	PUNCT
ejpam-5509	292	41	s(m−1))−	s(m−1))−	PROPN
ejpam-5509	292	42	l1(t	l1(t	PROPN
ejpam-5509	292	43	,	,	PUNCT
ejpam-5509	292	44	s(m−2)))∥	s(m−2)))∥	PROPN
ejpam-5509	292	45	+2	+2	PROPN
ejpam-5509	292	46	ς	ς	PROPN
ejpam-5509	292	47	(	(	PUNCT
ejpam-5509	292	48	2−	2−	NUM
ejpam-5509	292	49	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	292	50	)	)	PUNCT
ejpam-5509	292	51	∥∥∥∥∫	∥∥∥∥∫	NOUN
ejpam-5509	292	52	t	t	NOUN
ejpam-5509	292	53	0	0	PUNCT
ejpam-5509	292	54	(	(	PUNCT
ejpam-5509	292	55	l1(z	l1(z	PROPN
ejpam-5509	292	56	,	,	PUNCT
ejpam-5509	292	57	s(m−1))−	s(m−1))−	PROPN
ejpam-5509	292	58	l1(z	l1(z	PROPN
ejpam-5509	292	59	,	,	PUNCT
ejpam-5509	292	60	s(m−2)))dz	s(m−2)))dz	PROPN
ejpam-5509	292	61	∥∥∥∥.(26	∥∥∥∥.(26	PROPN
ejpam-5509	292	62	)	)	PUNCT
ejpam-5509	292	63	the	the	DET
ejpam-5509	292	64	aforementioned	aforementioned	ADJ
ejpam-5509	292	65	results	result	NOUN
ejpam-5509	292	66	in	in	ADP
ejpam-5509	292	67	∥sm(t)−	∥sm(t)−	PROPN
ejpam-5509	292	68	sm−1(t)∥	sm−1(t)∥	PUNCT
ejpam-5509	293	1	≤	≤	ADV
ejpam-5509	293	2	2	2	NUM
ejpam-5509	293	3	(	(	PUNCT
ejpam-5509	293	4	1−	1−	NUM
ejpam-5509	293	5	ς	ς	NOUN
ejpam-5509	293	6	)	)	PUNCT
ejpam-5509	293	7	(	(	PUNCT
ejpam-5509	293	8	2−	2−	NUM
ejpam-5509	293	9	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	293	10	)	)	PUNCT
ejpam-5509	293	11	ϖ1∥s(m−1	ϖ1∥s(m−1	NUM
ejpam-5509	293	12	)	)	PUNCT
ejpam-5509	294	1	−	−	X
ejpam-5509	294	2	s(m−2)∥+	s(m−2)∥+	ADJ
ejpam-5509	294	3	2	2	NUM
ejpam-5509	294	4	ς	ς	PROPN
ejpam-5509	294	5	(	(	PUNCT
ejpam-5509	294	6	2−	2−	NUM
ejpam-5509	294	7	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	294	8	)	)	PUNCT
ejpam-5509	294	9	ϖ1	ϖ1	VERB
ejpam-5509	294	10	×	×	NOUN
ejpam-5509	294	11	∫	∫	PROPN
ejpam-5509	294	12	t	t	PROPN
ejpam-5509	294	13	0	0	NUM
ejpam-5509	294	14	∥s(m−1	∥s(m−1	PROPN
ejpam-5509	294	15	)	)	PUNCT
ejpam-5509	295	1	−	−	PROPN
ejpam-5509	295	2	s(m−2)∥dz	s(m−2)∥dz	PROPN
ejpam-5509	295	3	.	.	PUNCT
ejpam-5509	296	1	(	(	PUNCT
ejpam-5509	296	2	27	27	NUM
ejpam-5509	296	3	)	)	PUNCT
ejpam-5509	296	4	furthermore	furthermore	ADV
ejpam-5509	296	5	∥κ1m(t)∥	∥κ1m(t)∥	NOUN
ejpam-5509	296	6	≤	≤	NUM
ejpam-5509	296	7	2	2	NUM
ejpam-5509	296	8	(	(	PUNCT
ejpam-5509	296	9	1−	1−	NUM
ejpam-5509	296	10	ς	ς	NOUN
ejpam-5509	296	11	)	)	PUNCT
ejpam-5509	296	12	(	(	PUNCT
ejpam-5509	296	13	2−	2−	NUM
ejpam-5509	296	14	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	296	15	)	)	PUNCT
ejpam-5509	296	16	ϖ1∥κ1(m−1)(t)∥+	ϖ1∥κ1(m−1)(t)∥+	ADJ
ejpam-5509	296	17	2	2	NUM
ejpam-5509	296	18	ς	ς	PROPN
ejpam-5509	296	19	(	(	PUNCT
ejpam-5509	296	20	2−	2−	NUM
ejpam-5509	296	21	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	296	22	)	)	PUNCT
ejpam-5509	296	23	ϖ1	ϖ1	VERB
ejpam-5509	296	24	∫	∫	PROPN
ejpam-5509	296	25	t	t	PROPN
ejpam-5509	296	26	0	0	NUM
ejpam-5509	296	27	∥κ1(m−1)(z)∥dz.(28	∥κ1(m−1)(z)∥dz.(28	NUM
ejpam-5509	296	28	)	)	PUNCT
ejpam-5509	296	29	similarly	similarly	ADV
ejpam-5509	296	30	∥κ2m(t)∥	∥κ2m(t)∥	ADV
ejpam-5509	296	31	≤	≤	NUM
ejpam-5509	296	32	2	2	NUM
ejpam-5509	296	33	(	(	PUNCT
ejpam-5509	296	34	1−	1−	NUM
ejpam-5509	296	35	ς	ς	NOUN
ejpam-5509	296	36	)	)	PUNCT
ejpam-5509	296	37	(	(	PUNCT
ejpam-5509	296	38	2−	2−	NUM
ejpam-5509	296	39	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	296	40	)	)	PUNCT
ejpam-5509	296	41	ϖ2∥κ2(m−1)(t)∥+	ϖ2∥κ2(m−1)(t)∥+	ADJ
ejpam-5509	296	42	2	2	NUM
ejpam-5509	296	43	ς	ς	PROPN
ejpam-5509	296	44	(	(	PUNCT
ejpam-5509	296	45	2−	2−	NUM
ejpam-5509	296	46	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	296	47	)	)	PUNCT
ejpam-5509	296	48	ϖ2	ϖ2	NOUN
ejpam-5509	297	1	∫	∫	PROPN
ejpam-5509	297	2	t	t	PROPN
ejpam-5509	297	3	0	0	X
ejpam-5509	297	4	∥κ2(m−1)(z)∥dz	∥κ2(m−1)(z)∥dz	PROPN
ejpam-5509	297	5	,	,	PUNCT
ejpam-5509	297	6	∥κ3m(t)∥	∥κ3m(t)∥	NOUN
ejpam-5509	297	7	≤	≤	ADV
ejpam-5509	297	8	2	2	NUM
ejpam-5509	297	9	(	(	PUNCT
ejpam-5509	297	10	1−	1−	NUM
ejpam-5509	297	11	ς	ς	NOUN
ejpam-5509	297	12	)	)	PUNCT
ejpam-5509	297	13	(	(	PUNCT
ejpam-5509	297	14	2−	2−	NUM
ejpam-5509	297	15	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	297	16	)	)	PUNCT
ejpam-5509	297	17	ϖ3∥κ3(m−1)(t)∥+	ϖ3∥κ3(m−1)(t)∥+	VERB
ejpam-5509	297	18	2	2	NUM
ejpam-5509	297	19	ς	ς	PROPN
ejpam-5509	297	20	(	(	PUNCT
ejpam-5509	297	21	2−	2−	NUM
ejpam-5509	297	22	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	297	23	)	)	PUNCT
ejpam-5509	297	24	ϖ1	ϖ1	VERB
ejpam-5509	297	25	∫	∫	PROPN
ejpam-5509	297	26	t	t	PROPN
ejpam-5509	297	27	0	0	NUM
ejpam-5509	297	28	∥κ3(m−1)(z)∥dz	∥κ3(m−1)(z)∥dz	PROPN
ejpam-5509	297	29	,	,	PUNCT
ejpam-5509	297	30	∥κ4m(t)∥	∥κ4m(t)∥	VERB
ejpam-5509	297	31	≤	≤	NOUN
ejpam-5509	297	32	2(1−	2(1−	NUM
ejpam-5509	297	33	ς	ς	NOUN
ejpam-5509	297	34	)	)	PUNCT
ejpam-5509	297	35	(	(	PUNCT
ejpam-5509	297	36	2−	2−	NUM
ejpam-5509	297	37	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	297	38	)	)	PUNCT
ejpam-5509	297	39	ϖ4∥κ4(m−1)(t)∥+	ϖ4∥κ4(m−1)(t)∥+	ADJ
ejpam-5509	297	40	2	2	NUM
ejpam-5509	297	41	ς	ς	PROPN
ejpam-5509	297	42	(	(	PUNCT
ejpam-5509	297	43	2−	2−	NUM
ejpam-5509	297	44	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	297	45	)	)	PUNCT
ejpam-5509	297	46	ϖ4	ϖ4	PROPN
ejpam-5509	297	47	∫	∫	PROPN
ejpam-5509	297	48	t	t	PROPN
ejpam-5509	297	49	0	0	NUM
ejpam-5509	297	50	∥κ4(m−1)(z)∥dz	∥κ4(m−1)(z)∥dz	PROPN
ejpam-5509	297	51	,	,	PUNCT
ejpam-5509	297	52	∥κ5m(t)∥	∥κ5m(t)∥	PROPN
ejpam-5509	297	53	≤	≤	NUM
ejpam-5509	297	54	2	2	NUM
ejpam-5509	297	55	(	(	PUNCT
ejpam-5509	297	56	1−	1−	NUM
ejpam-5509	297	57	ς	ς	NOUN
ejpam-5509	297	58	)	)	PUNCT
ejpam-5509	297	59	(	(	PUNCT
ejpam-5509	297	60	2−	2−	NUM
ejpam-5509	297	61	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	297	62	)	)	PUNCT
ejpam-5509	297	63	ϖ5∥κ5(m−1)(t)∥+	ϖ5∥κ5(m−1)(t)∥+	ADJ
ejpam-5509	297	64	2	2	NUM
ejpam-5509	297	65	ς	ς	PROPN
ejpam-5509	297	66	(	(	PUNCT
ejpam-5509	297	67	2−	2−	NUM
ejpam-5509	297	68	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	297	69	)	)	PUNCT
ejpam-5509	297	70	ϖ5	ϖ5	NOUN
ejpam-5509	297	71	∫	∫	PROPN
ejpam-5509	298	1	t	t	PROPN
ejpam-5509	298	2	0	0	X
ejpam-5509	298	3	∥κ5(m−1)(z)∥dz	∥κ5(m−1)(z)∥dz	PROPN
ejpam-5509	298	4	,	,	PUNCT
ejpam-5509	298	5	∥κ6m(t)∥	∥κ6m(t)∥	PROPN
ejpam-5509	298	6	≤	≤	ADV
ejpam-5509	298	7	2	2	NUM
ejpam-5509	298	8	(	(	PUNCT
ejpam-5509	298	9	1−	1−	NUM
ejpam-5509	298	10	ς	ς	NOUN
ejpam-5509	298	11	)	)	PUNCT
ejpam-5509	298	12	(	(	PUNCT
ejpam-5509	298	13	2−	2−	NUM
ejpam-5509	298	14	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	298	15	)	)	PUNCT
ejpam-5509	298	16	ϖ6∥κ6(m−1)(t)∥+	ϖ6∥κ6(m−1)(t)∥+	VERB
ejpam-5509	298	17	2	2	NUM
ejpam-5509	298	18	ς	ς	PROPN
ejpam-5509	298	19	(	(	PUNCT
ejpam-5509	298	20	2−	2−	NUM
ejpam-5509	298	21	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	298	22	)	)	PUNCT
ejpam-5509	298	23	ϖ6	ϖ6	PROPN
ejpam-5509	298	24	∫	∫	PROPN
ejpam-5509	298	25	t	t	PROPN
ejpam-5509	298	26	0	0	NUM
ejpam-5509	298	27	∥κ6(m−1)(z)∥dz.(29	∥κ6(m−1)(z)∥dz.(29	NOUN
ejpam-5509	298	28	)	)	PUNCT
ejpam-5509	298	29	i.	i.	PROPN
ejpam-5509	298	30	ahmad	ahmad	PROPN
ejpam-5509	298	31	et	et	PROPN
ejpam-5509	298	32	al	al	PROPN
ejpam-5509	298	33	.	.	PUNCT
ejpam-5509	298	34	/	/	SYM
ejpam-5509	298	35	eur	eur	PROPN
ejpam-5509	298	36	.	.	PUNCT
ejpam-5509	299	1	j.	j.	PROPN
ejpam-5509	299	2	pure	pure	PROPN
ejpam-5509	299	3	appl	appl	PROPN
ejpam-5509	299	4	.	.	PROPN
ejpam-5509	299	5	math	math	PROPN
ejpam-5509	299	6	,	,	PUNCT
ejpam-5509	299	7	18	18	NUM
ejpam-5509	299	8	(	(	PUNCT
ejpam-5509	299	9	1	1	NUM
ejpam-5509	299	10	)	)	PUNCT
ejpam-5509	299	11	(	(	PUNCT
ejpam-5509	299	12	2025	2025	NUM
ejpam-5509	299	13	)	)	PUNCT
ejpam-5509	299	14	,	,	PUNCT
ejpam-5509	299	15	5509	5509	NUM
ejpam-5509	299	16	14	14	NUM
ejpam-5509	299	17	of	of	ADP
ejpam-5509	299	18	27	27	NUM
ejpam-5509	299	19	theorem	theorem	NOUN
ejpam-5509	299	20	3	3	NUM
ejpam-5509	299	21	.	.	PUNCT
ejpam-5509	300	1	if	if	SCONJ
ejpam-5509	300	2	there	there	PRON
ejpam-5509	300	3	exists	exist	VERB
ejpam-5509	300	4	a	a	DET
ejpam-5509	300	5	t0	t0	NOUN
ejpam-5509	300	6	such	such	ADJ
ejpam-5509	300	7	that	that	SCONJ
ejpam-5509	300	8	the	the	DET
ejpam-5509	300	9	following	follow	VERB
ejpam-5509	300	10	condition	condition	NOUN
ejpam-5509	300	11	satisfies	satisfy	VERB
ejpam-5509	300	12	2	2	NUM
ejpam-5509	300	13	(	(	PUNCT
ejpam-5509	300	14	1−	1−	NUM
ejpam-5509	300	15	ς	ς	NOUN
ejpam-5509	300	16	)	)	PUNCT
ejpam-5509	300	17	(	(	PUNCT
ejpam-5509	300	18	2−	2−	NUM
ejpam-5509	300	19	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	300	20	)	)	PUNCT
ejpam-5509	300	21	ϖ1	ϖ1	VERB
ejpam-5509	301	1	+	+	CCONJ
ejpam-5509	301	2	2	2	NUM
ejpam-5509	301	3	ς	ς	PROPN
ejpam-5509	301	4	(	(	PUNCT
ejpam-5509	301	5	2−	2−	NUM
ejpam-5509	301	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	301	7	)	)	PUNCT
ejpam-5509	301	8	ϖ1t0	ϖ1t0	X
ejpam-5509	301	9	<	<	X
ejpam-5509	301	10	1	1	NUM
ejpam-5509	301	11	,	,	PUNCT
ejpam-5509	301	12	then	then	ADV
ejpam-5509	301	13	,	,	PUNCT
ejpam-5509	301	14	exact	exact	ADJ
ejpam-5509	301	15	coupled	couple	VERB
ejpam-5509	301	16	solutions	solution	NOUN
ejpam-5509	301	17	for	for	ADP
ejpam-5509	301	18	the	the	DET
ejpam-5509	301	19	formulated	formulate	VERB
ejpam-5509	301	20	fractional	fractional	ADJ
ejpam-5509	301	21	system	system	NOUN
ejpam-5509	301	22	(	(	PUNCT
ejpam-5509	301	23	10	10	NUM
ejpam-5509	301	24	)	)	PUNCT
ejpam-5509	301	25	are	be	AUX
ejpam-5509	301	26	obtained	obtain	VERB
ejpam-5509	301	27	.	.	PUNCT
ejpam-5509	302	1	proof	proof	NOUN
ejpam-5509	302	2	.	.	PUNCT
ejpam-5509	303	1	given	give	VERB
ejpam-5509	303	2	the	the	DET
ejpam-5509	303	3	satisfaction	satisfaction	NOUN
ejpam-5509	303	4	of	of	ADP
ejpam-5509	303	5	the	the	DET
ejpam-5509	303	6	lipschitz	lipschitz	NOUN
ejpam-5509	303	7	condition	condition	NOUN
ejpam-5509	303	8	and	and	CCONJ
ejpam-5509	303	9	the	the	DET
ejpam-5509	303	10	boundedness	boundedness	NOUN
ejpam-5509	303	11	of	of	ADP
ejpam-5509	303	12	s(t	s(t	PROPN
ejpam-5509	303	13	)	)	PUNCT
ejpam-5509	303	14	,	,	PUNCT
ejpam-5509	303	15	v1(t	v1(t	CCONJ
ejpam-5509	303	16	)	)	PUNCT
ejpam-5509	303	17	,	,	PUNCT
ejpam-5509	303	18	v2(t	v2(t	NOUN
ejpam-5509	303	19	)	)	PUNCT
ejpam-5509	303	20	,	,	PUNCT
ejpam-5509	303	21	a(t	a(t	NOUN
ejpam-5509	303	22	)	)	PUNCT
ejpam-5509	303	23	,	,	PUNCT
ejpam-5509	303	24	c(t	c(t	PROPN
ejpam-5509	303	25	)	)	PUNCT
ejpam-5509	303	26	,	,	PUNCT
ejpam-5509	303	27	and	and	CCONJ
ejpam-5509	303	28	r(t	r(t	NOUN
ejpam-5509	303	29	)	)	PUNCT
ejpam-5509	303	30	,	,	PUNCT
ejpam-5509	303	31	we	we	PRON
ejpam-5509	303	32	deduce	deduce	VERB
ejpam-5509	303	33	the	the	DET
ejpam-5509	303	34	following	following	NOUN
ejpam-5509	303	35	from	from	ADP
ejpam-5509	303	36	(	(	PUNCT
ejpam-5509	303	37	28	28	NUM
ejpam-5509	303	38	)	)	PUNCT
ejpam-5509	303	39	and	and	CCONJ
ejpam-5509	303	40	(	(	PUNCT
ejpam-5509	303	41	29	29	NUM
ejpam-5509	303	42	)	)	PUNCT
ejpam-5509	303	43	.	.	PUNCT
ejpam-5509	304	1	∥κ1m(t)∥	∥κ1m(t)∥	PROPN
ejpam-5509	304	2	≤	≤	NUM
ejpam-5509	304	3	||sm(0)||	||sm(0)||	NOUN
ejpam-5509	304	4	[	[	X
ejpam-5509	304	5	(	(	PUNCT
ejpam-5509	304	6	2	2	NUM
ejpam-5509	304	7	(	(	PUNCT
ejpam-5509	304	8	1−	1−	NUM
ejpam-5509	304	9	ς	ς	NOUN
ejpam-5509	304	10	)	)	PUNCT
ejpam-5509	304	11	(	(	PUNCT
ejpam-5509	304	12	2−	2−	NUM
ejpam-5509	304	13	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	304	14	)	)	PUNCT
ejpam-5509	304	15	ϖ1	ϖ1	VERB
ejpam-5509	304	16	)	)	PUNCT
ejpam-5509	305	1	+	+	CCONJ
ejpam-5509	305	2	(	(	PUNCT
ejpam-5509	305	3	2	2	NUM
ejpam-5509	305	4	ς	ς	PROPN
ejpam-5509	305	5	(	(	PUNCT
ejpam-5509	305	6	2−	2−	NUM
ejpam-5509	305	7	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	305	8	)	)	PUNCT
ejpam-5509	305	9	ϖ1	ϖ1	PROPN
ejpam-5509	305	10	t	t	PROPN
ejpam-5509	305	11	)	)	PUNCT
ejpam-5509	306	1	]	]	X
ejpam-5509	306	2	m	m	X
ejpam-5509	306	3	,	,	PUNCT
ejpam-5509	306	4	∥κ2m(t)∥	∥κ2m(t)∥	NOUN
ejpam-5509	306	5	≤	≤	PUNCT
ejpam-5509	306	6	||v1m(0)||	||v1m(0)||	NUM
ejpam-5509	307	1	[	[	X
ejpam-5509	307	2	(	(	PUNCT
ejpam-5509	307	3	2	2	NUM
ejpam-5509	307	4	(	(	PUNCT
ejpam-5509	307	5	1−	1−	NUM
ejpam-5509	307	6	ς	ς	NOUN
ejpam-5509	307	7	)	)	PUNCT
ejpam-5509	307	8	(	(	PUNCT
ejpam-5509	307	9	2−	2−	NUM
ejpam-5509	307	10	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	307	11	)	)	PUNCT
ejpam-5509	307	12	ϖ2	ϖ2	NOUN
ejpam-5509	307	13	)	)	PUNCT
ejpam-5509	308	1	+	+	CCONJ
ejpam-5509	308	2	(	(	PUNCT
ejpam-5509	308	3	2	2	NUM
ejpam-5509	308	4	ς	ς	PROPN
ejpam-5509	308	5	(	(	PUNCT
ejpam-5509	308	6	2−	2−	NUM
ejpam-5509	308	7	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	308	8	)	)	PUNCT
ejpam-5509	308	9	ϖ2	ϖ2	NOUN
ejpam-5509	308	10	t	t	PROPN
ejpam-5509	308	11	)	)	PUNCT
ejpam-5509	308	12	]	]	X
ejpam-5509	308	13	m	m	PROPN
ejpam-5509	308	14	,	,	PUNCT
ejpam-5509	308	15	∥κ3m(t)∥	∥κ3m(t)∥	PROPN
ejpam-5509	308	16	≤	≤	NOUN
ejpam-5509	308	17	||v2m(0)||	||v2m(0)||	ADP
ejpam-5509	309	1	[	[	X
ejpam-5509	309	2	(	(	PUNCT
ejpam-5509	309	3	2	2	NUM
ejpam-5509	309	4	(	(	PUNCT
ejpam-5509	309	5	1−	1−	NUM
ejpam-5509	309	6	ς	ς	NOUN
ejpam-5509	309	7	)	)	PUNCT
ejpam-5509	309	8	(	(	PUNCT
ejpam-5509	309	9	2−	2−	NUM
ejpam-5509	309	10	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	309	11	)	)	PUNCT
ejpam-5509	309	12	ϖ3	ϖ3	NOUN
ejpam-5509	309	13	)	)	PUNCT
ejpam-5509	310	1	+	+	CCONJ
ejpam-5509	310	2	(	(	PUNCT
ejpam-5509	310	3	2	2	NUM
ejpam-5509	310	4	ς	ς	PROPN
ejpam-5509	310	5	(	(	PUNCT
ejpam-5509	310	6	2−	2−	NUM
ejpam-5509	310	7	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	310	8	)	)	PUNCT
ejpam-5509	310	9	ϖ3	ϖ3	PROPN
ejpam-5509	310	10	t	t	PROPN
ejpam-5509	310	11	)	)	PUNCT
ejpam-5509	310	12	]	]	X
ejpam-5509	310	13	m	m	X
ejpam-5509	310	14	,	,	PUNCT
ejpam-5509	310	15	∥κ4m(t)∥	∥κ4m(t)∥	VERB
ejpam-5509	310	16	≤	≤	ADJ
ejpam-5509	310	17	||am(0)||	||am(0)||	NOUN
ejpam-5509	310	18	[	[	X
ejpam-5509	310	19	(	(	PUNCT
ejpam-5509	310	20	2	2	NUM
ejpam-5509	310	21	(	(	PUNCT
ejpam-5509	310	22	1−	1−	NUM
ejpam-5509	310	23	ς	ς	NOUN
ejpam-5509	310	24	)	)	PUNCT
ejpam-5509	310	25	(	(	PUNCT
ejpam-5509	310	26	2−	2−	NUM
ejpam-5509	310	27	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	310	28	)	)	PUNCT
ejpam-5509	310	29	ϖ4	ϖ4	NOUN
ejpam-5509	310	30	)	)	PUNCT
ejpam-5509	311	1	+	+	CCONJ
ejpam-5509	311	2	(	(	PUNCT
ejpam-5509	311	3	2	2	NUM
ejpam-5509	311	4	ς	ς	PROPN
ejpam-5509	311	5	(	(	PUNCT
ejpam-5509	311	6	2−	2−	NUM
ejpam-5509	311	7	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	311	8	)	)	PUNCT
ejpam-5509	311	9	ϖ4	ϖ4	PROPN
ejpam-5509	311	10	t	t	PROPN
ejpam-5509	311	11	)	)	PUNCT
ejpam-5509	311	12	]	]	X
ejpam-5509	311	13	m	m	X
ejpam-5509	311	14	,	,	PUNCT
ejpam-5509	311	15	∥κ5m(t)∥	∥κ5m(t)∥	ADJ
ejpam-5509	311	16	≤	≤	NUM
ejpam-5509	311	17	||cm(0)||	||cm(0)||	NUM
ejpam-5509	312	1	[	[	X
ejpam-5509	312	2	(	(	PUNCT
ejpam-5509	312	3	2	2	NUM
ejpam-5509	312	4	(	(	PUNCT
ejpam-5509	312	5	1−	1−	NUM
ejpam-5509	312	6	ς	ς	NOUN
ejpam-5509	312	7	)	)	PUNCT
ejpam-5509	312	8	(	(	PUNCT
ejpam-5509	312	9	2−	2−	NUM
ejpam-5509	312	10	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	312	11	)	)	PUNCT
ejpam-5509	312	12	ϖ5	ϖ5	NOUN
ejpam-5509	312	13	)	)	PUNCT
ejpam-5509	313	1	+	+	CCONJ
ejpam-5509	313	2	(	(	PUNCT
ejpam-5509	313	3	2	2	NUM
ejpam-5509	313	4	ς	ς	PROPN
ejpam-5509	313	5	(	(	PUNCT
ejpam-5509	313	6	2−	2−	NUM
ejpam-5509	313	7	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	313	8	)	)	PUNCT
ejpam-5509	313	9	ϖ5	ϖ5	NOUN
ejpam-5509	313	10	t	t	PROPN
ejpam-5509	313	11	)	)	PUNCT
ejpam-5509	313	12	]	]	X
ejpam-5509	313	13	m	m	X
ejpam-5509	313	14	,	,	PUNCT
ejpam-5509	313	15	∥κ6m(t)∥	∥κ6m(t)∥	PROPN
ejpam-5509	313	16	≤	≤	NOUN
ejpam-5509	313	17	||rm(0)||	||rm(0)||	PRON
ejpam-5509	313	18	[	[	X
ejpam-5509	313	19	(	(	PUNCT
ejpam-5509	313	20	2	2	NUM
ejpam-5509	313	21	(	(	PUNCT
ejpam-5509	313	22	1−	1−	NUM
ejpam-5509	313	23	ς	ς	NOUN
ejpam-5509	313	24	)	)	PUNCT
ejpam-5509	313	25	(	(	PUNCT
ejpam-5509	313	26	2−	2−	NUM
ejpam-5509	313	27	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	313	28	)	)	PUNCT
ejpam-5509	313	29	ϖ6	ϖ6	NOUN
ejpam-5509	313	30	)	)	PUNCT
ejpam-5509	314	1	+	+	CCONJ
ejpam-5509	314	2	(	(	PUNCT
ejpam-5509	314	3	2	2	NUM
ejpam-5509	314	4	ς	ς	PROPN
ejpam-5509	314	5	(	(	PUNCT
ejpam-5509	314	6	2−	2−	NUM
ejpam-5509	314	7	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	314	8	)	)	PUNCT
ejpam-5509	314	9	ϖ6	ϖ6	NOUN
ejpam-5509	314	10	t	t	PROPN
ejpam-5509	314	11	)	)	PUNCT
ejpam-5509	314	12	]	]	X
ejpam-5509	314	13	m	m	X
ejpam-5509	314	14	.	.	PUNCT
ejpam-5509	315	1	(	(	PUNCT
ejpam-5509	315	2	30	30	NUM
ejpam-5509	315	3	)	)	PUNCT
ejpam-5509	315	4	consequently	consequently	ADV
ejpam-5509	315	5	,	,	PUNCT
ejpam-5509	315	6	the	the	DET
ejpam-5509	315	7	continuity	continuity	NOUN
ejpam-5509	315	8	and	and	CCONJ
ejpam-5509	315	9	existence	existence	NOUN
ejpam-5509	315	10	of	of	ADP
ejpam-5509	315	11	solutions	solution	NOUN
ejpam-5509	315	12	are	be	AUX
ejpam-5509	315	13	established	establish	VERB
ejpam-5509	315	14	.	.	PUNCT
ejpam-5509	316	1	additionally	additionally	ADV
ejpam-5509	316	2	,	,	PUNCT
ejpam-5509	316	3	it	it	PRON
ejpam-5509	316	4	is	be	AUX
ejpam-5509	316	5	imperative	imperative	ADJ
ejpam-5509	316	6	to	to	PART
ejpam-5509	316	7	demonstrate	demonstrate	VERB
ejpam-5509	316	8	that	that	SCONJ
ejpam-5509	316	9	the	the	DET
ejpam-5509	316	10	aforementioned	aforementioned	ADJ
ejpam-5509	316	11	is	be	AUX
ejpam-5509	316	12	a	a	DET
ejpam-5509	316	13	solution	solution	NOUN
ejpam-5509	316	14	of	of	ADP
ejpam-5509	316	15	the	the	DET
ejpam-5509	316	16	model	model	NOUN
ejpam-5509	316	17	(	(	PUNCT
ejpam-5509	316	18	10	10	NUM
ejpam-5509	316	19	)	)	PUNCT
ejpam-5509	316	20	,	,	PUNCT
ejpam-5509	316	21	and	and	CCONJ
ejpam-5509	316	22	we	we	PRON
ejpam-5509	316	23	proceed	proceed	VERB
ejpam-5509	316	24	with	with	ADP
ejpam-5509	316	25	the	the	DET
ejpam-5509	316	26	following	follow	VERB
ejpam-5509	316	27	steps	step	NOUN
ejpam-5509	316	28	.	.	PUNCT
ejpam-5509	317	1	s(t)−	s(t)−	PROPN
ejpam-5509	317	2	s(0	s(0	PROPN
ejpam-5509	317	3	)	)	PUNCT
ejpam-5509	317	4	=	=	SYM
ejpam-5509	317	5	sm(t)−w1m(t	sm(t)−w1m(t	NOUN
ejpam-5509	317	6	)	)	PUNCT
ejpam-5509	317	7	,	,	PUNCT
ejpam-5509	317	8	v1(t)−	v1(t)−	PROPN
ejpam-5509	317	9	v1(0	v1(0	NOUN
ejpam-5509	317	10	)	)	PUNCT
ejpam-5509	317	11	=	=	PUNCT
ejpam-5509	317	12	v1m(t)−w2m(t	v1m(t)−w2m(t	NOUN
ejpam-5509	317	13	)	)	PUNCT
ejpam-5509	317	14	,	,	PUNCT
ejpam-5509	317	15	v2(t)−	v2(t)−	PUNCT
ejpam-5509	317	16	v2(0	v2(0	NOUN
ejpam-5509	317	17	)	)	PUNCT
ejpam-5509	317	18	=	=	SYM
ejpam-5509	317	19	v2m(t)−w3m(t	v2m(t)−w3m(t	NOUN
ejpam-5509	317	20	)	)	PUNCT
ejpam-5509	317	21	,	,	PUNCT
ejpam-5509	317	22	a(t)−a(0	a(t)−a(0	PUNCT
ejpam-5509	317	23	)	)	PUNCT
ejpam-5509	317	24	=	=	SYM
ejpam-5509	317	25	am(t)−w4m(t	am(t)−w4m(t	NOUN
ejpam-5509	317	26	)	)	PUNCT
ejpam-5509	317	27	,	,	PUNCT
ejpam-5509	317	28	c(t)−	c(t)−	PROPN
ejpam-5509	317	29	c(0	c(0	PROPN
ejpam-5509	317	30	)	)	PUNCT
ejpam-5509	317	31	=	=	SYM
ejpam-5509	318	1	cm(t)−w5m(t	cm(t)−w5m(t	NOUN
ejpam-5509	318	2	)	)	PUNCT
ejpam-5509	318	3	,	,	PUNCT
ejpam-5509	318	4	r(t)−r(0	r(t)−r(0	NUM
ejpam-5509	318	5	)	)	PUNCT
ejpam-5509	318	6	=	=	SYM
ejpam-5509	318	7	rm(t)−w6m(t	rm(t)−w6m(t	NOUN
ejpam-5509	318	8	)	)	PUNCT
ejpam-5509	318	9	.	.	PUNCT
ejpam-5509	319	1	(	(	PUNCT
ejpam-5509	319	2	31	31	NUM
ejpam-5509	319	3	)	)	PUNCT
ejpam-5509	319	4	subsequently	subsequently	ADV
ejpam-5509	319	5	,	,	PUNCT
ejpam-5509	319	6	we	we	PRON
ejpam-5509	319	7	proceed	proceed	VERB
ejpam-5509	319	8	to	to	ADP
ejpam-5509	319	9	the	the	DET
ejpam-5509	319	10	following	follow	VERB
ejpam-5509	319	11	stage	stage	NOUN
ejpam-5509	319	12	.	.	PUNCT
ejpam-5509	320	1	∥bm(t)∥	∥bm(t)∥	PROPN
ejpam-5509	320	2	=	=	SYM
ejpam-5509	320	3	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5509	320	4	2(1−	2(1−	PROPN
ejpam-5509	320	5	ς	ς	NOUN
ejpam-5509	320	6	)	)	PUNCT
ejpam-5509	320	7	(	(	PUNCT
ejpam-5509	320	8	2−	2−	NUM
ejpam-5509	320	9	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	320	10	)	)	PUNCT
ejpam-5509	320	11	(	(	PUNCT
ejpam-5509	320	12	l1(t	l1(t	PROPN
ejpam-5509	320	13	,	,	PUNCT
ejpam-5509	320	14	sm)−	sm)−	NOUN
ejpam-5509	320	15	l1(t	l1(t	PROPN
ejpam-5509	320	16	,	,	PUNCT
ejpam-5509	320	17	s(m−1	s(m−1	PROPN
ejpam-5509	320	18	)	)	PUNCT
ejpam-5509	320	19	)	)	PUNCT
ejpam-5509	320	20	)	)	PUNCT
ejpam-5509	321	1	+	+	CCONJ
ejpam-5509	321	2	2ς	2ς	NUM
ejpam-5509	321	3	(	(	PUNCT
ejpam-5509	321	4	2−	2−	NUM
ejpam-5509	321	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	321	6	)	)	PUNCT
ejpam-5509	321	7	×∫	×∫	PROPN
ejpam-5509	321	8	t	t	PROPN
ejpam-5509	321	9	0	0	NUM
ejpam-5509	321	10	(	(	PUNCT
ejpam-5509	321	11	l1(z	l1(z	PROPN
ejpam-5509	321	12	,	,	PUNCT
ejpam-5509	321	13	sm)−	sm)−	NOUN
ejpam-5509	321	14	l1(z	l1(z	PROPN
ejpam-5509	321	15	,	,	PUNCT
ejpam-5509	321	16	s(m−1)))dz	s(m−1)))dz	PROPN
ejpam-5509	321	17	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ejpam-5509	321	18	,	,	PUNCT
ejpam-5509	321	19	i.	i.	PROPN
ejpam-5509	321	20	ahmad	ahmad	PROPN
ejpam-5509	321	21	et	et	PROPN
ejpam-5509	321	22	al	al	PROPN
ejpam-5509	321	23	.	.	PUNCT
ejpam-5509	321	24	/	/	SYM
ejpam-5509	321	25	eur	eur	PROPN
ejpam-5509	321	26	.	.	PUNCT
ejpam-5509	322	1	j.	j.	PROPN
ejpam-5509	322	2	pure	pure	PROPN
ejpam-5509	322	3	appl	appl	PROPN
ejpam-5509	322	4	.	.	PROPN
ejpam-5509	322	5	math	math	PROPN
ejpam-5509	322	6	,	,	PUNCT
ejpam-5509	322	7	18	18	NUM
ejpam-5509	322	8	(	(	PUNCT
ejpam-5509	322	9	1	1	NUM
ejpam-5509	322	10	)	)	PUNCT
ejpam-5509	322	11	(	(	PUNCT
ejpam-5509	322	12	2025	2025	NUM
ejpam-5509	322	13	)	)	PUNCT
ejpam-5509	322	14	,	,	PUNCT
ejpam-5509	322	15	5509	5509	NUM
ejpam-5509	322	16	15	15	NUM
ejpam-5509	322	17	of	of	ADP
ejpam-5509	322	18	27	27	NUM
ejpam-5509	322	19	≤	≤	NOUN
ejpam-5509	322	20	2(1−	2(1−	NUM
ejpam-5509	322	21	ς	ς	NOUN
ejpam-5509	322	22	)	)	PUNCT
ejpam-5509	322	23	(	(	PUNCT
ejpam-5509	322	24	2−	2−	NUM
ejpam-5509	322	25	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	322	26	)	)	PUNCT
ejpam-5509	322	27	∥(l1(t	∥(l1(t	PROPN
ejpam-5509	322	28	,	,	PUNCT
ejpam-5509	322	29	sm)−	sm)−	NUM
ejpam-5509	322	30	(	(	PUNCT
ejpam-5509	322	31	l1(t	l1(t	PROPN
ejpam-5509	322	32	,	,	PUNCT
ejpam-5509	322	33	s(m−1)))∥+	s(m−1)))∥+	ADJ
ejpam-5509	322	34	2ς	2ς	NUM
ejpam-5509	322	35	(	(	PUNCT
ejpam-5509	322	36	2−	2−	NUM
ejpam-5509	322	37	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	322	38	)	)	PUNCT
ejpam-5509	322	39	×∫	×∫	VERB
ejpam-5509	322	40	t	t	PROPN
ejpam-5509	322	41	0	0	NUM
ejpam-5509	322	42	||(l1(z	||(l1(z	PROPN
ejpam-5509	322	43	,	,	PUNCT
ejpam-5509	322	44	s)−	s)−	PROPN
ejpam-5509	322	45	l1(z	l1(z	PROPN
ejpam-5509	322	46	,	,	PUNCT
ejpam-5509	322	47	s(m−1)))||dz	s(m−1)))||dz	NOUN
ejpam-5509	322	48	,	,	PUNCT
ejpam-5509	322	49	≤	≤	NUM
ejpam-5509	322	50	2(1−	2(1−	NUM
ejpam-5509	322	51	ς	ς	NOUN
ejpam-5509	322	52	)	)	PUNCT
ejpam-5509	322	53	(	(	PUNCT
ejpam-5509	322	54	2−	2−	NUM
ejpam-5509	322	55	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	322	56	)	)	PUNCT
ejpam-5509	322	57	ϖ1∥s	ϖ1∥s	NOUN
ejpam-5509	322	58	−	−	NOUN
ejpam-5509	322	59	s(m−1)∥+	s(m−1)∥+	ADJ
ejpam-5509	322	60	2ς	2ς	NOUN
ejpam-5509	322	61	(	(	PUNCT
ejpam-5509	322	62	2−	2−	NUM
ejpam-5509	322	63	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	322	64	)	)	PUNCT
ejpam-5509	322	65	ϖ1∥s	ϖ1∥s	NOUN
ejpam-5509	322	66	−	−	PROPN
ejpam-5509	322	67	s(m−1)∥t	s(m−1)∥t	PROPN
ejpam-5509	322	68	.	.	PUNCT
ejpam-5509	323	1	(	(	PUNCT
ejpam-5509	323	2	32	32	NUM
ejpam-5509	323	3	)	)	PUNCT
ejpam-5509	323	4	moreover	moreover	ADV
ejpam-5509	323	5	,	,	PUNCT
ejpam-5509	323	6	∥w1m(t)∥	∥w1m(t)∥	PROPN
ejpam-5509	323	7	≤	≤	NOUN
ejpam-5509	323	8	(	(	PUNCT
ejpam-5509	323	9	2(1−	2(1−	NUM
ejpam-5509	323	10	ς	ς	NOUN
ejpam-5509	323	11	)	)	PUNCT
ejpam-5509	323	12	(	(	PUNCT
ejpam-5509	323	13	2−	2−	NUM
ejpam-5509	323	14	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	323	15	)	)	PUNCT
ejpam-5509	323	16	+	+	NUM
ejpam-5509	323	17	2ς	2ς	NUM
ejpam-5509	323	18	(	(	PUNCT
ejpam-5509	323	19	2−	2−	NUM
ejpam-5509	323	20	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	323	21	)	)	PUNCT
ejpam-5509	323	22	t	t	NOUN
ejpam-5509	323	23	)	)	PUNCT
ejpam-5509	323	24	nm+1	nm+1	PROPN
ejpam-5509	323	25	µm+1	µm+1	PROPN
ejpam-5509	323	26	1	1	NUM
ejpam-5509	323	27	a.	a.	NOUN
ejpam-5509	323	28	(	(	PUNCT
ejpam-5509	323	29	33	33	NUM
ejpam-5509	323	30	)	)	PUNCT
ejpam-5509	323	31	at	at	ADP
ejpam-5509	323	32	the	the	DET
ejpam-5509	323	33	temporal	temporal	ADJ
ejpam-5509	323	34	point	point	NOUN
ejpam-5509	323	35	t0	t0	PROPN
ejpam-5509	323	36	,	,	PUNCT
ejpam-5509	323	37	we	we	PRON
ejpam-5509	323	38	have	have	VERB
ejpam-5509	323	39	∥w1m(t)∥	∥w1m(t)∥	PROPN
ejpam-5509	323	40	≤	≤	NOUN
ejpam-5509	323	41	(	(	PUNCT
ejpam-5509	323	42	2(1−	2(1−	NUM
ejpam-5509	323	43	ς	ς	NOUN
ejpam-5509	323	44	)	)	PUNCT
ejpam-5509	323	45	(	(	PUNCT
ejpam-5509	323	46	2−	2−	NUM
ejpam-5509	323	47	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	323	48	)	)	PUNCT
ejpam-5509	324	1	+	+	NUM
ejpam-5509	324	2	2ς	2ς	NUM
ejpam-5509	324	3	(	(	PUNCT
ejpam-5509	324	4	2−	2−	NUM
ejpam-5509	324	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	324	6	)	)	PUNCT
ejpam-5509	324	7	t0	t0	PROPN
ejpam-5509	324	8	)	)	PUNCT
ejpam-5509	325	1	m+1	m+1	PROPN
ejpam-5509	325	2	µm+1	µm+1	PROPN
ejpam-5509	325	3	1	1	NUM
ejpam-5509	325	4	a.	a.	NOUN
ejpam-5509	325	5	(	(	PUNCT
ejpam-5509	325	6	34	34	NUM
ejpam-5509	325	7	)	)	PUNCT
ejpam-5509	325	8	employing	employ	VERB
ejpam-5509	325	9	identical	identical	ADJ
ejpam-5509	325	10	procedures	procedure	NOUN
ejpam-5509	325	11	and	and	CCONJ
ejpam-5509	325	12	utilizing	utilize	VERB
ejpam-5509	325	13	(	(	PUNCT
ejpam-5509	325	14	34	34	NUM
ejpam-5509	325	15	)	)	PUNCT
ejpam-5509	325	16	,	,	PUNCT
ejpam-5509	325	17	we	we	PRON
ejpam-5509	325	18	have	have	VERB
ejpam-5509	325	19	∥w1m(t)∥	∥w1m(t)∥	NOUN
ejpam-5509	325	20	−→	−→	NOUN
ejpam-5509	325	21	0	0	NUM
ejpam-5509	325	22	,	,	PUNCT
ejpam-5509	325	23	n→	n→	PUNCT
ejpam-5509	325	24	∞.	∞.	PROPN
ejpam-5509	325	25	similarly	similarly	ADV
ejpam-5509	325	26	,	,	PUNCT
ejpam-5509	325	27	we	we	PRON
ejpam-5509	325	28	deduce	deduce	VERB
ejpam-5509	325	29	that	that	SCONJ
ejpam-5509	325	30	the	the	DET
ejpam-5509	325	31	functions	function	NOUN
ejpam-5509	325	32	w2m(t),w3m(t),w4m(t),w5m(t),w6m(t	w2m(t),w3m(t),w4m(t),w5m(t),w6m(t	NOUN
ejpam-5509	325	33	)	)	PUNCT
ejpam-5509	325	34	converge	converge	VERB
ejpam-5509	325	35	to	to	ADP
ejpam-5509	325	36	zero	zero	NUM
ejpam-5509	325	37	as	as	ADP
ejpam-5509	325	38	the	the	DET
ejpam-5509	325	39	parameter	parameter	NOUN
ejpam-5509	325	40	m	m	PROPN
ejpam-5509	325	41	approaches	approach	VERB
ejpam-5509	325	42	∞.	∞.	PROPN
ejpam-5509	325	43	in	in	ADP
ejpam-5509	325	44	order	order	NOUN
ejpam-5509	325	45	to	to	PART
ejpam-5509	325	46	establish	establish	VERB
ejpam-5509	325	47	the	the	DET
ejpam-5509	325	48	uniqueness	uniqueness	NOUN
ejpam-5509	325	49	of	of	ADP
ejpam-5509	325	50	the	the	DET
ejpam-5509	325	51	solution	solution	NOUN
ejpam-5509	325	52	for	for	ADP
ejpam-5509	325	53	the	the	DET
ejpam-5509	325	54	system	system	NOUN
ejpam-5509	325	55	(	(	PUNCT
ejpam-5509	325	56	10	10	NUM
ejpam-5509	325	57	)	)	PUNCT
ejpam-5509	325	58	,	,	PUNCT
ejpam-5509	325	59	we	we	PRON
ejpam-5509	325	60	assume	assume	VERB
ejpam-5509	325	61	an	an	DET
ejpam-5509	325	62	alternative	alternative	ADJ
ejpam-5509	325	63	solution	solution	NOUN
ejpam-5509	325	64	denoted	denote	VERB
ejpam-5509	325	65	as	as	ADP
ejpam-5509	325	66	(	(	PUNCT
ejpam-5509	325	67	s1(t	s1(t	X
ejpam-5509	325	68	)	)	PUNCT
ejpam-5509	325	69	,	,	PUNCT
ejpam-5509	325	70	v11(t	v11(t	ADJ
ejpam-5509	325	71	)	)	PUNCT
ejpam-5509	325	72	,	,	PUNCT
ejpam-5509	325	73	v21(t	v21(t	PROPN
ejpam-5509	325	74	)	)	PUNCT
ejpam-5509	325	75	,	,	PUNCT
ejpam-5509	325	76	a1(t	a1(t	PROPN
ejpam-5509	325	77	)	)	PUNCT
ejpam-5509	325	78	,	,	PUNCT
ejpam-5509	325	79	c1(t	c1(t	NOUN
ejpam-5509	325	80	)	)	PUNCT
ejpam-5509	325	81	r1(t	r1(t	PROPN
ejpam-5509	325	82	)	)	PUNCT
ejpam-5509	325	83	)	)	PUNCT
ejpam-5509	325	84	.	.	PUNCT
ejpam-5509	326	1	s(t)−	s(t)−	PROPN
ejpam-5509	326	2	s1(t	s1(t	PROPN
ejpam-5509	326	3	)	)	PUNCT
ejpam-5509	326	4	=	=	PUNCT
ejpam-5509	327	1	2(1−	2(1−	NUM
ejpam-5509	327	2	ς	ς	NOUN
ejpam-5509	327	3	)	)	PUNCT
ejpam-5509	327	4	(	(	PUNCT
ejpam-5509	327	5	2−	2−	NUM
ejpam-5509	327	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	327	7	)	)	PUNCT
ejpam-5509	327	8	(	(	PUNCT
ejpam-5509	327	9	l1(t	l1(t	PROPN
ejpam-5509	327	10	,	,	PUNCT
ejpam-5509	327	11	s)−	s)−	PROPN
ejpam-5509	327	12	l1(t	l1(t	PROPN
ejpam-5509	327	13	,	,	PUNCT
ejpam-5509	327	14	s1	s1	NOUN
ejpam-5509	327	15	)	)	PUNCT
ejpam-5509	327	16	)	)	PUNCT
ejpam-5509	328	1	+	+	CCONJ
ejpam-5509	328	2	2ς	2ς	NUM
ejpam-5509	328	3	(	(	PUNCT
ejpam-5509	328	4	2−	2−	NUM
ejpam-5509	328	5	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	328	6	)	)	PUNCT
ejpam-5509	328	7	×∫	×∫	PROPN
ejpam-5509	328	8	t	t	PROPN
ejpam-5509	328	9	0	0	NUM
ejpam-5509	328	10	(	(	PUNCT
ejpam-5509	328	11	l1(z	l1(z	PROPN
ejpam-5509	328	12	,	,	PUNCT
ejpam-5509	328	13	s)−	s)−	PROPN
ejpam-5509	328	14	l1(z	l1(z	PROPN
ejpam-5509	328	15	,	,	PUNCT
ejpam-5509	328	16	s1	s1	NOUN
ejpam-5509	328	17	)	)	PUNCT
ejpam-5509	328	18	)	)	PUNCT
ejpam-5509	329	1	dz	dz	PROPN
ejpam-5509	329	2	.	.	PUNCT
ejpam-5509	330	1	(	(	PUNCT
ejpam-5509	330	2	35	35	NUM
ejpam-5509	330	3	)	)	PUNCT
ejpam-5509	330	4	applying	apply	VERB
ejpam-5509	330	5	a	a	DET
ejpam-5509	330	6	norm	norm	NOUN
ejpam-5509	330	7	to	to	ADP
ejpam-5509	330	8	(	(	PUNCT
ejpam-5509	330	9	35	35	NUM
ejpam-5509	330	10	)	)	PUNCT
ejpam-5509	330	11	,	,	PUNCT
ejpam-5509	330	12	we	we	PRON
ejpam-5509	330	13	obtain	obtain	VERB
ejpam-5509	330	14	∥s(t)−	∥s(t)−	PROPN
ejpam-5509	330	15	s1(t)∥	s1(t)∥	ADP
ejpam-5509	330	16	≤	≤	NUM
ejpam-5509	331	1	2(1−	2(1−	NUM
ejpam-5509	331	2	ς	ς	NOUN
ejpam-5509	331	3	)	)	PUNCT
ejpam-5509	331	4	(	(	PUNCT
ejpam-5509	331	5	2−	2−	NUM
ejpam-5509	331	6	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	331	7	)	)	PUNCT
ejpam-5509	331	8	∥l1(t	∥l1(t	ADJ
ejpam-5509	331	9	,	,	PUNCT
ejpam-5509	331	10	s)−	s)−	PROPN
ejpam-5509	331	11	l1(t	l1(t	PROPN
ejpam-5509	331	12	,	,	PUNCT
ejpam-5509	331	13	s1)∥+	s1)∥+	ADJ
ejpam-5509	331	14	2ℓ	2ℓ	NOUN
ejpam-5509	331	15	(	(	PUNCT
ejpam-5509	331	16	2−	2−	NUM
ejpam-5509	331	17	ℓ)u(ℓ	ℓ)u(ℓ	NOUN
ejpam-5509	331	18	)	)	PUNCT
ejpam-5509	331	19	×∫	×∫	ADJ
ejpam-5509	331	20	t	t	PROPN
ejpam-5509	331	21	0	0	NUM
ejpam-5509	331	22	∥l1(z	∥l1(z	PROPN
ejpam-5509	331	23	,	,	PUNCT
ejpam-5509	331	24	sh)−	sh)−	PROPN
ejpam-5509	331	25	l1(z	l1(z	SYM
ejpam-5509	331	26	,	,	PUNCT
ejpam-5509	331	27	s1h)∥dz	s1h)∥dz	ADJ
ejpam-5509	331	28	.	.	PUNCT
ejpam-5509	332	1	(	(	PUNCT
ejpam-5509	332	2	36	36	NUM
ejpam-5509	332	3	)	)	PUNCT
ejpam-5509	332	4	here	here	ADV
ejpam-5509	332	5	,	,	PUNCT
ejpam-5509	332	6	we	we	PRON
ejpam-5509	332	7	establish	establish	VERB
ejpam-5509	332	8	the	the	DET
ejpam-5509	332	9	following	following	NOUN
ejpam-5509	332	10	via	via	ADP
ejpam-5509	332	11	the	the	DET
ejpam-5509	332	12	lipschitz	lipschitz	NOUN
ejpam-5509	332	13	condition	condition	NOUN
ejpam-5509	332	14	.	.	PUNCT
ejpam-5509	333	1	∥s(t)−	∥s(t)−	PROPN
ejpam-5509	333	2	s1(t)∥	s1(t)∥	VERB
ejpam-5509	333	3	≤	≤	NUM
ejpam-5509	333	4	2(1−	2(1−	NUM
ejpam-5509	333	5	ς	ς	NOUN
ejpam-5509	333	6	)	)	PUNCT
ejpam-5509	333	7	(	(	PUNCT
ejpam-5509	333	8	2−	2−	NUM
ejpam-5509	333	9	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	333	10	)	)	PUNCT
ejpam-5509	333	11	ϖ1∥sh(t)−	ϖ1∥sh(t)−	PROPN
ejpam-5509	333	12	s1(t)∥+	s1(t)∥+	ADJ
ejpam-5509	333	13	2ς	2ς	NUM
ejpam-5509	333	14	(	(	PUNCT
ejpam-5509	333	15	2−	2−	NUM
ejpam-5509	333	16	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	333	17	)	)	PUNCT
ejpam-5509	333	18	×∫	×∫	PROPN
ejpam-5509	333	19	t	t	PROPN
ejpam-5509	333	20	0	0	NUM
ejpam-5509	333	21	ϖ1t∥s(t)−	ϖ1t∥s(t)−	PROPN
ejpam-5509	333	22	s1(t)∥dz	s1(t)∥dz	PROPN
ejpam-5509	333	23	.	.	PUNCT
ejpam-5509	334	1	(	(	PUNCT
ejpam-5509	334	2	37	37	NUM
ejpam-5509	334	3	)	)	PUNCT
ejpam-5509	334	4	this	this	PRON
ejpam-5509	334	5	implies	imply	VERB
ejpam-5509	334	6	that	that	SCONJ
ejpam-5509	334	7	∥s(t)−	∥s(t)−	PROPN
ejpam-5509	334	8	s1(t)∥	s1(t)∥	PROPN
ejpam-5509	334	9	(	(	PUNCT
ejpam-5509	334	10	1−	1−	NUM
ejpam-5509	334	11	2(1−	2(1−	NUM
ejpam-5509	334	12	ς	ς	NOUN
ejpam-5509	334	13	)	)	PUNCT
ejpam-5509	334	14	(	(	PUNCT
ejpam-5509	334	15	2−	2−	NUM
ejpam-5509	334	16	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	334	17	)	)	PUNCT
ejpam-5509	334	18	ϖ1	ϖ1	VERB
ejpam-5509	334	19	−	−	NOUN
ejpam-5509	334	20	2ς	2ς	NUM
ejpam-5509	334	21	(	(	PUNCT
ejpam-5509	334	22	2−	2−	NUM
ejpam-5509	334	23	ℓ)u(ς	ℓ)u(ς	NOUN
ejpam-5509	334	24	)	)	PUNCT
ejpam-5509	334	25	ϖ1	ϖ1	PROPN
ejpam-5509	334	26	t	t	PROPN
ejpam-5509	334	27	)	)	PUNCT
ejpam-5509	334	28	≤	≤	NOUN
ejpam-5509	334	29	0	0	NUM
ejpam-5509	334	30	.	.	PUNCT
ejpam-5509	335	1	(	(	PUNCT
ejpam-5509	335	2	38	38	NUM
ejpam-5509	335	3	)	)	PUNCT
ejpam-5509	335	4	i.	i.	PROPN
ejpam-5509	335	5	ahmad	ahmad	PROPN
ejpam-5509	335	6	et	et	PROPN
ejpam-5509	335	7	al	al	PROPN
ejpam-5509	335	8	.	.	PUNCT
ejpam-5509	335	9	/	/	SYM
ejpam-5509	335	10	eur	eur	PROPN
ejpam-5509	335	11	.	.	PUNCT
ejpam-5509	336	1	j.	j.	PROPN
ejpam-5509	336	2	pure	pure	PROPN
ejpam-5509	336	3	appl	appl	PROPN
ejpam-5509	336	4	.	.	PROPN
ejpam-5509	336	5	math	math	PROPN
ejpam-5509	336	6	,	,	PUNCT
ejpam-5509	336	7	18	18	NUM
ejpam-5509	336	8	(	(	PUNCT
ejpam-5509	336	9	1	1	NUM
ejpam-5509	336	10	)	)	PUNCT
ejpam-5509	336	11	(	(	PUNCT
ejpam-5509	336	12	2025	2025	NUM
ejpam-5509	336	13	)	)	PUNCT
ejpam-5509	336	14	,	,	PUNCT
ejpam-5509	336	15	5509	5509	NUM
ejpam-5509	336	16	16	16	NUM
ejpam-5509	336	17	of	of	ADP
ejpam-5509	336	18	27	27	NUM
ejpam-5509	336	19	theorem	theorem	NOUN
ejpam-5509	336	20	4	4	NUM
ejpam-5509	336	21	.	.	PUNCT
ejpam-5509	337	1	if	if	SCONJ
ejpam-5509	337	2	the	the	DET
ejpam-5509	337	3	condition	condition	NOUN
ejpam-5509	337	4	expressed	express	VERB
ejpam-5509	337	5	by	by	ADP
ejpam-5509	337	6	the	the	DET
ejpam-5509	337	7	following	follow	VERB
ejpam-5509	337	8	equation	equation	NOUN
ejpam-5509	337	9	is	be	AUX
ejpam-5509	337	10	satisfied	satisfied	ADJ
ejpam-5509	337	11	(	(	PUNCT
ejpam-5509	337	12	1−	1−	NUM
ejpam-5509	337	13	2(1−	2(1−	NUM
ejpam-5509	337	14	ς	ς	NOUN
ejpam-5509	337	15	)	)	PUNCT
ejpam-5509	337	16	(	(	PUNCT
ejpam-5509	337	17	2−	2−	NUM
ejpam-5509	337	18	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	337	19	)	)	PUNCT
ejpam-5509	337	20	ϖ1	ϖ1	VERB
ejpam-5509	337	21	−	−	NOUN
ejpam-5509	337	22	2ς	2ς	NUM
ejpam-5509	337	23	(	(	PUNCT
ejpam-5509	337	24	2−	2−	NUM
ejpam-5509	337	25	ς)u(ς	ς)u(ς	NOUN
ejpam-5509	337	26	)	)	PUNCT
ejpam-5509	337	27	ϖ1	ϖ1	PROPN
ejpam-5509	337	28	t	t	PROPN
ejpam-5509	337	29	)	)	PUNCT
ejpam-5509	337	30	>	>	X
ejpam-5509	338	1	0	0	X
ejpam-5509	338	2	.	.	PUNCT
ejpam-5509	339	1	(	(	PUNCT
ejpam-5509	339	2	39	39	NUM
ejpam-5509	339	3	)	)	PUNCT
ejpam-5509	339	4	then	then	ADV
ejpam-5509	339	5	the	the	DET
ejpam-5509	339	6	system	system	NOUN
ejpam-5509	339	7	(	(	PUNCT
ejpam-5509	339	8	10	10	NUM
ejpam-5509	339	9	)	)	PUNCT
ejpam-5509	339	10	possesses	possess	VERB
ejpam-5509	339	11	a	a	DET
ejpam-5509	339	12	unique	unique	ADJ
ejpam-5509	339	13	solution	solution	NOUN
ejpam-5509	339	14	.	.	PUNCT
ejpam-5509	340	1	proof	proof	NOUN
ejpam-5509	340	2	.	.	PUNCT
ejpam-5509	341	1	assuming	assume	VERB
ejpam-5509	341	2	that	that	SCONJ
ejpam-5509	341	3	the	the	DET
ejpam-5509	341	4	expression	expression	NOUN
ejpam-5509	341	5	in	in	ADP
ejpam-5509	341	6	(	(	PUNCT
ejpam-5509	341	7	39	39	NUM
ejpam-5509	341	8	)	)	PUNCT
ejpam-5509	341	9	holds	hold	VERB
ejpam-5509	341	10	,	,	PUNCT
ejpam-5509	341	11	the	the	DET
ejpam-5509	341	12	subsequent	subsequent	ADJ
ejpam-5509	341	13	(	(	PUNCT
ejpam-5509	341	14	38	38	NUM
ejpam-5509	341	15	)	)	PUNCT
ejpam-5509	341	16	yields	yield	VERB
ejpam-5509	341	17	the	the	DET
ejpam-5509	341	18	following	follow	VERB
ejpam-5509	341	19	expression	expression	NOUN
ejpam-5509	341	20	∥s(t)−	∥s(t)−	PROPN
ejpam-5509	341	21	s1(t)∥	s1(t)∥	ADP
ejpam-5509	341	22	=	=	SYM
ejpam-5509	342	1	0	0	X
ejpam-5509	342	2	.	.	PUNCT
ejpam-5509	343	1	(	(	PUNCT
ejpam-5509	343	2	40	40	NUM
ejpam-5509	343	3	)	)	PUNCT
ejpam-5509	343	4	consequently	consequently	ADV
ejpam-5509	343	5	,	,	PUNCT
ejpam-5509	343	6	we	we	PRON
ejpam-5509	343	7	obtain	obtain	VERB
ejpam-5509	343	8	s(t	s(t	NUM
ejpam-5509	343	9	)	)	PUNCT
ejpam-5509	343	10	=	=	PUNCT
ejpam-5509	344	1	s1(t	s1(t	PROPN
ejpam-5509	344	2	)	)	PUNCT
ejpam-5509	344	3	.	.	PUNCT
ejpam-5509	345	1	(	(	PUNCT
ejpam-5509	345	2	41	41	NUM
ejpam-5509	345	3	)	)	PUNCT
ejpam-5509	345	4	similarly	similarly	ADV
ejpam-5509	345	5	,	,	PUNCT
ejpam-5509	345	6	we	we	PRON
ejpam-5509	345	7	achieve	achieve	VERB
ejpam-5509	345	8	the	the	DET
ejpam-5509	345	9	following	following	NOUN
ejpam-5509	345	10	v1(t	v1(t	PART
ejpam-5509	345	11	)	)	PUNCT
ejpam-5509	345	12	=	=	SYM
ejpam-5509	345	13	v11(t	v11(t	ADJ
ejpam-5509	345	14	)	)	PUNCT
ejpam-5509	345	15	,	,	PUNCT
ejpam-5509	345	16	v2(t	v2(t	X
ejpam-5509	345	17	)	)	PUNCT
ejpam-5509	345	18	=	=	SYM
ejpam-5509	345	19	v21(t	v21(t	NOUN
ejpam-5509	345	20	)	)	PUNCT
ejpam-5509	345	21	,	,	PUNCT
ejpam-5509	345	22	a(t	a(t	NOUN
ejpam-5509	345	23	)	)	PUNCT
ejpam-5509	345	24	=	=	SYM
ejpam-5509	346	1	a1(t	a1(t	PROPN
ejpam-5509	346	2	)	)	PUNCT
ejpam-5509	346	3	,	,	PUNCT
ejpam-5509	346	4	c(t	c(t	PROPN
ejpam-5509	346	5	)	)	PUNCT
ejpam-5509	346	6	=	=	SYM
ejpam-5509	346	7	c1(t	c1(t	NOUN
ejpam-5509	346	8	)	)	PUNCT
ejpam-5509	346	9	,	,	PUNCT
ejpam-5509	346	10	r(t	r(t	NOUN
ejpam-5509	346	11	)	)	PUNCT
ejpam-5509	346	12	=	=	SYM
ejpam-5509	346	13	r1(t	r1(t	PROPN
ejpam-5509	346	14	)	)	PUNCT
ejpam-5509	346	15	.	.	PUNCT
ejpam-5509	347	1	4	4	X
ejpam-5509	347	2	.	.	X
ejpam-5509	347	3	computational	computational	ADJ
ejpam-5509	347	4	scheme	scheme	NOUN
ejpam-5509	347	5	for	for	ADP
ejpam-5509	347	6	the	the	DET
ejpam-5509	347	7	model	model	NOUN
ejpam-5509	347	8	here	here	ADV
ejpam-5509	347	9	we	we	PRON
ejpam-5509	347	10	provide	provide	VERB
ejpam-5509	347	11	the	the	DET
ejpam-5509	347	12	numerical	numerical	ADJ
ejpam-5509	347	13	solution	solution	NOUN
ejpam-5509	347	14	for	for	ADP
ejpam-5509	347	15	the	the	DET
ejpam-5509	347	16	proposed	propose	VERB
ejpam-5509	347	17	fractional	fractional	ADJ
ejpam-5509	347	18	model	model	NOUN
ejpam-5509	347	19	(	(	PUNCT
ejpam-5509	347	20	10	10	NUM
ejpam-5509	347	21	)	)	PUNCT
ejpam-5509	347	22	utilizing	utilize	VERB
ejpam-5509	347	23	the	the	DET
ejpam-5509	347	24	approach	approach	NOUN
ejpam-5509	347	25	outlined	outline	VERB
ejpam-5509	347	26	in	in	ADP
ejpam-5509	347	27	[	[	X
ejpam-5509	347	28	12	12	NUM
ejpam-5509	347	29	]	]	PUNCT
ejpam-5509	347	30	.	.	PUNCT
ejpam-5509	348	1	the	the	DET
ejpam-5509	348	2	subsequent	subsequent	ADJ
ejpam-5509	348	3	steps	step	NOUN
ejpam-5509	348	4	adhere	adhere	VERB
ejpam-5509	348	5	to	to	ADP
ejpam-5509	348	6	the	the	DET
ejpam-5509	348	7	procedure	procedure	NOUN
ejpam-5509	348	8	outlined	outline	VERB
ejpam-5509	348	9	for	for	ADP
ejpam-5509	348	10	solving	solve	VERB
ejpam-5509	348	11	(	(	PUNCT
ejpam-5509	348	12	10	10	NUM
ejpam-5509	348	13	):	):	PUNCT
ejpam-5509	348	14	s(t)−	s(t)−	PROPN
ejpam-5509	348	15	s(0	s(0	PROPN
ejpam-5509	348	16	)	)	PUNCT
ejpam-5509	348	17	=	=	PUNCT
ejpam-5509	349	1	(	(	PUNCT
ejpam-5509	349	2	1−	1−	NUM
ejpam-5509	349	3	ς	ς	NOUN
ejpam-5509	349	4	)	)	PUNCT
ejpam-5509	349	5	b(ς	b(ς	PROPN
ejpam-5509	349	6	)	)	PUNCT
ejpam-5509	349	7	f1(t	f1(t	PROPN
ejpam-5509	349	8	,	,	PUNCT
ejpam-5509	349	9	s	s	PART
ejpam-5509	349	10	)	)	PUNCT
ejpam-5509	350	1	+	+	CCONJ
ejpam-5509	350	2	ς	ς	PROPN
ejpam-5509	350	3	b(ς	b(ς	PROPN
ejpam-5509	350	4	)	)	PUNCT
ejpam-5509	350	5	∫	∫	PROPN
ejpam-5509	351	1	t	t	PROPN
ejpam-5509	351	2	0	0	NUM
ejpam-5509	351	3	f1(ς	f1(ς	PROPN
ejpam-5509	351	4	,	,	PUNCT
ejpam-5509	351	5	s)dς	s)dς	PROPN
ejpam-5509	351	6	.	.	PUNCT
ejpam-5509	352	1	(	(	PUNCT
ejpam-5509	352	2	42	42	NUM
ejpam-5509	352	3	)	)	PUNCT
ejpam-5509	352	4	at	at	ADP
ejpam-5509	352	5	each	each	DET
ejpam-5509	352	6	time	time	NOUN
ejpam-5509	352	7	step	step	NOUN
ejpam-5509	352	8	tm+1	tm+1	PROPN
ejpam-5509	352	9	,	,	PUNCT
ejpam-5509	352	10	where	where	SCONJ
ejpam-5509	352	11	m	m	VERB
ejpam-5509	352	12	=	=	SYM
ejpam-5509	352	13	0	0	NUM
ejpam-5509	352	14	,	,	PUNCT
ejpam-5509	352	15	1	1	NUM
ejpam-5509	352	16	,	,	PUNCT
ejpam-5509	352	17	2	2	NUM
ejpam-5509	352	18	,	,	PUNCT
ejpam-5509	352	19	...	...	PUNCT
ejpam-5509	352	20	,	,	PUNCT
ejpam-5509	352	21	,	,	PUNCT
ejpam-5509	352	22	we	we	PRON
ejpam-5509	352	23	acquire	acquire	VERB
ejpam-5509	352	24	s(tm+1)−	s(tm+1)−	PROPN
ejpam-5509	352	25	s0	s0	NOUN
ejpam-5509	352	26	=	=	SYM
ejpam-5509	352	27	1−	1−	NUM
ejpam-5509	352	28	ς	ς	PROPN
ejpam-5509	352	29	b(ς	b(ς	PROPN
ejpam-5509	352	30	)	)	PUNCT
ejpam-5509	352	31	f1(tm	f1(tm	PROPN
ejpam-5509	352	32	,	,	PUNCT
ejpam-5509	352	33	sm	sm	PROPN
ejpam-5509	352	34	)	)	PUNCT
ejpam-5509	353	1	+	+	CCONJ
ejpam-5509	353	2	ς	ς	PROPN
ejpam-5509	353	3	b(ς	b(ς	PROPN
ejpam-5509	353	4	)	)	PUNCT
ejpam-5509	353	5	∫	∫	PROPN
ejpam-5509	353	6	tm+1	tm+1	PROPN
ejpam-5509	353	7	0	0	NUM
ejpam-5509	353	8	f1(t	f1(t	PROPN
ejpam-5509	353	9	,	,	PUNCT
ejpam-5509	353	10	s)dt	s)dt	PROPN
ejpam-5509	353	11	.	.	PUNCT
ejpam-5509	354	1	(	(	PUNCT
ejpam-5509	354	2	43	43	NUM
ejpam-5509	354	3	)	)	PUNCT
ejpam-5509	354	4	the	the	DET
ejpam-5509	354	5	difference	difference	NOUN
ejpam-5509	354	6	between	between	ADP
ejpam-5509	354	7	successive	successive	ADJ
ejpam-5509	354	8	terms	term	NOUN
ejpam-5509	354	9	is	be	AUX
ejpam-5509	354	10	expressed	express	VERB
ejpam-5509	354	11	as	as	SCONJ
ejpam-5509	354	12	follows	follow	VERB
ejpam-5509	354	13	:	:	PUNCT
ejpam-5509	354	14	sm+1	sm+1	NUM
ejpam-5509	354	15	−	−	PROPN
ejpam-5509	354	16	sm	sm	NOUN
ejpam-5509	354	17	=	=	SYM
ejpam-5509	354	18	1−	1−	NUM
ejpam-5509	354	19	ς	ς	PROPN
ejpam-5509	354	20	b(ς	b(ς	PROPN
ejpam-5509	354	21	)	)	PUNCT
ejpam-5509	354	22	{	{	PUNCT
ejpam-5509	354	23	f1(tm	f1(tm	NOUN
ejpam-5509	354	24	,	,	PUNCT
ejpam-5509	354	25	sm)−f1(tm−1	sm)−f1(tm−1	PROPN
ejpam-5509	354	26	,	,	PUNCT
ejpam-5509	354	27	sm−1)}+	sm−1)}+	NOUN
ejpam-5509	354	28	ς	ς	PROPN
ejpam-5509	354	29	b(ς	b(ς	PROPN
ejpam-5509	354	30	)	)	PUNCT
ejpam-5509	354	31	∫	∫	PROPN
ejpam-5509	354	32	tm+1	tm+1	PROPN
ejpam-5509	354	33	tn	tn	PROPN
ejpam-5509	354	34	f1(t	f1(t	PROPN
ejpam-5509	354	35	,	,	PUNCT
ejpam-5509	354	36	s)dt	s)dt	PROPN
ejpam-5509	354	37	.	.	PUNCT
ejpam-5509	355	1	(	(	PUNCT
ejpam-5509	355	2	44	44	NUM
ejpam-5509	355	3	)	)	PUNCT
ejpam-5509	355	4	within	within	ADP
ejpam-5509	355	5	the	the	DET
ejpam-5509	355	6	close	close	ADJ
ejpam-5509	355	7	interval	interval	NOUN
ejpam-5509	356	1	[	[	X
ejpam-5509	356	2	tk	tk	NOUN
ejpam-5509	356	3	,	,	PUNCT
ejpam-5509	356	4	t(k+1	t(k+1	NUM
ejpam-5509	356	5	)	)	PUNCT
ejpam-5509	356	6	]	]	PUNCT
ejpam-5509	356	7	,	,	PUNCT
ejpam-5509	356	8	one	one	PRON
ejpam-5509	356	9	can	can	AUX
ejpam-5509	356	10	estimate	estimate	VERB
ejpam-5509	356	11	the	the	DET
ejpam-5509	356	12	function	function	NOUN
ejpam-5509	356	13	f1(t	f1(t	PROPN
ejpam-5509	356	14	,	,	PUNCT
ejpam-5509	356	15	s	s	AUX
ejpam-5509	356	16	)	)	PUNCT
ejpam-5509	356	17	by	by	ADP
ejpam-5509	356	18	employing	employ	VERB
ejpam-5509	356	19	an	an	DET
ejpam-5509	356	20	interpolation	interpolation	NOUN
ejpam-5509	356	21	polynomial	polynomial	NOUN
ejpam-5509	356	22	.	.	PUNCT
ejpam-5509	357	1	pk(t	pk(t	NOUN
ejpam-5509	357	2	)	)	PUNCT
ejpam-5509	357	3	∼=	∼=	NOUN
ejpam-5509	357	4	f(tk	f(tk	NOUN
ejpam-5509	357	5	,	,	PUNCT
ejpam-5509	357	6	zk	zk	NOUN
ejpam-5509	357	7	)	)	PUNCT
ejpam-5509	357	8	h	h	NOUN
ejpam-5509	357	9	(	(	PUNCT
ejpam-5509	357	10	t−	t−	PROPN
ejpam-5509	357	11	tk−1)−	tk−1)−	PROPN
ejpam-5509	357	12	f(tk−1	f(tk−1	NOUN
ejpam-5509	357	13	,	,	PUNCT
ejpam-5509	357	14	zk−1	zk−1	NOUN
ejpam-5509	357	15	)	)	PUNCT
ejpam-5509	357	16	h	h	NOUN
ejpam-5509	357	17	(	(	PUNCT
ejpam-5509	357	18	t−	t−	PROPN
ejpam-5509	357	19	tk	tk	PROPN
ejpam-5509	357	20	)	)	PUNCT
ejpam-5509	357	21	,	,	PUNCT
ejpam-5509	357	22	(	(	PUNCT
ejpam-5509	357	23	45	45	NUM
ejpam-5509	357	24	)	)	PUNCT
ejpam-5509	357	25	i.	i.	PROPN
ejpam-5509	357	26	ahmad	ahmad	PROPN
ejpam-5509	357	27	et	et	PROPN
ejpam-5509	357	28	al	al	PROPN
ejpam-5509	357	29	.	.	PUNCT
ejpam-5509	357	30	/	/	SYM
ejpam-5509	357	31	eur	eur	PROPN
ejpam-5509	357	32	.	.	PUNCT
ejpam-5509	358	1	j.	j.	PROPN
ejpam-5509	358	2	pure	pure	PROPN
ejpam-5509	358	3	appl	appl	PROPN
ejpam-5509	358	4	.	.	PROPN
ejpam-5509	358	5	math	math	PROPN
ejpam-5509	358	6	,	,	PUNCT
ejpam-5509	358	7	18	18	NUM
ejpam-5509	358	8	(	(	PUNCT
ejpam-5509	358	9	1	1	NUM
ejpam-5509	358	10	)	)	PUNCT
ejpam-5509	358	11	(	(	PUNCT
ejpam-5509	358	12	2025	2025	NUM
ejpam-5509	358	13	)	)	PUNCT
ejpam-5509	358	14	,	,	PUNCT
ejpam-5509	358	15	5509	5509	NUM
ejpam-5509	358	16	17	17	NUM
ejpam-5509	358	17	of	of	ADP
ejpam-5509	358	18	27	27	NUM
ejpam-5509	358	19	where	where	SCONJ
ejpam-5509	358	20	h	h	NOUN
ejpam-5509	358	21	=	=	NOUN
ejpam-5509	359	1	tm	tm	ADP
ejpam-5509	359	2	−	−	PROPN
ejpam-5509	359	3	tm−1	tm−1	NOUN
ejpam-5509	359	4	.	.	PUNCT
ejpam-5509	360	1	by	by	ADP
ejpam-5509	360	2	applying	apply	VERB
ejpam-5509	360	3	the	the	DET
ejpam-5509	360	4	previously	previously	ADV
ejpam-5509	360	5	mentioned	mention	VERB
ejpam-5509	360	6	polynomial	polynomial	ADJ
ejpam-5509	360	7	approximation	approximation	NOUN
ejpam-5509	360	8	,	,	PUNCT
ejpam-5509	360	9	we	we	PRON
ejpam-5509	360	10	can	can	AUX
ejpam-5509	360	11	compute	compute	VERB
ejpam-5509	360	12	the	the	DET
ejpam-5509	360	13	integral	integral	ADJ
ejpam-5509	360	14	in	in	ADP
ejpam-5509	360	15	equation	equation	NOUN
ejpam-5509	360	16	(	(	PUNCT
ejpam-5509	360	17	44).∫	44).∫	NOUN
ejpam-5509	360	18	tm+1	tm+1	PROPN
ejpam-5509	360	19	tm	tm	PROPN
ejpam-5509	360	20	f1(t	f1(t	PROPN
ejpam-5509	360	21	,	,	PUNCT
ejpam-5509	361	1	s)dt	s)dt	PROPN
ejpam-5509	361	2	=	=	SYM
ejpam-5509	361	3	∫	∫	PROPN
ejpam-5509	361	4	tm+1	tm+1	PROPN
ejpam-5509	361	5	tm	tm	PROPN
ejpam-5509	361	6	f1(tm	f1(tm	PROPN
ejpam-5509	361	7	,	,	PUNCT
ejpam-5509	361	8	sm	sm	PROPN
ejpam-5509	361	9	)	)	PUNCT
ejpam-5509	361	10	h	h	NOUN
ejpam-5509	361	11	(	(	PUNCT
ejpam-5509	361	12	t−	t−	PROPN
ejpam-5509	361	13	tm−1)−	tm−1)−	PROPN
ejpam-5509	361	14	f1(tm−1	f1(tm−1	NOUN
ejpam-5509	361	15	,	,	PUNCT
ejpam-5509	361	16	sm−1	sm−1	NOUN
ejpam-5509	361	17	)	)	PUNCT
ejpam-5509	362	1	h	h	NOUN
ejpam-5509	362	2	(	(	PUNCT
ejpam-5509	362	3	t−	t−	PROPN
ejpam-5509	362	4	tm)dt	tm)dt	NOUN
ejpam-5509	362	5	=	=	SYM
ejpam-5509	362	6	3h	3h	NUM
ejpam-5509	362	7	2	2	NUM
ejpam-5509	362	8	f1(tm	f1(tm	PROPN
ejpam-5509	362	9	,	,	PUNCT
ejpam-5509	362	10	sm)−	sm)−	NOUN
ejpam-5509	362	11	h	h	NOUN
ejpam-5509	362	12	2	2	NUM
ejpam-5509	362	13	f1(tm−1	f1(tm−1	NOUN
ejpam-5509	362	14	,	,	PUNCT
ejpam-5509	362	15	sm−1	sm−1	NOUN
ejpam-5509	362	16	)	)	PUNCT
ejpam-5509	362	17	.	.	PUNCT
ejpam-5509	363	1	(	(	PUNCT
ejpam-5509	363	2	46	46	X
ejpam-5509	363	3	)	)	PUNCT
ejpam-5509	363	4	substituting	substitute	VERB
ejpam-5509	363	5	(	(	PUNCT
ejpam-5509	363	6	46	46	NUM
ejpam-5509	363	7	)	)	PUNCT
ejpam-5509	363	8	into	into	ADP
ejpam-5509	363	9	(	(	PUNCT
ejpam-5509	363	10	44	44	NUM
ejpam-5509	363	11	)	)	PUNCT
ejpam-5509	363	12	and	and	CCONJ
ejpam-5509	363	13	subsequent	subsequent	ADJ
ejpam-5509	363	14	simplification	simplification	NOUN
ejpam-5509	363	15	yielded	yield	VERB
ejpam-5509	363	16	the	the	DET
ejpam-5509	363	17	following	follow	VERB
ejpam-5509	363	18	result	result	NOUN
ejpam-5509	363	19	.	.	PUNCT
ejpam-5509	364	1	sm+1	sm+1	X
ejpam-5509	365	1	=	=	PUNCT
ejpam-5509	365	2	sm	sm	X
ejpam-5509	365	3	+	+	CCONJ
ejpam-5509	365	4	(	(	PUNCT
ejpam-5509	365	5	1−	1−	NUM
ejpam-5509	365	6	ς	ς	X
ejpam-5509	365	7	b(ς	b(ς	PROPN
ejpam-5509	365	8	)	)	PUNCT
ejpam-5509	366	1	+	+	CCONJ
ejpam-5509	366	2	3h	3h	NUM
ejpam-5509	366	3	2b(ς	2b(ς	NUM
ejpam-5509	366	4	)	)	PUNCT
ejpam-5509	366	5	)	)	PUNCT
ejpam-5509	367	1	f1(tm	f1(tm	NOUN
ejpam-5509	367	2	,	,	PUNCT
ejpam-5509	367	3	sm)−	sm)−	NUM
ejpam-5509	367	4	(	(	PUNCT
ejpam-5509	367	5	1−	1−	NUM
ejpam-5509	367	6	ς	ς	X
ejpam-5509	367	7	b(ς	b(ς	PROPN
ejpam-5509	367	8	)	)	PUNCT
ejpam-5509	368	1	+	+	CCONJ
ejpam-5509	368	2	ςh	ςh	PRON
ejpam-5509	368	3	2b(ς	2b(ς	NUM
ejpam-5509	368	4	)	)	PUNCT
ejpam-5509	368	5	)	)	PUNCT
ejpam-5509	368	6	f1(tm−1	f1(tm−1	NOUN
ejpam-5509	368	7	,	,	PUNCT
ejpam-5509	368	8	sm−1).(47	sm−1).(47	NOUN
ejpam-5509	368	9	)	)	PUNCT
ejpam-5509	368	10	similarly	similarly	ADV
ejpam-5509	368	11	,	,	PUNCT
ejpam-5509	368	12	for	for	ADP
ejpam-5509	368	13	the	the	DET
ejpam-5509	368	14	remaining	remain	VERB
ejpam-5509	368	15	equations	equation	NOUN
ejpam-5509	368	16	within	within	ADP
ejpam-5509	368	17	the	the	DET
ejpam-5509	368	18	system	system	NOUN
ejpam-5509	368	19	(	(	PUNCT
ejpam-5509	368	20	10	10	NUM
ejpam-5509	368	21	)	)	PUNCT
ejpam-5509	368	22	,	,	PUNCT
ejpam-5509	368	23	we	we	PRON
ejpam-5509	368	24	derived	derive	VERB
ejpam-5509	368	25	the	the	DET
ejpam-5509	368	26	recursive	recursive	ADJ
ejpam-5509	368	27	formula	formula	NOUN
ejpam-5509	368	28	as	as	SCONJ
ejpam-5509	368	29	presented	present	VERB
ejpam-5509	368	30	below	below	ADV
ejpam-5509	368	31	.	.	PUNCT
ejpam-5509	369	1	v1(m+1	v1(m+1	NOUN
ejpam-5509	369	2	)	)	PUNCT
ejpam-5509	369	3	=	=	SYM
ejpam-5509	369	4	v10	v10	NOUN
ejpam-5509	369	5	+	+	CCONJ
ejpam-5509	369	6	(	(	PUNCT
ejpam-5509	369	7	1−	1−	NUM
ejpam-5509	369	8	ς	ς	X
ejpam-5509	369	9	b(ς	b(ς	PROPN
ejpam-5509	369	10	)	)	PUNCT
ejpam-5509	370	1	+	+	CCONJ
ejpam-5509	370	2	3h	3h	NUM
ejpam-5509	370	3	2b(ς	2b(ς	NUM
ejpam-5509	370	4	)	)	PUNCT
ejpam-5509	370	5	)	)	PUNCT
ejpam-5509	371	1	f2(tm	f2(tm	PROPN
ejpam-5509	371	2	,	,	PUNCT
ejpam-5509	371	3	v1m)−	v1m)−	PROPN
ejpam-5509	371	4	(	(	PUNCT
ejpam-5509	371	5	1−	1−	NUM
ejpam-5509	371	6	ς	ς	X
ejpam-5509	371	7	b(ς	b(ς	PROPN
ejpam-5509	371	8	)	)	PUNCT
ejpam-5509	372	1	+	+	CCONJ
ejpam-5509	372	2	ςh	ςh	PRON
ejpam-5509	372	3	2b(ς	2b(ς	NUM
ejpam-5509	372	4	)	)	PUNCT
ejpam-5509	372	5	)	)	PUNCT
ejpam-5509	372	6	f2(tm−1	f2(tm−1	NUM
ejpam-5509	372	7	,	,	PUNCT
ejpam-5509	372	8	v1(m−1	v1(m−1	PROPN
ejpam-5509	372	9	)	)	PUNCT
ejpam-5509	372	10	)	)	PUNCT
ejpam-5509	372	11	,	,	PUNCT
ejpam-5509	372	12	v2(m+1	v2(m+1	PRON
ejpam-5509	372	13	)	)	PUNCT
ejpam-5509	372	14	=	=	SYM
ejpam-5509	372	15	v20	v20	NOUN
ejpam-5509	372	16	+	+	CCONJ
ejpam-5509	372	17	(	(	PUNCT
ejpam-5509	372	18	1−	1−	NUM
ejpam-5509	372	19	ς	ς	X
ejpam-5509	372	20	b(ς	b(ς	PROPN
ejpam-5509	372	21	)	)	PUNCT
ejpam-5509	373	1	+	+	CCONJ
ejpam-5509	373	2	3h	3h	NUM
ejpam-5509	373	3	2b(ς	2b(ς	NUM
ejpam-5509	373	4	)	)	PUNCT
ejpam-5509	373	5	)	)	PUNCT
ejpam-5509	374	1	f3(tm	f3(tm	PROPN
ejpam-5509	374	2	,	,	PUNCT
ejpam-5509	374	3	v2m)−	v2m)−	PROPN
ejpam-5509	374	4	(	(	PUNCT
ejpam-5509	374	5	1−	1−	NUM
ejpam-5509	374	6	ς	ς	X
ejpam-5509	374	7	b(ς	b(ς	PROPN
ejpam-5509	374	8	)	)	PUNCT
ejpam-5509	375	1	+	+	CCONJ
ejpam-5509	375	2	ςh	ςh	PRON
ejpam-5509	375	3	2b(ς	2b(ς	NUM
ejpam-5509	375	4	)	)	PUNCT
ejpam-5509	375	5	)	)	PUNCT
ejpam-5509	375	6	f3(tm−1	f3(tm−1	NOUN
ejpam-5509	375	7	,	,	PUNCT
ejpam-5509	375	8	v2(m−1	v2(m−1	NOUN
ejpam-5509	375	9	)	)	PUNCT
ejpam-5509	375	10	)	)	PUNCT
ejpam-5509	375	11	,	,	PUNCT
ejpam-5509	375	12	am+1	am+1	PROPN
ejpam-5509	375	13	=	=	PROPN
ejpam-5509	375	14	a0	a0	PROPN
ejpam-5509	375	15	+	+	CCONJ
ejpam-5509	375	16	(	(	PUNCT
ejpam-5509	375	17	1−	1−	NUM
ejpam-5509	375	18	ς	ς	X
ejpam-5509	375	19	b(ς	b(ς	PROPN
ejpam-5509	375	20	)	)	PUNCT
ejpam-5509	376	1	+	+	CCONJ
ejpam-5509	376	2	3h	3h	NUM
ejpam-5509	376	3	2b(ς	2b(ς	NUM
ejpam-5509	376	4	)	)	PUNCT
ejpam-5509	376	5	)	)	PUNCT
ejpam-5509	377	1	f4(tm	f4(tm	NOUN
ejpam-5509	377	2	,	,	PUNCT
ejpam-5509	377	3	am)−	am)−	PROPN
ejpam-5509	377	4	(	(	PUNCT
ejpam-5509	377	5	1−	1−	NUM
ejpam-5509	377	6	ς	ς	X
ejpam-5509	377	7	b(ς	b(ς	PROPN
ejpam-5509	377	8	)	)	PUNCT
ejpam-5509	378	1	+	+	CCONJ
ejpam-5509	378	2	ςh	ςh	PRON
ejpam-5509	378	3	2b(ς	2b(ς	NUM
ejpam-5509	378	4	)	)	PUNCT
ejpam-5509	378	5	)	)	PUNCT
ejpam-5509	378	6	f4(tm−1	f4(tm−1	NOUN
ejpam-5509	378	7	,	,	PUNCT
ejpam-5509	378	8	am−1	am−1	PROPN
ejpam-5509	378	9	)	)	PUNCT
ejpam-5509	378	10	,	,	PUNCT
ejpam-5509	378	11	cm+1	cm+1	PROPN
ejpam-5509	378	12	=	=	SYM
ejpam-5509	378	13	c0	c0	PROPN
ejpam-5509	378	14	+	+	CCONJ
ejpam-5509	378	15	(	(	PUNCT
ejpam-5509	378	16	1−	1−	NUM
ejpam-5509	378	17	α	α	NOUN
ejpam-5509	378	18	b(ς	b(ς	PROPN
ejpam-5509	378	19	)	)	PUNCT
ejpam-5509	379	1	+	+	CCONJ
ejpam-5509	379	2	3h	3h	NUM
ejpam-5509	379	3	2b(ς	2b(ς	NUM
ejpam-5509	379	4	)	)	PUNCT
ejpam-5509	379	5	)	)	PUNCT
ejpam-5509	380	1	f5(tm	f5(tm	PROPN
ejpam-5509	380	2	,	,	PUNCT
ejpam-5509	380	3	cm)−	cm)−	NOUN
ejpam-5509	380	4	(	(	PUNCT
ejpam-5509	380	5	1−	1−	NUM
ejpam-5509	380	6	ς	ς	X
ejpam-5509	380	7	b(ς	b(ς	PROPN
ejpam-5509	380	8	)	)	PUNCT
ejpam-5509	381	1	+	+	CCONJ
ejpam-5509	381	2	ςh	ςh	PRON
ejpam-5509	381	3	2b(ς	2b(ς	NUM
ejpam-5509	381	4	)	)	PUNCT
ejpam-5509	381	5	)	)	PUNCT
ejpam-5509	382	1	f5(tm−1	f5(tm−1	NOUN
ejpam-5509	382	2	,	,	PUNCT
ejpam-5509	382	3	cm−1	cm−1	NOUN
ejpam-5509	382	4	)	)	PUNCT
ejpam-5509	382	5	,	,	PUNCT
ejpam-5509	382	6	rm+1	rm+1	PROPN
ejpam-5509	382	7	=	=	PUNCT
ejpam-5509	382	8	r0	r0	NOUN
ejpam-5509	382	9	+	+	CCONJ
ejpam-5509	382	10	(	(	PUNCT
ejpam-5509	382	11	1−	1−	NUM
ejpam-5509	382	12	ς	ς	X
ejpam-5509	382	13	b(ς	b(ς	PROPN
ejpam-5509	382	14	)	)	PUNCT
ejpam-5509	383	1	+	+	CCONJ
ejpam-5509	383	2	3h	3h	NUM
ejpam-5509	383	3	2b(ς	2b(ς	NUM
ejpam-5509	383	4	)	)	PUNCT
ejpam-5509	383	5	)	)	PUNCT
ejpam-5509	384	1	f6(tm	f6(tm	PROPN
ejpam-5509	384	2	,	,	PUNCT
ejpam-5509	384	3	rm)−	rm)−	NOUN
ejpam-5509	384	4	(	(	PUNCT
ejpam-5509	384	5	1−	1−	NUM
ejpam-5509	384	6	ς	ς	X
ejpam-5509	384	7	b(ς	b(ς	PROPN
ejpam-5509	384	8	)	)	PUNCT
ejpam-5509	385	1	+	+	CCONJ
ejpam-5509	385	2	ςh	ςh	PRON
ejpam-5509	385	3	2b(ς	2b(ς	NUM
ejpam-5509	385	4	)	)	PUNCT
ejpam-5509	385	5	)	)	PUNCT
ejpam-5509	386	1	f6(tm−1	f6(tm−1	PROPN
ejpam-5509	386	2	,	,	PUNCT
ejpam-5509	386	3	rm−1).(48	rm−1).(48	PROPN
ejpam-5509	386	4	)	)	PUNCT
ejpam-5509	386	5	this	this	DET
ejpam-5509	386	6	numerical	numerical	ADJ
ejpam-5509	386	7	scheme	scheme	NOUN
ejpam-5509	386	8	will	will	AUX
ejpam-5509	386	9	be	be	AUX
ejpam-5509	386	10	utilized	utilize	VERB
ejpam-5509	386	11	to	to	PART
ejpam-5509	386	12	examine	examine	VERB
ejpam-5509	386	13	the	the	DET
ejpam-5509	386	14	dynamic	dynamic	ADJ
ejpam-5509	386	15	behavior	behavior	NOUN
ejpam-5509	386	16	of	of	ADP
ejpam-5509	386	17	the	the	DET
ejpam-5509	386	18	proposed	propose	VERB
ejpam-5509	386	19	model	model	NOUN
ejpam-5509	386	20	under	under	ADP
ejpam-5509	386	21	different	different	ADJ
ejpam-5509	386	22	input	input	NOUN
ejpam-5509	386	23	parameters	parameter	NOUN
ejpam-5509	386	24	.	.	PUNCT
ejpam-5509	387	1	this	this	DET
ejpam-5509	387	2	investigation	investigation	NOUN
ejpam-5509	387	3	aims	aim	VERB
ejpam-5509	387	4	to	to	PART
ejpam-5509	387	5	predict	predict	VERB
ejpam-5509	387	6	the	the	DET
ejpam-5509	387	7	spread	spread	NOUN
ejpam-5509	387	8	of	of	ADP
ejpam-5509	387	9	infectious	infectious	ADJ
ejpam-5509	387	10	diseases	disease	NOUN
ejpam-5509	387	11	within	within	ADP
ejpam-5509	387	12	populations	population	NOUN
ejpam-5509	387	13	,	,	PUNCT
ejpam-5509	387	14	providing	provide	VERB
ejpam-5509	387	15	critical	critical	ADJ
ejpam-5509	387	16	insights	insight	NOUN
ejpam-5509	387	17	into	into	ADP
ejpam-5509	387	18	their	their	PRON
ejpam-5509	387	19	propagation	propagation	NOUN
ejpam-5509	387	20	patterns	pattern	NOUN
ejpam-5509	387	21	.	.	PUNCT
ejpam-5509	388	1	understanding	understand	VERB
ejpam-5509	388	2	these	these	DET
ejpam-5509	388	3	dynamics	dynamic	NOUN
ejpam-5509	388	4	is	be	AUX
ejpam-5509	388	5	essential	essential	ADJ
ejpam-5509	388	6	for	for	ADP
ejpam-5509	388	7	developing	develop	VERB
ejpam-5509	388	8	strategies	strategy	NOUN
ejpam-5509	388	9	to	to	PART
ejpam-5509	388	10	control	control	VERB
ejpam-5509	388	11	or	or	CCONJ
ejpam-5509	388	12	mitigate	mitigate	VERB
ejpam-5509	388	13	the	the	DET
ejpam-5509	388	14	disease	disease	NOUN
ejpam-5509	388	15	’s	’s	PART
ejpam-5509	388	16	impact	impact	NOUN
ejpam-5509	388	17	.	.	PUNCT
ejpam-5509	389	1	such	such	ADJ
ejpam-5509	389	2	findings	finding	NOUN
ejpam-5509	389	3	equip	equip	VERB
ejpam-5509	389	4	public	public	ADJ
ejpam-5509	389	5	health	health	NOUN
ejpam-5509	389	6	officials	official	NOUN
ejpam-5509	389	7	with	with	ADP
ejpam-5509	389	8	the	the	DET
ejpam-5509	389	9	knowledge	knowledge	NOUN
ejpam-5509	389	10	needed	need	VERB
ejpam-5509	389	11	to	to	PART
ejpam-5509	389	12	implement	implement	VERB
ejpam-5509	389	13	effective	effective	ADJ
ejpam-5509	389	14	measures	measure	NOUN
ejpam-5509	389	15	to	to	PART
ejpam-5509	389	16	reduce	reduce	VERB
ejpam-5509	389	17	infection	infection	NOUN
ejpam-5509	389	18	rates	rate	NOUN
ejpam-5509	389	19	and	and	CCONJ
ejpam-5509	389	20	alleviate	alleviate	VERB
ejpam-5509	389	21	the	the	DET
ejpam-5509	389	22	associated	associated	ADJ
ejpam-5509	389	23	public	public	ADJ
ejpam-5509	389	24	health	health	NOUN
ejpam-5509	389	25	burden	burden	NOUN
ejpam-5509	389	26	.	.	PUNCT
ejpam-5509	390	1	i.	i.	PROPN
ejpam-5509	390	2	ahmad	ahmad	PROPN
ejpam-5509	390	3	et	et	PROPN
ejpam-5509	390	4	al	al	PROPN
ejpam-5509	390	5	.	.	PUNCT
ejpam-5509	390	6	/	/	SYM
ejpam-5509	390	7	eur	eur	PROPN
ejpam-5509	390	8	.	.	PUNCT
ejpam-5509	391	1	j.	j.	PROPN
ejpam-5509	391	2	pure	pure	PROPN
ejpam-5509	391	3	appl	appl	PROPN
ejpam-5509	391	4	.	.	PROPN
ejpam-5509	391	5	math	math	PROPN
ejpam-5509	391	6	,	,	PUNCT
ejpam-5509	391	7	18	18	NUM
ejpam-5509	391	8	(	(	PUNCT
ejpam-5509	391	9	1	1	NUM
ejpam-5509	391	10	)	)	PUNCT
ejpam-5509	391	11	(	(	PUNCT
ejpam-5509	391	12	2025	2025	NUM
ejpam-5509	391	13	)	)	PUNCT
ejpam-5509	391	14	,	,	PUNCT
ejpam-5509	391	15	5509	5509	NUM
ejpam-5509	391	16	18	18	NUM
ejpam-5509	391	17	of	of	ADP
ejpam-5509	391	18	27	27	NUM
ejpam-5509	391	19	time	time	NOUN
ejpam-5509	391	20	in	in	ADP
ejpam-5509	391	21	days	day	NOUN
ejpam-5509	391	22	0	0	NUM
ejpam-5509	391	23	10	10	NUM
ejpam-5509	391	24	20	20	NUM
ejpam-5509	391	25	30	30	NUM
ejpam-5509	391	26	40	40	NUM
ejpam-5509	391	27	50	50	NUM
ejpam-5509	391	28	60	60	NUM
ejpam-5509	391	29	o	o	NOUN
ejpam-5509	391	30	n	n	NOUN
ejpam-5509	391	31	e	e	NOUN
ejpam-5509	391	32	d	d	NOUN
ejpam-5509	391	33	o	o	X
ejpam-5509	391	34	s	s	X
ejpam-5509	391	35	e	e	X
ejpam-5509	391	36	v	v	ADP
ejpam-5509	391	37	a	a	DET
ejpam-5509	391	38	c	c	NOUN
ejpam-5509	391	39	c	c	NOUN
ejpam-5509	391	40	in	in	ADP
ejpam-5509	391	41	a	a	DET
ejpam-5509	391	42	te	te	X
ejpam-5509	391	43	d	d	NOUN
ejpam-5509	391	44	0	0	NUM
ejpam-5509	391	45	0.05	0.05	NUM
ejpam-5509	391	46	0.1	0.1	NUM
ejpam-5509	391	47	0.15	0.15	NUM
ejpam-5509	391	48	0.2	0.2	NUM
ejpam-5509	391	49	0.25	0.25	NUM
ejpam-5509	391	50	0.3	0.3	NUM
ejpam-5509	391	51	0.35	0.35	NUM
ejpam-5509	391	52	0.4	0.4	NUM
ejpam-5509	391	53	ζ=	ζ=	ADJ
ejpam-5509	391	54	0.85	0.85	NUM
ejpam-5509	391	55	ζ=0.90	ζ=0.90	NOUN
ejpam-5509	391	56	ζ=	ζ=	ADJ
ejpam-5509	391	57	0.95	0.95	NUM
ejpam-5509	391	58	ζ	ζ	NOUN
ejpam-5509	391	59	=	=	SYM
ejpam-5509	391	60	1.00	1.00	NUM
ejpam-5509	391	61	(	(	PUNCT
ejpam-5509	391	62	a	a	PRON
ejpam-5509	391	63	)	)	PUNCT
ejpam-5509	391	64	time	time	NOUN
ejpam-5509	391	65	in	in	ADP
ejpam-5509	391	66	days	day	NOUN
ejpam-5509	391	67	0	0	NUM
ejpam-5509	391	68	10	10	NUM
ejpam-5509	391	69	20	20	NUM
ejpam-5509	391	70	30	30	NUM
ejpam-5509	391	71	40	40	NUM
ejpam-5509	391	72	50	50	NUM
ejpam-5509	391	73	60	60	NUM
ejpam-5509	391	74	t	t	NOUN
ejpam-5509	391	75	w	w	NOUN
ejpam-5509	391	76	o	o	PROPN
ejpam-5509	392	1	d	d	X
ejpam-5509	392	2	o	o	X
ejpam-5509	392	3	s	s	X
ejpam-5509	392	4	e	e	X
ejpam-5509	392	5	v	v	ADP
ejpam-5509	392	6	a	a	DET
ejpam-5509	392	7	c	c	NOUN
ejpam-5509	392	8	c	c	NOUN
ejpam-5509	392	9	in	in	ADP
ejpam-5509	392	10	a	a	DET
ejpam-5509	392	11	te	te	NOUN
ejpam-5509	392	12	d	d	NUM
ejpam-5509	392	13	0.25	0.25	NUM
ejpam-5509	392	14	0.3	0.3	NUM
ejpam-5509	392	15	0.35	0.35	NUM
ejpam-5509	392	16	0.4	0.4	NUM
ejpam-5509	392	17	0.45	0.45	NUM
ejpam-5509	392	18	0.5	0.5	NUM
ejpam-5509	392	19	0.55	0.55	NUM
ejpam-5509	392	20	ζ=	ζ=	ADJ
ejpam-5509	392	21	0.85	0.85	NUM
ejpam-5509	392	22	ζ=0.90	ζ=0.90	NOUN
ejpam-5509	392	23	ζ=	ζ=	ADJ
ejpam-5509	392	24	0.95	0.95	NUM
ejpam-5509	392	25	ζ	ζ	NOUN
ejpam-5509	392	26	=	=	SYM
ejpam-5509	392	27	1.00	1.00	NUM
ejpam-5509	392	28	(	(	PUNCT
ejpam-5509	392	29	b	b	NOUN
ejpam-5509	392	30	)	)	PUNCT
ejpam-5509	392	31	time	time	NOUN
ejpam-5509	392	32	in	in	ADP
ejpam-5509	392	33	days	day	NOUN
ejpam-5509	392	34	0	0	NUM
ejpam-5509	392	35	10	10	NUM
ejpam-5509	392	36	20	20	NUM
ejpam-5509	392	37	30	30	NUM
ejpam-5509	392	38	40	40	NUM
ejpam-5509	392	39	50	50	NUM
ejpam-5509	392	40	60	60	NUM
ejpam-5509	392	41	a	a	DET
ejpam-5509	392	42	c	c	NOUN
ejpam-5509	392	43	u	u	NOUN
ejpam-5509	392	44	te	te	PROPN
ejpam-5509	392	45	i	i	PRON
ejpam-5509	392	46	n	n	X
ejpam-5509	392	47	fe	fe	X
ejpam-5509	392	48	c	c	NOUN
ejpam-5509	392	49	ti	ti	X
ejpam-5509	392	50	o	o	X
ejpam-5509	392	51	u	u	NOUN
ejpam-5509	392	52	s	s	PROPN
ejpam-5509	392	53	0	0	NUM
ejpam-5509	392	54	0.2	0.2	NUM
ejpam-5509	392	55	0.4	0.4	NUM
ejpam-5509	392	56	0.6	0.6	NUM
ejpam-5509	392	57	0.8	0.8	NUM
ejpam-5509	392	58	1	1	NUM
ejpam-5509	392	59	1.2	1.2	NUM
ejpam-5509	392	60	1.4	1.4	NUM
ejpam-5509	392	61	ζ=	ζ=	ADJ
ejpam-5509	392	62	0.85	0.85	NUM
ejpam-5509	392	63	ζ=0.90	ζ=0.90	NOUN
ejpam-5509	392	64	ζ=	ζ=	ADJ
ejpam-5509	392	65	0.95	0.95	NUM
ejpam-5509	392	66	ζ	ζ	NOUN
ejpam-5509	392	67	=	=	SYM
ejpam-5509	392	68	1.00	1.00	NUM
ejpam-5509	392	69	(	(	PUNCT
ejpam-5509	392	70	c	c	NOUN
ejpam-5509	392	71	)	)	PUNCT
ejpam-5509	392	72	time	time	NOUN
ejpam-5509	392	73	in	in	ADP
ejpam-5509	392	74	days	day	NOUN
ejpam-5509	392	75	0	0	NUM
ejpam-5509	392	76	10	10	NUM
ejpam-5509	392	77	20	20	NUM
ejpam-5509	392	78	30	30	NUM
ejpam-5509	392	79	40	40	NUM
ejpam-5509	392	80	50	50	NUM
ejpam-5509	392	81	60	60	NUM
ejpam-5509	392	82	c	c	NOUN
ejpam-5509	392	83	h	h	NOUN
ejpam-5509	393	1	ro	ro	PROPN
ejpam-5509	394	1	n	n	ADV
ejpam-5509	395	1	ic	ic	INTJ
ejpam-5509	396	1	i	i	PRON
ejpam-5509	396	2	n	n	X
ejpam-5509	396	3	fe	fe	X
ejpam-5509	396	4	c	c	NOUN
ejpam-5509	396	5	ti	ti	X
ejpam-5509	396	6	o	o	X
ejpam-5509	396	7	u	u	NOUN
ejpam-5509	396	8	s	s	VERB
ejpam-5509	396	9	0.2	0.2	NUM
ejpam-5509	396	10	0.3	0.3	NUM
ejpam-5509	396	11	0.4	0.4	NUM
ejpam-5509	396	12	0.5	0.5	NUM
ejpam-5509	396	13	0.6	0.6	NUM
ejpam-5509	396	14	0.7	0.7	NUM
ejpam-5509	396	15	0.8	0.8	NUM
ejpam-5509	396	16	ζ=	ζ=	ADJ
ejpam-5509	396	17	0.85	0.85	NUM
ejpam-5509	396	18	ζ=0.90	ζ=0.90	NOUN
ejpam-5509	396	19	ζ=	ζ=	ADJ
ejpam-5509	396	20	0.95	0.95	NUM
ejpam-5509	396	21	ζ	ζ	NOUN
ejpam-5509	396	22	=	=	SYM
ejpam-5509	396	23	1.00	1.00	NUM
ejpam-5509	396	24	(	(	PUNCT
ejpam-5509	396	25	d	d	NOUN
ejpam-5509	396	26	)	)	PUNCT
ejpam-5509	396	27	time	time	NOUN
ejpam-5509	396	28	in	in	ADP
ejpam-5509	396	29	days	day	NOUN
ejpam-5509	396	30	0	0	NUM
ejpam-5509	396	31	10	10	NUM
ejpam-5509	396	32	20	20	NUM
ejpam-5509	396	33	30	30	NUM
ejpam-5509	396	34	40	40	NUM
ejpam-5509	396	35	50	50	NUM
ejpam-5509	396	36	60	60	NUM
ejpam-5509	396	37	r	r	NOUN
ejpam-5509	396	38	e	e	NOUN
ejpam-5509	396	39	c	c	NOUN
ejpam-5509	396	40	o	o	X
ejpam-5509	396	41	v	v	X
ejpam-5509	396	42	e	e	X
ejpam-5509	396	43	re	re	NOUN
ejpam-5509	396	44	d	d	PROPN
ejpam-5509	396	45	i	i	PRON
ejpam-5509	396	46	n	n	PROPN
ejpam-5509	396	47	d	d	NOUN
ejpam-5509	396	48	iv	iv	X
ejpam-5509	397	1	i	i	PROPN
ejpam-5509	397	2	d	d	PROPN
ejpam-5509	397	3	u	u	PROPN
ejpam-5509	397	4	a	a	DET
ejpam-5509	397	5	ls	ls	ADJ
ejpam-5509	397	6	0.41	0.41	NUM
ejpam-5509	397	7	0.42	0.42	NUM
ejpam-5509	397	8	0.43	0.43	NUM
ejpam-5509	397	9	0.44	0.44	NUM
ejpam-5509	397	10	0.45	0.45	NUM
ejpam-5509	397	11	0.46	0.46	NUM
ejpam-5509	397	12	0.47	0.47	NUM
ejpam-5509	397	13	0.48	0.48	NUM
ejpam-5509	397	14	0.49	0.49	NUM
ejpam-5509	397	15	ζ=	ζ=	ADJ
ejpam-5509	397	16	0.85	0.85	NUM
ejpam-5509	397	17	ζ=0.90	ζ=0.90	NOUN
ejpam-5509	397	18	ζ=	ζ=	ADJ
ejpam-5509	397	19	0.95	0.95	NUM
ejpam-5509	397	20	ζ	ζ	NOUN
ejpam-5509	397	21	=	=	SYM
ejpam-5509	397	22	1.00	1.00	NUM
ejpam-5509	397	23	(	(	PUNCT
ejpam-5509	397	24	e	e	NOUN
ejpam-5509	397	25	)	)	PUNCT
ejpam-5509	397	26	figure	figure	NOUN
ejpam-5509	397	27	1	1	NUM
ejpam-5509	397	28	:	:	PUNCT
ejpam-5509	397	29	visualization	visualization	NOUN
ejpam-5509	397	30	of	of	ADP
ejpam-5509	397	31	the	the	DET
ejpam-5509	397	32	solution	solution	NOUN
ejpam-5509	397	33	trajectories	trajectory	NOUN
ejpam-5509	397	34	of	of	ADP
ejpam-5509	397	35	vaccinated	vaccinated	ADJ
ejpam-5509	397	36	,	,	PUNCT
ejpam-5509	397	37	acutely	acutely	ADV
ejpam-5509	397	38	infected	infect	VERB
ejpam-5509	397	39	,	,	PUNCT
ejpam-5509	397	40	chronically	chronically	ADV
ejpam-5509	397	41	infected	infect	VERB
ejpam-5509	397	42	,	,	PUNCT
ejpam-5509	397	43	and	and	CCONJ
ejpam-5509	397	44	recovered	recover	VERB
ejpam-5509	397	45	individuals	individual	NOUN
ejpam-5509	397	46	within	within	ADP
ejpam-5509	397	47	the	the	DET
ejpam-5509	397	48	proposed	propose	VERB
ejpam-5509	397	49	infection	infection	NOUN
ejpam-5509	397	50	system	system	NOUN
ejpam-5509	397	51	under	under	ADP
ejpam-5509	397	52	varying	vary	VERB
ejpam-5509	397	53	values	value	NOUN
ejpam-5509	397	54	of	of	ADP
ejpam-5509	397	55	the	the	DET
ejpam-5509	397	56	parameter	parameter	NOUN
ejpam-5509	397	57	ς	ς	PROPN
ejpam-5509	397	58	,	,	PUNCT
ejpam-5509	397	59	specifically	specifically	ADV
ejpam-5509	397	60	,	,	PUNCT
ejpam-5509	397	61	ς	ς	PROPN
ejpam-5509	397	62	=	=	PROPN
ejpam-5509	397	63	1.00	1.00	NUM
ejpam-5509	397	64	,	,	PUNCT
ejpam-5509	397	65	0.95	0.95	NUM
ejpam-5509	397	66	,	,	PUNCT
ejpam-5509	397	67	0.90	0.90	NUM
ejpam-5509	397	68	,	,	PUNCT
ejpam-5509	397	69	0.85	0.85	NUM
ejpam-5509	397	70	.	.	PUNCT
ejpam-5509	398	1	i.	i.	PROPN
ejpam-5509	398	2	ahmad	ahmad	PROPN
ejpam-5509	398	3	et	et	PROPN
ejpam-5509	398	4	al	al	PROPN
ejpam-5509	398	5	.	.	PUNCT
ejpam-5509	398	6	/	/	SYM
ejpam-5509	398	7	eur	eur	PROPN
ejpam-5509	398	8	.	.	PUNCT
ejpam-5509	399	1	j.	j.	PROPN
ejpam-5509	399	2	pure	pure	PROPN
ejpam-5509	399	3	appl	appl	PROPN
ejpam-5509	399	4	.	.	PROPN
ejpam-5509	399	5	math	math	PROPN
ejpam-5509	399	6	,	,	PUNCT
ejpam-5509	399	7	18	18	NUM
ejpam-5509	399	8	(	(	PUNCT
ejpam-5509	399	9	1	1	NUM
ejpam-5509	399	10	)	)	PUNCT
ejpam-5509	399	11	(	(	PUNCT
ejpam-5509	399	12	2025	2025	NUM
ejpam-5509	399	13	)	)	PUNCT
ejpam-5509	399	14	,	,	PUNCT
ejpam-5509	399	15	5509	5509	NUM
ejpam-5509	399	16	19	19	NUM
ejpam-5509	399	17	of	of	ADP
ejpam-5509	399	18	27	27	NUM
ejpam-5509	399	19	time	time	NOUN
ejpam-5509	399	20	in	in	ADP
ejpam-5509	399	21	days	day	NOUN
ejpam-5509	399	22	0	0	NUM
ejpam-5509	399	23	10	10	NUM
ejpam-5509	399	24	20	20	NUM
ejpam-5509	399	25	30	30	NUM
ejpam-5509	399	26	40	40	NUM
ejpam-5509	399	27	50	50	NUM
ejpam-5509	399	28	60	60	NUM
ejpam-5509	399	29	o	o	NOUN
ejpam-5509	399	30	n	n	NOUN
ejpam-5509	399	31	e	e	NOUN
ejpam-5509	399	32	d	d	NOUN
ejpam-5509	399	33	o	o	X
ejpam-5509	399	34	s	s	X
ejpam-5509	399	35	e	e	X
ejpam-5509	399	36	v	v	ADP
ejpam-5509	399	37	a	a	DET
ejpam-5509	399	38	c	c	NOUN
ejpam-5509	399	39	c	c	NOUN
ejpam-5509	399	40	in	in	ADP
ejpam-5509	399	41	a	a	DET
ejpam-5509	399	42	te	te	X
ejpam-5509	399	43	d	d	NOUN
ejpam-5509	399	44	0	0	NUM
ejpam-5509	399	45	0.05	0.05	NUM
ejpam-5509	399	46	0.1	0.1	NUM
ejpam-5509	399	47	0.15	0.15	NUM
ejpam-5509	399	48	0.2	0.2	NUM
ejpam-5509	399	49	0.25	0.25	NUM
ejpam-5509	399	50	0.3	0.3	NUM
ejpam-5509	399	51	0.35	0.35	NUM
ejpam-5509	399	52	0.4	0.4	NUM
ejpam-5509	399	53	ζ=	ζ=	ADJ
ejpam-5509	399	54	0.5	0.5	NUM
ejpam-5509	399	55	ζ=0.6	ζ=0.6	NOUN
ejpam-5509	399	56	ζ=	ζ=	ADV
ejpam-5509	399	57	0.7	0.7	NUM
ejpam-5509	399	58	ζ	ζ	NOUN
ejpam-5509	399	59	=	=	NUM
ejpam-5509	399	60	0.8	0.8	NUM
ejpam-5509	399	61	(	(	PUNCT
ejpam-5509	399	62	a	a	NOUN
ejpam-5509	399	63	)	)	PUNCT
ejpam-5509	399	64	time	time	NOUN
ejpam-5509	399	65	in	in	ADP
ejpam-5509	399	66	days	day	NOUN
ejpam-5509	399	67	0	0	NUM
ejpam-5509	399	68	10	10	NUM
ejpam-5509	399	69	20	20	NUM
ejpam-5509	399	70	30	30	NUM
ejpam-5509	399	71	40	40	NUM
ejpam-5509	399	72	50	50	NUM
ejpam-5509	399	73	60	60	NUM
ejpam-5509	399	74	t	t	NOUN
ejpam-5509	399	75	w	w	NOUN
ejpam-5509	399	76	o	o	PROPN
ejpam-5509	400	1	d	d	X
ejpam-5509	400	2	o	o	X
ejpam-5509	400	3	s	s	X
ejpam-5509	400	4	e	e	X
ejpam-5509	400	5	v	v	ADP
ejpam-5509	400	6	a	a	DET
ejpam-5509	400	7	c	c	NOUN
ejpam-5509	400	8	c	c	NOUN
ejpam-5509	400	9	in	in	ADP
ejpam-5509	400	10	a	a	DET
ejpam-5509	400	11	te	te	X
ejpam-5509	400	12	d	d	ADP
ejpam-5509	400	13	0.1	0.1	NUM
ejpam-5509	400	14	0.15	0.15	NUM
ejpam-5509	400	15	0.2	0.2	NUM
ejpam-5509	400	16	0.25	0.25	NUM
ejpam-5509	400	17	0.3	0.3	NUM
ejpam-5509	400	18	0.35	0.35	NUM
ejpam-5509	400	19	0.4	0.4	NUM
ejpam-5509	400	20	0.45	0.45	NUM
ejpam-5509	400	21	0.5	0.5	NUM
ejpam-5509	400	22	0.55	0.55	NUM
ejpam-5509	400	23	ζ=	ζ=	ADJ
ejpam-5509	400	24	0.5	0.5	NUM
ejpam-5509	400	25	ζ=0.6	ζ=0.6	NOUN
ejpam-5509	400	26	ζ=	ζ=	ADV
ejpam-5509	400	27	0.7	0.7	NUM
ejpam-5509	400	28	ζ	ζ	NOUN
ejpam-5509	400	29	=	=	NUM
ejpam-5509	400	30	0.8	0.8	NUM
ejpam-5509	400	31	(	(	PUNCT
ejpam-5509	400	32	b	b	NOUN
ejpam-5509	400	33	)	)	PUNCT
ejpam-5509	400	34	time	time	NOUN
ejpam-5509	400	35	in	in	ADP
ejpam-5509	400	36	days	day	NOUN
ejpam-5509	400	37	0	0	NUM
ejpam-5509	400	38	10	10	NUM
ejpam-5509	400	39	20	20	NUM
ejpam-5509	400	40	30	30	NUM
ejpam-5509	400	41	40	40	NUM
ejpam-5509	400	42	50	50	NUM
ejpam-5509	400	43	60	60	NUM
ejpam-5509	400	44	a	a	DET
ejpam-5509	400	45	c	c	NOUN
ejpam-5509	400	46	u	u	NOUN
ejpam-5509	400	47	te	te	PROPN
ejpam-5509	400	48	i	i	PRON
ejpam-5509	400	49	n	n	X
ejpam-5509	400	50	fe	fe	X
ejpam-5509	400	51	c	c	NOUN
ejpam-5509	400	52	ti	ti	X
ejpam-5509	400	53	o	o	X
ejpam-5509	400	54	u	u	NOUN
ejpam-5509	400	55	s	s	PROPN
ejpam-5509	400	56	0	0	NUM
ejpam-5509	400	57	0.2	0.2	NUM
ejpam-5509	400	58	0.4	0.4	NUM
ejpam-5509	400	59	0.6	0.6	NUM
ejpam-5509	400	60	0.8	0.8	NUM
ejpam-5509	400	61	1	1	NUM
ejpam-5509	400	62	1.2	1.2	NUM
ejpam-5509	400	63	1.4	1.4	NUM
ejpam-5509	400	64	ζ=	ζ=	NOUN
ejpam-5509	400	65	0.5	0.5	NUM
ejpam-5509	400	66	ζ=0.6	ζ=0.6	NOUN
ejpam-5509	400	67	ζ=	ζ=	ADV
ejpam-5509	400	68	0.7	0.7	NUM
ejpam-5509	400	69	ζ	ζ	NOUN
ejpam-5509	400	70	=	=	NUM
ejpam-5509	400	71	0.8	0.8	NUM
ejpam-5509	400	72	(	(	PUNCT
ejpam-5509	400	73	c	c	NOUN
ejpam-5509	400	74	)	)	PUNCT
ejpam-5509	400	75	time	time	NOUN
ejpam-5509	400	76	in	in	ADP
ejpam-5509	400	77	days	day	NOUN
ejpam-5509	400	78	0	0	NUM
ejpam-5509	400	79	10	10	NUM
ejpam-5509	400	80	20	20	NUM
ejpam-5509	400	81	30	30	NUM
ejpam-5509	400	82	40	40	NUM
ejpam-5509	400	83	50	50	NUM
ejpam-5509	400	84	60	60	NUM
ejpam-5509	400	85	c	c	NOUN
ejpam-5509	400	86	h	h	NOUN
ejpam-5509	401	1	ro	ro	PROPN
ejpam-5509	402	1	n	n	ADV
ejpam-5509	403	1	ic	ic	INTJ
ejpam-5509	404	1	i	i	PRON
ejpam-5509	404	2	n	n	X
ejpam-5509	404	3	fe	fe	X
ejpam-5509	404	4	c	c	NOUN
ejpam-5509	404	5	ti	ti	X
ejpam-5509	404	6	o	o	X
ejpam-5509	404	7	u	u	NOUN
ejpam-5509	404	8	s	s	VERB
ejpam-5509	404	9	0.2	0.2	NUM
ejpam-5509	404	10	0.3	0.3	NUM
ejpam-5509	404	11	0.4	0.4	NUM
ejpam-5509	404	12	0.5	0.5	NUM
ejpam-5509	404	13	0.6	0.6	NUM
ejpam-5509	404	14	0.7	0.7	NUM
ejpam-5509	404	15	0.8	0.8	NUM
ejpam-5509	404	16	ζ=	ζ=	ADJ
ejpam-5509	404	17	0.5	0.5	NUM
ejpam-5509	404	18	ζ=0.6	ζ=0.6	NOUN
ejpam-5509	404	19	ζ=	ζ=	ADV
ejpam-5509	404	20	0.7	0.7	NUM
ejpam-5509	404	21	ζ	ζ	NOUN
ejpam-5509	404	22	=	=	NUM
ejpam-5509	404	23	0.8	0.8	NUM
ejpam-5509	404	24	(	(	PUNCT
ejpam-5509	404	25	d	d	NOUN
ejpam-5509	404	26	)	)	PUNCT
ejpam-5509	404	27	time	time	NOUN
ejpam-5509	404	28	in	in	ADP
ejpam-5509	404	29	days	day	NOUN
ejpam-5509	404	30	0	0	NUM
ejpam-5509	404	31	10	10	NUM
ejpam-5509	404	32	20	20	NUM
ejpam-5509	404	33	30	30	NUM
ejpam-5509	404	34	40	40	NUM
ejpam-5509	404	35	50	50	NUM
ejpam-5509	404	36	60	60	NUM
ejpam-5509	404	37	r	r	NOUN
ejpam-5509	404	38	e	e	NOUN
ejpam-5509	404	39	c	c	NOUN
ejpam-5509	404	40	o	o	X
ejpam-5509	404	41	v	v	X
ejpam-5509	404	42	e	e	X
ejpam-5509	404	43	re	re	NOUN
ejpam-5509	404	44	d	d	PROPN
ejpam-5509	404	45	i	i	PRON
ejpam-5509	404	46	n	n	PROPN
ejpam-5509	404	47	d	d	NOUN
ejpam-5509	404	48	iv	iv	X
ejpam-5509	405	1	i	i	PROPN
ejpam-5509	405	2	d	d	PROPN
ejpam-5509	405	3	u	u	PROPN
ejpam-5509	405	4	a	a	DET
ejpam-5509	405	5	ls	ls	ADJ
ejpam-5509	405	6	0.2	0.2	NUM
ejpam-5509	405	7	0.25	0.25	NUM
ejpam-5509	405	8	0.3	0.3	NUM
ejpam-5509	405	9	0.35	0.35	NUM
ejpam-5509	405	10	0.4	0.4	NUM
ejpam-5509	405	11	0.45	0.45	NUM
ejpam-5509	405	12	0.5	0.5	NUM
ejpam-5509	405	13	ζ=	ζ=	ADJ
ejpam-5509	405	14	0.5	0.5	NUM
ejpam-5509	405	15	ζ=0.6	ζ=0.6	NOUN
ejpam-5509	405	16	ζ=	ζ=	ADV
ejpam-5509	405	17	0.7	0.7	NUM
ejpam-5509	405	18	ζ	ζ	NOUN
ejpam-5509	405	19	=	=	NUM
ejpam-5509	405	20	0.8	0.8	NUM
ejpam-5509	405	21	(	(	PUNCT
ejpam-5509	405	22	e	e	NOUN
ejpam-5509	405	23	)	)	PUNCT
ejpam-5509	405	24	figure	figure	NOUN
ejpam-5509	405	25	2	2	NUM
ejpam-5509	405	26	:	:	PUNCT
ejpam-5509	405	27	visualization	visualization	NOUN
ejpam-5509	405	28	of	of	ADP
ejpam-5509	405	29	the	the	DET
ejpam-5509	405	30	solution	solution	NOUN
ejpam-5509	405	31	trajectories	trajectory	NOUN
ejpam-5509	405	32	of	of	ADP
ejpam-5509	405	33	vaccinated	vaccinated	ADJ
ejpam-5509	405	34	,	,	PUNCT
ejpam-5509	405	35	acutely	acutely	ADV
ejpam-5509	405	36	infected	infect	VERB
ejpam-5509	405	37	,	,	PUNCT
ejpam-5509	405	38	chronically	chronically	ADV
ejpam-5509	405	39	infected	infect	VERB
ejpam-5509	405	40	,	,	PUNCT
ejpam-5509	405	41	and	and	CCONJ
ejpam-5509	405	42	recovered	recover	VERB
ejpam-5509	405	43	individuals	individual	NOUN
ejpam-5509	405	44	within	within	ADP
ejpam-5509	405	45	the	the	DET
ejpam-5509	405	46	proposed	propose	VERB
ejpam-5509	405	47	infection	infection	NOUN
ejpam-5509	405	48	system	system	NOUN
ejpam-5509	405	49	under	under	ADP
ejpam-5509	405	50	varying	vary	VERB
ejpam-5509	405	51	values	value	NOUN
ejpam-5509	405	52	of	of	ADP
ejpam-5509	405	53	the	the	DET
ejpam-5509	405	54	parameter	parameter	NOUN
ejpam-5509	405	55	ς	ς	PROPN
ejpam-5509	405	56	,	,	PUNCT
ejpam-5509	405	57	specifically	specifically	ADV
ejpam-5509	405	58	,	,	PUNCT
ejpam-5509	405	59	ς	ς	PROPN
ejpam-5509	405	60	=	=	SYM
ejpam-5509	405	61	0.5	0.5	NUM
ejpam-5509	405	62	,	,	PUNCT
ejpam-5509	405	63	0.6	0.6	NUM
ejpam-5509	405	64	,	,	PUNCT
ejpam-5509	405	65	0.7	0.7	NUM
ejpam-5509	405	66	,	,	PUNCT
ejpam-5509	405	67	0.8	0.8	NUM
ejpam-5509	405	68	.	.	PUNCT
ejpam-5509	406	1	i.	i.	PROPN
ejpam-5509	406	2	ahmad	ahmad	PROPN
ejpam-5509	406	3	et	et	PROPN
ejpam-5509	406	4	al	al	PROPN
ejpam-5509	406	5	.	.	PUNCT
ejpam-5509	406	6	/	/	SYM
ejpam-5509	406	7	eur	eur	PROPN
ejpam-5509	406	8	.	.	PUNCT
ejpam-5509	407	1	j.	j.	PROPN
ejpam-5509	407	2	pure	pure	PROPN
ejpam-5509	407	3	appl	appl	PROPN
ejpam-5509	407	4	.	.	PROPN
ejpam-5509	407	5	math	math	PROPN
ejpam-5509	407	6	,	,	PUNCT
ejpam-5509	407	7	18	18	NUM
ejpam-5509	407	8	(	(	PUNCT
ejpam-5509	407	9	1	1	NUM
ejpam-5509	407	10	)	)	PUNCT
ejpam-5509	407	11	(	(	PUNCT
ejpam-5509	407	12	2025	2025	NUM
ejpam-5509	407	13	)	)	PUNCT
ejpam-5509	407	14	,	,	PUNCT
ejpam-5509	407	15	5509	5509	NUM
ejpam-5509	407	16	20	20	NUM
ejpam-5509	407	17	of	of	ADP
ejpam-5509	407	18	27	27	NUM
ejpam-5509	407	19	time	time	NOUN
ejpam-5509	407	20	in	in	ADP
ejpam-5509	407	21	days	day	NOUN
ejpam-5509	407	22	0	0	NUM
ejpam-5509	407	23	10	10	NUM
ejpam-5509	407	24	20	20	NUM
ejpam-5509	407	25	30	30	NUM
ejpam-5509	407	26	40	40	NUM
ejpam-5509	407	27	50	50	NUM
ejpam-5509	407	28	60	60	NUM
ejpam-5509	407	29	o	o	NOUN
ejpam-5509	407	30	n	n	NOUN
ejpam-5509	407	31	e	e	NOUN
ejpam-5509	407	32	d	d	NOUN
ejpam-5509	407	33	o	o	X
ejpam-5509	407	34	s	s	X
ejpam-5509	407	35	e	e	X
ejpam-5509	407	36	v	v	ADP
ejpam-5509	407	37	a	a	DET
ejpam-5509	407	38	c	c	NOUN
ejpam-5509	407	39	c	c	NOUN
ejpam-5509	407	40	in	in	ADP
ejpam-5509	407	41	a	a	DET
ejpam-5509	407	42	te	te	X
ejpam-5509	407	43	d	d	NOUN
ejpam-5509	407	44	0	0	NUM
ejpam-5509	407	45	0.1	0.1	NUM
ejpam-5509	407	46	0.2	0.2	NUM
ejpam-5509	407	47	0.3	0.3	NUM
ejpam-5509	407	48	0.4	0.4	NUM
ejpam-5509	407	49	0.5	0.5	NUM
ejpam-5509	407	50	0.6	0.6	NUM
ejpam-5509	407	51	0.7	0.7	NUM
ejpam-5509	407	52	ϕ1=	ϕ1=	NOUN
ejpam-5509	407	53	0.25	0.25	NUM
ejpam-5509	407	54	ϕ1=0.35	ϕ1=0.35	NOUN
ejpam-5509	408	1	ϕ1=	ϕ1=	NOUN
ejpam-5509	408	2	0.45	0.45	NUM
ejpam-5509	408	3	ϕ1	ϕ1	NOUN
ejpam-5509	408	4	=	=	SYM
ejpam-5509	408	5	0.55	0.55	NUM
ejpam-5509	408	6	(	(	PUNCT
ejpam-5509	408	7	a	a	PRON
ejpam-5509	408	8	)	)	PUNCT
ejpam-5509	408	9	time	time	NOUN
ejpam-5509	408	10	in	in	ADP
ejpam-5509	408	11	days	day	NOUN
ejpam-5509	408	12	0	0	NUM
ejpam-5509	408	13	10	10	NUM
ejpam-5509	408	14	20	20	NUM
ejpam-5509	408	15	30	30	NUM
ejpam-5509	408	16	40	40	NUM
ejpam-5509	408	17	50	50	NUM
ejpam-5509	408	18	60	60	NUM
ejpam-5509	408	19	t	t	NOUN
ejpam-5509	408	20	w	w	NOUN
ejpam-5509	408	21	o	o	PROPN
ejpam-5509	409	1	d	d	X
ejpam-5509	409	2	o	o	X
ejpam-5509	409	3	s	s	X
ejpam-5509	409	4	e	e	X
ejpam-5509	409	5	v	v	ADP
ejpam-5509	409	6	a	a	DET
ejpam-5509	409	7	c	c	NOUN
ejpam-5509	409	8	c	c	NOUN
ejpam-5509	409	9	in	in	ADP
ejpam-5509	409	10	a	a	PRON
ejpam-5509	409	11	te	te	X
ejpam-5509	409	12	d	d	ADP
ejpam-5509	409	13	0.4	0.4	NUM
ejpam-5509	409	14	0.45	0.45	NUM
ejpam-5509	409	15	0.5	0.5	NUM
ejpam-5509	409	16	0.55	0.55	NUM
ejpam-5509	409	17	0.6	0.6	NUM
ejpam-5509	409	18	0.65	0.65	NUM
ejpam-5509	409	19	0.7	0.7	NUM
ejpam-5509	409	20	0.75	0.75	NUM
ejpam-5509	409	21	ϕ1=	ϕ1=	PROPN
ejpam-5509	409	22	0.25	0.25	NUM
ejpam-5509	409	23	ϕ1=0.35	ϕ1=0.35	NOUN
ejpam-5509	410	1	ϕ1=	ϕ1=	NOUN
ejpam-5509	410	2	0.45	0.45	NUM
ejpam-5509	410	3	ϕ1	ϕ1	NOUN
ejpam-5509	410	4	=	=	SYM
ejpam-5509	410	5	0.55	0.55	NUM
ejpam-5509	410	6	(	(	PUNCT
ejpam-5509	410	7	b	b	NOUN
ejpam-5509	410	8	)	)	PUNCT
ejpam-5509	410	9	time	time	NOUN
ejpam-5509	410	10	in	in	ADP
ejpam-5509	410	11	days	day	NOUN
ejpam-5509	410	12	0	0	NUM
ejpam-5509	410	13	10	10	NUM
ejpam-5509	410	14	20	20	NUM
ejpam-5509	410	15	30	30	NUM
ejpam-5509	410	16	40	40	NUM
ejpam-5509	410	17	50	50	NUM
ejpam-5509	410	18	60	60	NUM
ejpam-5509	410	19	a	a	DET
ejpam-5509	410	20	c	c	NOUN
ejpam-5509	410	21	u	u	NOUN
ejpam-5509	410	22	te	te	PROPN
ejpam-5509	410	23	i	i	PRON
ejpam-5509	410	24	n	n	X
ejpam-5509	410	25	fe	fe	X
ejpam-5509	410	26	c	c	NOUN
ejpam-5509	410	27	ti	ti	X
ejpam-5509	410	28	o	o	X
ejpam-5509	410	29	u	u	NOUN
ejpam-5509	410	30	s	s	PROPN
ejpam-5509	410	31	0	0	NUM
ejpam-5509	410	32	0.2	0.2	NUM
ejpam-5509	410	33	0.4	0.4	NUM
ejpam-5509	410	34	0.6	0.6	NUM
ejpam-5509	410	35	0.8	0.8	NUM
ejpam-5509	410	36	1	1	NUM
ejpam-5509	410	37	1.2	1.2	NUM
ejpam-5509	410	38	ϕ1=	ϕ1=	NOUN
ejpam-5509	410	39	0.25	0.25	NUM
ejpam-5509	410	40	ϕ1=0.35	ϕ1=0.35	NOUN
ejpam-5509	411	1	ϕ1=	ϕ1=	NOUN
ejpam-5509	411	2	0.45	0.45	NUM
ejpam-5509	411	3	ϕ1	ϕ1	NOUN
ejpam-5509	411	4	=	=	SYM
ejpam-5509	411	5	0.55	0.55	NUM
ejpam-5509	411	6	(	(	PUNCT
ejpam-5509	411	7	c	c	NOUN
ejpam-5509	411	8	)	)	PUNCT
ejpam-5509	411	9	time	time	NOUN
ejpam-5509	411	10	in	in	ADP
ejpam-5509	411	11	days	day	NOUN
ejpam-5509	411	12	0	0	NUM
ejpam-5509	411	13	10	10	NUM
ejpam-5509	411	14	20	20	NUM
ejpam-5509	411	15	30	30	NUM
ejpam-5509	411	16	40	40	NUM
ejpam-5509	411	17	50	50	NUM
ejpam-5509	411	18	60	60	NUM
ejpam-5509	411	19	c	c	NOUN
ejpam-5509	411	20	h	h	NOUN
ejpam-5509	411	21	ro	ro	PROPN
ejpam-5509	412	1	n	n	ADV
ejpam-5509	412	2	ic	ic	INTJ
ejpam-5509	413	1	i	i	PRON
ejpam-5509	413	2	n	n	X
ejpam-5509	413	3	fe	fe	X
ejpam-5509	413	4	c	c	NOUN
ejpam-5509	413	5	ti	ti	X
ejpam-5509	413	6	o	o	X
ejpam-5509	413	7	u	u	NOUN
ejpam-5509	413	8	s	s	PROPN
ejpam-5509	413	9	0.25	0.25	NUM
ejpam-5509	413	10	0.3	0.3	NUM
ejpam-5509	413	11	0.35	0.35	NUM
ejpam-5509	413	12	0.4	0.4	NUM
ejpam-5509	413	13	0.45	0.45	NUM
ejpam-5509	413	14	0.5	0.5	NUM
ejpam-5509	413	15	0.55	0.55	NUM
ejpam-5509	413	16	0.6	0.6	NUM
ejpam-5509	413	17	0.65	0.65	NUM
ejpam-5509	413	18	0.7	0.7	NUM
ejpam-5509	413	19	0.75	0.75	NUM
ejpam-5509	413	20	ϕ1=	ϕ1=	PROPN
ejpam-5509	413	21	0.25	0.25	NUM
ejpam-5509	413	22	ϕ1=0.35	ϕ1=0.35	NOUN
ejpam-5509	414	1	ϕ1=	ϕ1=	NOUN
ejpam-5509	414	2	0.45	0.45	NUM
ejpam-5509	414	3	ϕ1	ϕ1	NOUN
ejpam-5509	414	4	=	=	SYM
ejpam-5509	414	5	0.55	0.55	NUM
ejpam-5509	414	6	(	(	PUNCT
ejpam-5509	414	7	d	d	NOUN
ejpam-5509	414	8	)	)	PUNCT
ejpam-5509	414	9	time	time	NOUN
ejpam-5509	414	10	in	in	ADP
ejpam-5509	414	11	days	day	NOUN
ejpam-5509	414	12	0	0	NUM
ejpam-5509	414	13	10	10	NUM
ejpam-5509	414	14	20	20	NUM
ejpam-5509	414	15	30	30	NUM
ejpam-5509	414	16	40	40	NUM
ejpam-5509	414	17	50	50	NUM
ejpam-5509	414	18	60	60	NUM
ejpam-5509	414	19	r	r	NOUN
ejpam-5509	414	20	e	e	NOUN
ejpam-5509	414	21	c	c	NOUN
ejpam-5509	414	22	o	o	X
ejpam-5509	414	23	v	v	X
ejpam-5509	414	24	e	e	X
ejpam-5509	414	25	re	re	NOUN
ejpam-5509	414	26	d	d	PROPN
ejpam-5509	414	27	i	i	PRON
ejpam-5509	414	28	n	n	PROPN
ejpam-5509	414	29	d	d	NOUN
ejpam-5509	414	30	iv	iv	X
ejpam-5509	415	1	i	i	PROPN
ejpam-5509	415	2	d	d	PROPN
ejpam-5509	415	3	u	u	PROPN
ejpam-5509	415	4	a	a	PRON
ejpam-5509	415	5	ls	ls	ADJ
ejpam-5509	415	6	0.43	0.43	NUM
ejpam-5509	415	7	0.44	0.44	NUM
ejpam-5509	415	8	0.45	0.45	NUM
ejpam-5509	415	9	0.46	0.46	NUM
ejpam-5509	415	10	0.47	0.47	NUM
ejpam-5509	415	11	0.48	0.48	NUM
ejpam-5509	415	12	0.49	0.49	NUM
ejpam-5509	415	13	ϕ1=	ϕ1=	NOUN
ejpam-5509	415	14	0.25	0.25	NUM
ejpam-5509	415	15	ϕ1=0.35	ϕ1=0.35	NOUN
ejpam-5509	416	1	ϕ1=	ϕ1=	NOUN
ejpam-5509	416	2	0.45	0.45	NUM
ejpam-5509	416	3	ϕ1	ϕ1	NOUN
ejpam-5509	416	4	=	=	SYM
ejpam-5509	416	5	0.55	0.55	NUM
ejpam-5509	416	6	(	(	PUNCT
ejpam-5509	416	7	e	e	NOUN
ejpam-5509	416	8	)	)	PUNCT
ejpam-5509	416	9	figure	figure	NOUN
ejpam-5509	416	10	3	3	NUM
ejpam-5509	416	11	:	:	PUNCT
ejpam-5509	416	12	graphical	graphical	ADJ
ejpam-5509	416	13	analysis	analysis	NOUN
ejpam-5509	416	14	of	of	ADP
ejpam-5509	416	15	vaccinated	vaccinated	ADJ
ejpam-5509	416	16	,	,	PUNCT
ejpam-5509	416	17	acutely	acutely	ADV
ejpam-5509	416	18	infected	infect	VERB
ejpam-5509	416	19	,	,	PUNCT
ejpam-5509	416	20	chronically	chronically	ADV
ejpam-5509	416	21	infected	infect	VERB
ejpam-5509	416	22	,	,	PUNCT
ejpam-5509	416	23	and	and	CCONJ
ejpam-5509	416	24	recovered	recover	VERB
ejpam-5509	416	25	individuals	individual	NOUN
ejpam-5509	416	26	within	within	ADP
ejpam-5509	416	27	the	the	DET
ejpam-5509	416	28	proposed	propose	VERB
ejpam-5509	416	29	infection	infection	NOUN
ejpam-5509	416	30	model	model	NOUN
ejpam-5509	416	31	,	,	PUNCT
ejpam-5509	416	32	considering	consider	VERB
ejpam-5509	416	33	varying	vary	VERB
ejpam-5509	416	34	values	value	NOUN
ejpam-5509	416	35	of	of	ADP
ejpam-5509	416	36	the	the	DET
ejpam-5509	416	37	parameter	parameter	NOUN
ejpam-5509	416	38	φ1	φ1	PROPN
ejpam-5509	416	39	,	,	PUNCT
ejpam-5509	416	40	specifically	specifically	ADV
ejpam-5509	416	41	φ1	φ1	NOUN
ejpam-5509	416	42	=	=	NOUN
ejpam-5509	416	43	0.25	0.25	NUM
ejpam-5509	416	44	,	,	PUNCT
ejpam-5509	416	45	0.35	0.35	NUM
ejpam-5509	416	46	,	,	PUNCT
ejpam-5509	416	47	0.45	0.45	NUM
ejpam-5509	416	48	,	,	PUNCT
ejpam-5509	416	49	0.55	0.55	NUM
ejpam-5509	416	50	.	.	PUNCT
ejpam-5509	417	1	i.	i.	PROPN
ejpam-5509	417	2	ahmad	ahmad	PROPN
ejpam-5509	417	3	et	et	PROPN
ejpam-5509	417	4	al	al	PROPN
ejpam-5509	417	5	.	.	PUNCT
ejpam-5509	417	6	/	/	SYM
ejpam-5509	417	7	eur	eur	PROPN
ejpam-5509	417	8	.	.	PUNCT
ejpam-5509	418	1	j.	j.	PROPN
ejpam-5509	418	2	pure	pure	PROPN
ejpam-5509	418	3	appl	appl	PROPN
ejpam-5509	418	4	.	.	PROPN
ejpam-5509	418	5	math	math	PROPN
ejpam-5509	418	6	,	,	PUNCT
ejpam-5509	418	7	18	18	NUM
ejpam-5509	418	8	(	(	PUNCT
ejpam-5509	418	9	1	1	NUM
ejpam-5509	418	10	)	)	PUNCT
ejpam-5509	418	11	(	(	PUNCT
ejpam-5509	418	12	2025	2025	NUM
ejpam-5509	418	13	)	)	PUNCT
ejpam-5509	418	14	,	,	PUNCT
ejpam-5509	418	15	5509	5509	NUM
ejpam-5509	418	16	21	21	NUM
ejpam-5509	418	17	of	of	ADP
ejpam-5509	418	18	27	27	NUM
ejpam-5509	418	19	time	time	NOUN
ejpam-5509	418	20	in	in	ADP
ejpam-5509	418	21	days	day	NOUN
ejpam-5509	418	22	0	0	NUM
ejpam-5509	418	23	10	10	NUM
ejpam-5509	418	24	20	20	NUM
ejpam-5509	418	25	30	30	NUM
ejpam-5509	418	26	40	40	NUM
ejpam-5509	418	27	50	50	NUM
ejpam-5509	418	28	60	60	NUM
ejpam-5509	418	29	o	o	NOUN
ejpam-5509	418	30	n	n	NOUN
ejpam-5509	418	31	e	e	NOUN
ejpam-5509	418	32	d	d	NOUN
ejpam-5509	418	33	o	o	X
ejpam-5509	418	34	s	s	X
ejpam-5509	418	35	e	e	X
ejpam-5509	418	36	v	v	ADP
ejpam-5509	418	37	a	a	DET
ejpam-5509	418	38	c	c	NOUN
ejpam-5509	418	39	c	c	NOUN
ejpam-5509	418	40	in	in	ADP
ejpam-5509	418	41	a	a	DET
ejpam-5509	418	42	te	te	X
ejpam-5509	418	43	d	d	NOUN
ejpam-5509	418	44	0	0	NUM
ejpam-5509	418	45	0.05	0.05	NUM
ejpam-5509	418	46	0.1	0.1	NUM
ejpam-5509	418	47	0.15	0.15	NUM
ejpam-5509	418	48	0.2	0.2	NUM
ejpam-5509	418	49	0.25	0.25	NUM
ejpam-5509	418	50	0.3	0.3	NUM
ejpam-5509	418	51	0.35	0.35	NUM
ejpam-5509	418	52	0.4	0.4	NUM
ejpam-5509	418	53	ξ=	ξ=	NOUN
ejpam-5509	418	54	0.45	0.45	NUM
ejpam-5509	418	55	ξ=0.55	ξ=0.55	NOUN
ejpam-5509	418	56	ξ=	ξ=	ADV
ejpam-5509	418	57	0.65	0.65	NUM
ejpam-5509	418	58	ξ	ξ	X
ejpam-5509	418	59	=	=	SYM
ejpam-5509	418	60	0.75	0.75	NUM
ejpam-5509	418	61	(	(	PUNCT
ejpam-5509	418	62	a	a	NOUN
ejpam-5509	418	63	)	)	PUNCT
ejpam-5509	418	64	time	time	NOUN
ejpam-5509	418	65	in	in	ADP
ejpam-5509	418	66	days	day	NOUN
ejpam-5509	418	67	0	0	NUM
ejpam-5509	418	68	10	10	NUM
ejpam-5509	418	69	20	20	NUM
ejpam-5509	418	70	30	30	NUM
ejpam-5509	418	71	40	40	NUM
ejpam-5509	418	72	50	50	NUM
ejpam-5509	418	73	60	60	NUM
ejpam-5509	418	74	t	t	NOUN
ejpam-5509	418	75	w	w	NOUN
ejpam-5509	418	76	o	o	PROPN
ejpam-5509	419	1	d	d	X
ejpam-5509	419	2	o	o	X
ejpam-5509	419	3	s	s	X
ejpam-5509	419	4	e	e	X
ejpam-5509	419	5	v	v	ADP
ejpam-5509	419	6	a	a	DET
ejpam-5509	419	7	c	c	NOUN
ejpam-5509	419	8	c	c	NOUN
ejpam-5509	419	9	in	in	ADP
ejpam-5509	419	10	a	a	DET
ejpam-5509	419	11	te	te	X
ejpam-5509	419	12	d	d	ADP
ejpam-5509	419	13	0.36	0.36	NUM
ejpam-5509	419	14	0.38	0.38	NUM
ejpam-5509	419	15	0.4	0.4	NUM
ejpam-5509	419	16	0.42	0.42	NUM
ejpam-5509	419	17	0.44	0.44	NUM
ejpam-5509	419	18	0.46	0.46	NUM
ejpam-5509	419	19	0.48	0.48	NUM
ejpam-5509	419	20	0.5	0.5	NUM
ejpam-5509	419	21	0.52	0.52	NUM
ejpam-5509	419	22	0.54	0.54	NUM
ejpam-5509	419	23	ξ=	ξ=	NOUN
ejpam-5509	419	24	0.45	0.45	NUM
ejpam-5509	419	25	ξ=0.55	ξ=0.55	NOUN
ejpam-5509	419	26	ξ=	ξ=	ADV
ejpam-5509	419	27	0.65	0.65	NUM
ejpam-5509	419	28	ξ	ξ	X
ejpam-5509	419	29	=	=	SYM
ejpam-5509	419	30	0.75	0.75	NUM
ejpam-5509	419	31	(	(	PUNCT
ejpam-5509	419	32	b	b	NOUN
ejpam-5509	419	33	)	)	PUNCT
ejpam-5509	419	34	time	time	NOUN
ejpam-5509	419	35	in	in	ADP
ejpam-5509	419	36	days	day	NOUN
ejpam-5509	419	37	0	0	NUM
ejpam-5509	419	38	10	10	NUM
ejpam-5509	419	39	20	20	NUM
ejpam-5509	419	40	30	30	NUM
ejpam-5509	419	41	40	40	NUM
ejpam-5509	419	42	50	50	NUM
ejpam-5509	419	43	60	60	NUM
ejpam-5509	419	44	a	a	DET
ejpam-5509	419	45	c	c	NOUN
ejpam-5509	419	46	u	u	NOUN
ejpam-5509	419	47	te	te	PROPN
ejpam-5509	419	48	i	i	PRON
ejpam-5509	419	49	n	n	X
ejpam-5509	419	50	fe	fe	X
ejpam-5509	419	51	c	c	NOUN
ejpam-5509	419	52	ti	ti	X
ejpam-5509	419	53	o	o	X
ejpam-5509	419	54	u	u	NOUN
ejpam-5509	419	55	s	s	VERB
ejpam-5509	419	56	0.2	0.2	NUM
ejpam-5509	419	57	0.4	0.4	NUM
ejpam-5509	419	58	0.6	0.6	NUM
ejpam-5509	419	59	0.8	0.8	NUM
ejpam-5509	419	60	1	1	NUM
ejpam-5509	419	61	1.2	1.2	NUM
ejpam-5509	419	62	1.4	1.4	NUM
ejpam-5509	419	63	ξ=	ξ=	NOUN
ejpam-5509	419	64	0.45	0.45	NUM
ejpam-5509	419	65	ξ=0.55	ξ=0.55	NOUN
ejpam-5509	419	66	ξ=	ξ=	ADV
ejpam-5509	419	67	0.65	0.65	NUM
ejpam-5509	419	68	ξ	ξ	X
ejpam-5509	419	69	=	=	SYM
ejpam-5509	419	70	0.75	0.75	NUM
ejpam-5509	419	71	(	(	PUNCT
ejpam-5509	419	72	c	c	NOUN
ejpam-5509	419	73	)	)	PUNCT
ejpam-5509	419	74	time	time	NOUN
ejpam-5509	419	75	in	in	ADP
ejpam-5509	419	76	days	day	NOUN
ejpam-5509	419	77	0	0	NUM
ejpam-5509	419	78	10	10	NUM
ejpam-5509	419	79	20	20	NUM
ejpam-5509	419	80	30	30	NUM
ejpam-5509	419	81	40	40	NUM
ejpam-5509	419	82	50	50	NUM
ejpam-5509	419	83	60	60	NUM
ejpam-5509	419	84	c	c	NOUN
ejpam-5509	419	85	h	h	NOUN
ejpam-5509	420	1	ro	ro	PROPN
ejpam-5509	421	1	n	n	ADV
ejpam-5509	422	1	ic	ic	INTJ
ejpam-5509	423	1	i	i	PRON
ejpam-5509	423	2	n	n	X
ejpam-5509	423	3	fe	fe	X
ejpam-5509	423	4	c	c	NOUN
ejpam-5509	423	5	ti	ti	X
ejpam-5509	423	6	o	o	X
ejpam-5509	423	7	u	u	NOUN
ejpam-5509	423	8	s	s	VERB
ejpam-5509	423	9	0.2	0.2	NUM
ejpam-5509	423	10	0.3	0.3	NUM
ejpam-5509	423	11	0.4	0.4	NUM
ejpam-5509	423	12	0.5	0.5	NUM
ejpam-5509	423	13	0.6	0.6	NUM
ejpam-5509	423	14	0.7	0.7	NUM
ejpam-5509	423	15	0.8	0.8	NUM
ejpam-5509	423	16	ξ=	ξ=	NOUN
ejpam-5509	423	17	0.45	0.45	NUM
ejpam-5509	423	18	ξ=0.55	ξ=0.55	NOUN
ejpam-5509	423	19	ξ=	ξ=	ADV
ejpam-5509	423	20	0.65	0.65	NUM
ejpam-5509	423	21	ξ	ξ	X
ejpam-5509	423	22	=	=	SYM
ejpam-5509	423	23	0.75	0.75	NUM
ejpam-5509	423	24	(	(	PUNCT
ejpam-5509	423	25	d	d	NOUN
ejpam-5509	423	26	)	)	PUNCT
ejpam-5509	423	27	time	time	NOUN
ejpam-5509	423	28	in	in	ADP
ejpam-5509	423	29	days	day	NOUN
ejpam-5509	423	30	0	0	NUM
ejpam-5509	423	31	10	10	NUM
ejpam-5509	423	32	20	20	NUM
ejpam-5509	423	33	30	30	NUM
ejpam-5509	423	34	40	40	NUM
ejpam-5509	423	35	50	50	NUM
ejpam-5509	423	36	60	60	NUM
ejpam-5509	423	37	r	r	NOUN
ejpam-5509	423	38	e	e	NOUN
ejpam-5509	423	39	c	c	NOUN
ejpam-5509	423	40	o	o	X
ejpam-5509	423	41	v	v	X
ejpam-5509	423	42	e	e	X
ejpam-5509	423	43	re	re	NOUN
ejpam-5509	423	44	d	d	PROPN
ejpam-5509	423	45	i	i	PRON
ejpam-5509	423	46	n	n	PROPN
ejpam-5509	423	47	d	d	NOUN
ejpam-5509	423	48	iv	iv	X
ejpam-5509	424	1	i	i	PROPN
ejpam-5509	424	2	d	d	PROPN
ejpam-5509	424	3	u	u	PROPN
ejpam-5509	424	4	a	a	DET
ejpam-5509	424	5	ls	ls	ADJ
ejpam-5509	424	6	0.455	0.455	NUM
ejpam-5509	424	7	0.46	0.46	NUM
ejpam-5509	424	8	0.465	0.465	NUM
ejpam-5509	424	9	0.47	0.47	NUM
ejpam-5509	424	10	0.475	0.475	NUM
ejpam-5509	424	11	0.48	0.48	NUM
ejpam-5509	424	12	0.485	0.485	NUM
ejpam-5509	424	13	0.49	0.49	NUM
ejpam-5509	424	14	ξ=	ξ=	NOUN
ejpam-5509	424	15	0.45	0.45	NUM
ejpam-5509	424	16	ξ=0.55	ξ=0.55	NOUN
ejpam-5509	424	17	ξ=	ξ=	ADV
ejpam-5509	424	18	0.65	0.65	NUM
ejpam-5509	424	19	ξ	ξ	X
ejpam-5509	424	20	=	=	SYM
ejpam-5509	424	21	0.75	0.75	NUM
ejpam-5509	424	22	(	(	PUNCT
ejpam-5509	424	23	e	e	NOUN
ejpam-5509	424	24	)	)	PUNCT
ejpam-5509	424	25	figure	figure	NOUN
ejpam-5509	424	26	4	4	NUM
ejpam-5509	424	27	:	:	PUNCT
ejpam-5509	424	28	graphical	graphical	ADJ
ejpam-5509	424	29	analysis	analysis	NOUN
ejpam-5509	424	30	of	of	ADP
ejpam-5509	424	31	vaccinated	vaccinated	ADJ
ejpam-5509	424	32	,	,	PUNCT
ejpam-5509	424	33	acutely	acutely	ADV
ejpam-5509	424	34	infected	infect	VERB
ejpam-5509	424	35	,	,	PUNCT
ejpam-5509	424	36	chronically	chronically	ADV
ejpam-5509	424	37	infected	infect	VERB
ejpam-5509	424	38	,	,	PUNCT
ejpam-5509	424	39	and	and	CCONJ
ejpam-5509	424	40	recovered	recover	VERB
ejpam-5509	424	41	individuals	individual	NOUN
ejpam-5509	424	42	within	within	ADP
ejpam-5509	424	43	the	the	DET
ejpam-5509	424	44	proposed	propose	VERB
ejpam-5509	424	45	infection	infection	NOUN
ejpam-5509	424	46	model	model	NOUN
ejpam-5509	424	47	,	,	PUNCT
ejpam-5509	424	48	considering	consider	VERB
ejpam-5509	424	49	varying	vary	VERB
ejpam-5509	424	50	values	value	NOUN
ejpam-5509	424	51	of	of	ADP
ejpam-5509	424	52	the	the	DET
ejpam-5509	424	53	parameter	parameter	NOUN
ejpam-5509	424	54	ξ	ξ	PROPN
ejpam-5509	424	55	,	,	PUNCT
ejpam-5509	424	56	specifically	specifically	ADV
ejpam-5509	424	57	ξ	ξ	X
ejpam-5509	424	58	=	=	SYM
ejpam-5509	424	59	0.45	0.45	NUM
ejpam-5509	424	60	,	,	PUNCT
ejpam-5509	424	61	0.55	0.55	NUM
ejpam-5509	424	62	,	,	PUNCT
ejpam-5509	424	63	0.65	0.65	NUM
ejpam-5509	424	64	,	,	PUNCT
ejpam-5509	424	65	0.75	0.75	NUM
ejpam-5509	424	66	.	.	PUNCT
ejpam-5509	425	1	i.	i.	PROPN
ejpam-5509	425	2	ahmad	ahmad	PROPN
ejpam-5509	425	3	et	et	PROPN
ejpam-5509	425	4	al	al	PROPN
ejpam-5509	425	5	.	.	PUNCT
ejpam-5509	425	6	/	/	SYM
ejpam-5509	425	7	eur	eur	PROPN
ejpam-5509	425	8	.	.	PUNCT
ejpam-5509	426	1	j.	j.	PROPN
ejpam-5509	426	2	pure	pure	PROPN
ejpam-5509	426	3	appl	appl	PROPN
ejpam-5509	426	4	.	.	PROPN
ejpam-5509	426	5	math	math	PROPN
ejpam-5509	426	6	,	,	PUNCT
ejpam-5509	426	7	18	18	NUM
ejpam-5509	426	8	(	(	PUNCT
ejpam-5509	426	9	1	1	NUM
ejpam-5509	426	10	)	)	PUNCT
ejpam-5509	426	11	(	(	PUNCT
ejpam-5509	426	12	2025	2025	NUM
ejpam-5509	426	13	)	)	PUNCT
ejpam-5509	426	14	,	,	PUNCT
ejpam-5509	426	15	5509	5509	NUM
ejpam-5509	426	16	22	22	NUM
ejpam-5509	426	17	of	of	ADP
ejpam-5509	426	18	27	27	NUM
ejpam-5509	426	19	time	time	NOUN
ejpam-5509	426	20	in	in	ADP
ejpam-5509	426	21	days	day	NOUN
ejpam-5509	426	22	0	0	NUM
ejpam-5509	426	23	10	10	NUM
ejpam-5509	426	24	20	20	NUM
ejpam-5509	426	25	30	30	NUM
ejpam-5509	426	26	40	40	NUM
ejpam-5509	426	27	50	50	NUM
ejpam-5509	426	28	60	60	NUM
ejpam-5509	426	29	a	a	DET
ejpam-5509	426	30	c	c	NOUN
ejpam-5509	426	31	u	u	NOUN
ejpam-5509	426	32	te	te	PROPN
ejpam-5509	426	33	i	i	PRON
ejpam-5509	426	34	n	n	X
ejpam-5509	426	35	fe	fe	X
ejpam-5509	426	36	c	c	NOUN
ejpam-5509	426	37	ti	ti	X
ejpam-5509	426	38	o	o	X
ejpam-5509	426	39	u	u	NOUN
ejpam-5509	426	40	s	s	PROPN
ejpam-5509	426	41	0	0	NUM
ejpam-5509	426	42	0.2	0.2	NUM
ejpam-5509	426	43	0.4	0.4	NUM
ejpam-5509	426	44	0.6	0.6	NUM
ejpam-5509	426	45	0.8	0.8	NUM
ejpam-5509	426	46	1	1	NUM
ejpam-5509	426	47	1.2	1.2	NUM
ejpam-5509	426	48	δ=	δ=	NOUN
ejpam-5509	426	49	0.126	0.126	NUM
ejpam-5509	426	50	δ=0.226	δ=0.226	NOUN
ejpam-5509	426	51	δ=	δ=	NOUN
ejpam-5509	426	52	0.326	0.326	NUM
ejpam-5509	426	53	δ	δ	NOUN
ejpam-5509	426	54	=	=	PUNCT
ejpam-5509	426	55	0.426	0.426	NUM
ejpam-5509	426	56	(	(	PUNCT
ejpam-5509	426	57	a	a	NOUN
ejpam-5509	426	58	)	)	PUNCT
ejpam-5509	426	59	time	time	NOUN
ejpam-5509	426	60	in	in	ADP
ejpam-5509	426	61	days	day	NOUN
ejpam-5509	426	62	0	0	NUM
ejpam-5509	426	63	10	10	NUM
ejpam-5509	426	64	20	20	NUM
ejpam-5509	426	65	30	30	NUM
ejpam-5509	426	66	40	40	NUM
ejpam-5509	426	67	50	50	NUM
ejpam-5509	426	68	60	60	NUM
ejpam-5509	426	69	c	c	NOUN
ejpam-5509	426	70	h	h	NOUN
ejpam-5509	427	1	ro	ro	PROPN
ejpam-5509	428	1	n	n	ADV
ejpam-5509	429	1	ic	ic	INTJ
ejpam-5509	430	1	i	i	PRON
ejpam-5509	430	2	n	n	X
ejpam-5509	430	3	fe	fe	X
ejpam-5509	430	4	c	c	NOUN
ejpam-5509	430	5	ti	ti	X
ejpam-5509	430	6	o	o	X
ejpam-5509	430	7	u	u	NOUN
ejpam-5509	430	8	s	s	VERB
ejpam-5509	430	9	0.2	0.2	NUM
ejpam-5509	430	10	0.4	0.4	NUM
ejpam-5509	430	11	0.6	0.6	NUM
ejpam-5509	430	12	0.8	0.8	NUM
ejpam-5509	430	13	1	1	NUM
ejpam-5509	430	14	1.2	1.2	NUM
ejpam-5509	430	15	1.4	1.4	NUM
ejpam-5509	430	16	1.6	1.6	NUM
ejpam-5509	430	17	δ=	δ=	NOUN
ejpam-5509	430	18	0.126	0.126	NUM
ejpam-5509	430	19	δ=0.226	δ=0.226	NOUN
ejpam-5509	430	20	δ=	δ=	NOUN
ejpam-5509	430	21	0.326	0.326	NUM
ejpam-5509	430	22	δ	δ	NOUN
ejpam-5509	430	23	=	=	PUNCT
ejpam-5509	430	24	0.426	0.426	NUM
ejpam-5509	430	25	(	(	PUNCT
ejpam-5509	430	26	b	b	NOUN
ejpam-5509	430	27	)	)	PUNCT
ejpam-5509	430	28	time	time	NOUN
ejpam-5509	430	29	in	in	ADP
ejpam-5509	430	30	days	day	NOUN
ejpam-5509	430	31	0	0	NUM
ejpam-5509	430	32	10	10	NUM
ejpam-5509	430	33	20	20	NUM
ejpam-5509	430	34	30	30	NUM
ejpam-5509	430	35	40	40	NUM
ejpam-5509	430	36	50	50	NUM
ejpam-5509	430	37	60	60	NUM
ejpam-5509	430	38	r	r	NOUN
ejpam-5509	430	39	e	e	NOUN
ejpam-5509	430	40	c	c	NOUN
ejpam-5509	430	41	o	o	X
ejpam-5509	430	42	v	v	X
ejpam-5509	430	43	e	e	X
ejpam-5509	430	44	re	re	NOUN
ejpam-5509	430	45	d	d	PROPN
ejpam-5509	430	46	i	i	PRON
ejpam-5509	430	47	n	n	PROPN
ejpam-5509	430	48	d	d	NOUN
ejpam-5509	430	49	iv	iv	X
ejpam-5509	431	1	i	i	PROPN
ejpam-5509	431	2	d	d	PROPN
ejpam-5509	431	3	u	u	PROPN
ejpam-5509	431	4	a	a	DET
ejpam-5509	431	5	ls	ls	ADJ
ejpam-5509	431	6	0.43	0.43	NUM
ejpam-5509	431	7	0.44	0.44	NUM
ejpam-5509	431	8	0.45	0.45	NUM
ejpam-5509	431	9	0.46	0.46	NUM
ejpam-5509	431	10	0.47	0.47	NUM
ejpam-5509	431	11	0.48	0.48	NUM
ejpam-5509	431	12	0.49	0.49	NUM
ejpam-5509	431	13	δ=	δ=	NOUN
ejpam-5509	431	14	0.126	0.126	NUM
ejpam-5509	431	15	δ=0.226	δ=0.226	NOUN
ejpam-5509	431	16	δ=	δ=	NOUN
ejpam-5509	431	17	0.326	0.326	NUM
ejpam-5509	431	18	δ	δ	NOUN
ejpam-5509	431	19	=	=	PUNCT
ejpam-5509	431	20	0.426	0.426	NUM
ejpam-5509	431	21	(	(	PUNCT
ejpam-5509	431	22	c	c	NOUN
ejpam-5509	431	23	)	)	PUNCT
ejpam-5509	431	24	figure	figure	NOUN
ejpam-5509	431	25	5	5	NUM
ejpam-5509	431	26	:	:	PUNCT
ejpam-5509	431	27	plotting	plot	VERB
ejpam-5509	431	28	the	the	DET
ejpam-5509	431	29	dynamic	dynamic	ADJ
ejpam-5509	431	30	response	response	NOUN
ejpam-5509	431	31	of	of	ADP
ejpam-5509	431	32	the	the	DET
ejpam-5509	431	33	solution	solution	NOUN
ejpam-5509	431	34	trajectories	trajectory	NOUN
ejpam-5509	431	35	of	of	ADP
ejpam-5509	431	36	the	the	DET
ejpam-5509	431	37	proposed	propose	VERB
ejpam-5509	431	38	system	system	NOUN
ejpam-5509	431	39	as	as	ADP
ejpam-5509	431	40	a	a	DET
ejpam-5509	431	41	function	function	NOUN
ejpam-5509	431	42	of	of	ADP
ejpam-5509	431	43	the	the	DET
ejpam-5509	431	44	system	system	NOUN
ejpam-5509	431	45	’s	’s	PART
ejpam-5509	431	46	input	input	NOUN
ejpam-5509	431	47	parameter	parameter	PROPN
ejpam-5509	431	48	δ	δ	PROPN
ejpam-5509	431	49	i.e.	i.e.	X
ejpam-5509	431	50	,	,	PUNCT
ejpam-5509	431	51	δ	δ	X
ejpam-5509	431	52	=	=	NOUN
ejpam-5509	431	53	0.126	0.126	NUM
ejpam-5509	431	54	,	,	PUNCT
ejpam-5509	431	55	0.226	0.226	NUM
ejpam-5509	431	56	,	,	PUNCT
ejpam-5509	431	57	0.326	0.326	NUM
ejpam-5509	431	58	,	,	PUNCT
ejpam-5509	431	59	0.426	0.426	NUM
ejpam-5509	431	60	.	.	PUNCT
ejpam-5509	432	1	5	5	NUM
ejpam-5509	432	2	.	.	X
ejpam-5509	432	3	numerical	numerical	PROPN
ejpam-5509	432	4	findings	finding	NOUN
ejpam-5509	432	5	in	in	ADP
ejpam-5509	432	6	this	this	DET
ejpam-5509	432	7	section	section	NOUN
ejpam-5509	432	8	,	,	PUNCT
ejpam-5509	432	9	we	we	PRON
ejpam-5509	432	10	will	will	AUX
ejpam-5509	432	11	examine	examine	VERB
ejpam-5509	432	12	the	the	DET
ejpam-5509	432	13	dynamical	dynamical	ADJ
ejpam-5509	432	14	behaviour	behaviour	NOUN
ejpam-5509	432	15	of	of	ADP
ejpam-5509	432	16	the	the	DET
ejpam-5509	432	17	recommended	recommend	VERB
ejpam-5509	432	18	system	system	NOUN
ejpam-5509	432	19	to	to	PART
ejpam-5509	432	20	show	show	VERB
ejpam-5509	432	21	the	the	DET
ejpam-5509	432	22	impact	impact	NOUN
ejpam-5509	432	23	of	of	ADP
ejpam-5509	432	24	input	input	NOUN
ejpam-5509	432	25	factors	factor	NOUN
ejpam-5509	432	26	on	on	ADP
ejpam-5509	432	27	the	the	DET
ejpam-5509	432	28	output	output	NOUN
ejpam-5509	432	29	of	of	ADP
ejpam-5509	432	30	the	the	DET
ejpam-5509	432	31	system	system	NOUN
ejpam-5509	432	32	.	.	PUNCT
ejpam-5509	433	1	these	these	DET
ejpam-5509	433	2	analysis	analysis	NOUN
ejpam-5509	433	3	will	will	AUX
ejpam-5509	433	4	provide	provide	VERB
ejpam-5509	433	5	a	a	DET
ejpam-5509	433	6	roadmap	roadmap	NOUN
ejpam-5509	433	7	for	for	ADP
ejpam-5509	433	8	responding	respond	VERB
ejpam-5509	433	9	to	to	ADP
ejpam-5509	433	10	and	and	CCONJ
ejpam-5509	433	11	managing	manage	VERB
ejpam-5509	433	12	outbreaks	outbreak	NOUN
ejpam-5509	433	13	effectively	effectively	ADV
ejpam-5509	433	14	,	,	PUNCT
ejpam-5509	433	15	benefiting	benefit	VERB
ejpam-5509	433	16	public	public	ADJ
ejpam-5509	433	17	health	health	NOUN
ejpam-5509	433	18	on	on	ADP
ejpam-5509	433	19	both	both	CCONJ
ejpam-5509	433	20	local	local	ADJ
ejpam-5509	433	21	and	and	CCONJ
ejpam-5509	433	22	global	global	ADJ
ejpam-5509	433	23	scales	scale	NOUN
ejpam-5509	433	24	.	.	PUNCT
ejpam-5509	434	1	in	in	ADP
ejpam-5509	434	2	a	a	DET
ejpam-5509	434	3	progressively	progressively	ADV
ejpam-5509	434	4	interconnected	interconnect	VERB
ejpam-5509	434	5	global	global	ADJ
ejpam-5509	434	6	landscape	landscape	NOUN
ejpam-5509	434	7	,	,	PUNCT
ejpam-5509	434	8	the	the	DET
ejpam-5509	434	9	capacity	capacity	NOUN
ejpam-5509	434	10	to	to	PART
ejpam-5509	434	11	model	model	VERB
ejpam-5509	434	12	and	and	CCONJ
ejpam-5509	434	13	forecast	forecast	NOUN
ejpam-5509	434	14	disease	disease	NOUN
ejpam-5509	434	15	dissemination	dissemination	NOUN
ejpam-5509	434	16	is	be	AUX
ejpam-5509	434	17	imperative	imperative	ADJ
ejpam-5509	434	18	for	for	ADP
ejpam-5509	434	19	global	global	ADJ
ejpam-5509	434	20	preparedness	preparedness	NOUN
ejpam-5509	434	21	.	.	PUNCT
ejpam-5509	435	1	epidemic	epidemic	NOUN
ejpam-5509	435	2	models	model	NOUN
ejpam-5509	435	3	play	play	VERB
ejpam-5509	435	4	a	a	DET
ejpam-5509	435	5	crucial	crucial	ADJ
ejpam-5509	435	6	role	role	NOUN
ejpam-5509	435	7	in	in	ADP
ejpam-5509	435	8	guiding	guide	VERB
ejpam-5509	435	9	early	early	ADJ
ejpam-5509	435	10	detection	detection	NOUN
ejpam-5509	435	11	and	and	CCONJ
ejpam-5509	435	12	containment	containment	NOUN
ejpam-5509	435	13	strategies	strategy	NOUN
ejpam-5509	435	14	,	,	PUNCT
ejpam-5509	435	15	thereby	thereby	ADV
ejpam-5509	435	16	mitigating	mitigate	VERB
ejpam-5509	435	17	the	the	DET
ejpam-5509	435	18	swift	swift	ADJ
ejpam-5509	435	19	worldwide	worldwide	ADJ
ejpam-5509	435	20	transmission	transmission	NOUN
ejpam-5509	435	21	of	of	ADP
ejpam-5509	435	22	infectious	infectious	ADJ
ejpam-5509	435	23	diseases.in	diseases.in	PRON
ejpam-5509	435	24	this	this	DET
ejpam-5509	435	25	context	context	NOUN
ejpam-5509	435	26	,	,	PUNCT
ejpam-5509	435	27	specific	specific	ADJ
ejpam-5509	435	28	values	value	NOUN
ejpam-5509	435	29	for	for	ADP
ejpam-5509	435	30	input	input	NOUN
ejpam-5509	435	31	parameters	parameter	NOUN
ejpam-5509	435	32	and	and	CCONJ
ejpam-5509	435	33	state	state	NOUN
ejpam-5509	435	34	variables	variable	NOUN
ejpam-5509	435	35	were	be	AUX
ejpam-5509	435	36	assumed	assume	VERB
ejpam-5509	435	37	to	to	PART
ejpam-5509	435	38	facilitate	facilitate	VERB
ejpam-5509	435	39	the	the	DET
ejpam-5509	435	40	simulations	simulation	NOUN
ejpam-5509	435	41	.	.	PUNCT
ejpam-5509	436	1	all	all	DET
ejpam-5509	436	2	computations	computation	NOUN
ejpam-5509	436	3	were	be	AUX
ejpam-5509	436	4	performed	perform	VERB
ejpam-5509	436	5	on	on	ADP
ejpam-5509	436	6	an	an	DET
ejpam-5509	436	7	hp	hp	PROPN
ejpam-5509	436	8	pc	pc	NOUN
ejpam-5509	436	9	laptop	laptop	NOUN
ejpam-5509	436	10	equipped	equip	VERB
ejpam-5509	436	11	with	with	ADP
ejpam-5509	436	12	an	an	DET
ejpam-5509	436	13	intel(r	intel(r	NOUN
ejpam-5509	436	14	)	)	PUNCT
ejpam-5509	436	15	i.	i.	PROPN
ejpam-5509	436	16	ahmad	ahmad	PROPN
ejpam-5509	436	17	et	et	PROPN
ejpam-5509	436	18	al	al	PROPN
ejpam-5509	436	19	.	.	PUNCT
ejpam-5509	436	20	/	/	SYM
ejpam-5509	436	21	eur	eur	PROPN
ejpam-5509	436	22	.	.	PUNCT
ejpam-5509	437	1	j.	j.	PROPN
ejpam-5509	437	2	pure	pure	PROPN
ejpam-5509	437	3	appl	appl	PROPN
ejpam-5509	437	4	.	.	PROPN
ejpam-5509	437	5	math	math	PROPN
ejpam-5509	437	6	,	,	PUNCT
ejpam-5509	437	7	18	18	NUM
ejpam-5509	437	8	(	(	PUNCT
ejpam-5509	437	9	1	1	NUM
ejpam-5509	437	10	)	)	PUNCT
ejpam-5509	437	11	(	(	PUNCT
ejpam-5509	437	12	2025	2025	NUM
ejpam-5509	437	13	)	)	PUNCT
ejpam-5509	437	14	,	,	PUNCT
ejpam-5509	437	15	5509	5509	NUM
ejpam-5509	437	16	23	23	NUM
ejpam-5509	437	17	of	of	ADP
ejpam-5509	437	18	27	27	NUM
ejpam-5509	437	19	core(tm	core(tm	NOUN
ejpam-5509	437	20	)	)	PUNCT
ejpam-5509	437	21	i5	i5	ADJ
ejpam-5509	437	22	-	-	PUNCT
ejpam-5509	437	23	7200u	7200u	NUM
ejpam-5509	437	24	cpu	cpu	NOUN
ejpam-5509	437	25	@	@	ADP
ejpam-5509	437	26	2.50	2.50	NUM
ejpam-5509	437	27	ghz	ghz	NOUN
ejpam-5509	437	28	(	(	PUNCT
ejpam-5509	437	29	2.71	2.71	NUM
ejpam-5509	437	30	ghz	ghz	NOUN
ejpam-5509	437	31	)	)	PUNCT
ejpam-5509	437	32	and	and	CCONJ
ejpam-5509	437	33	8	8	NUM
ejpam-5509	437	34	gb	gb	NOUN
ejpam-5509	437	35	of	of	ADP
ejpam-5509	437	36	ram	ram	NOUN
ejpam-5509	437	37	.	.	PUNCT
ejpam-5509	438	1	the	the	DET
ejpam-5509	438	2	simulations	simulation	NOUN
ejpam-5509	438	3	and	and	CCONJ
ejpam-5509	438	4	numerical	numerical	ADJ
ejpam-5509	438	5	analysis	analysis	NOUN
ejpam-5509	438	6	were	be	AUX
ejpam-5509	438	7	carried	carry	VERB
ejpam-5509	438	8	out	out	ADP
ejpam-5509	438	9	using	use	VERB
ejpam-5509	438	10	matlab	matlab	PROPN
ejpam-5509	438	11	(	(	PUNCT
ejpam-5509	438	12	r2012a	r2012a	NOUN
ejpam-5509	438	13	)	)	PUNCT
ejpam-5509	438	14	software	software	NOUN
ejpam-5509	438	15	.	.	PUNCT
ejpam-5509	439	1	in	in	ADP
ejpam-5509	439	2	the	the	DET
ejpam-5509	439	3	first	first	ADJ
ejpam-5509	439	4	simulation	simulation	NOUN
ejpam-5509	439	5	presented	present	VERB
ejpam-5509	439	6	in	in	ADP
ejpam-5509	439	7	figure	figure	NOUN
ejpam-5509	439	8	1	1	NUM
ejpam-5509	439	9	and	and	CCONJ
ejpam-5509	439	10	figure	figure	NOUN
ejpam-5509	439	11	2	2	NUM
ejpam-5509	439	12	,	,	PUNCT
ejpam-5509	439	13	we	we	PRON
ejpam-5509	439	14	have	have	AUX
ejpam-5509	439	15	show	show	VERB
ejpam-5509	439	16	the	the	DET
ejpam-5509	439	17	effect	effect	NOUN
ejpam-5509	439	18	of	of	ADP
ejpam-5509	439	19	fractional	fractional	ADJ
ejpam-5509	439	20	order	order	NOUN
ejpam-5509	439	21	on	on	ADP
ejpam-5509	439	22	the	the	DET
ejpam-5509	439	23	vaccinated	vaccinated	ADJ
ejpam-5509	439	24	,	,	PUNCT
ejpam-5509	439	25	acute	acute	ADJ
ejpam-5509	439	26	,	,	PUNCT
ejpam-5509	439	27	chronic	chronic	ADJ
ejpam-5509	439	28	and	and	CCONJ
ejpam-5509	439	29	recovered	recover	VERB
ejpam-5509	439	30	individuals	individual	NOUN
ejpam-5509	439	31	of	of	ADP
ejpam-5509	439	32	the	the	DET
ejpam-5509	439	33	system	system	NOUN
ejpam-5509	439	34	.	.	PUNCT
ejpam-5509	440	1	in	in	ADP
ejpam-5509	440	2	figure	figure	NOUN
ejpam-5509	440	3	1	1	NUM
ejpam-5509	440	4	,	,	PUNCT
ejpam-5509	440	5	the	the	DET
ejpam-5509	440	6	value	value	NOUN
ejpam-5509	440	7	of	of	ADP
ejpam-5509	440	8	zeta	zeta	NOUN
ejpam-5509	440	9	is	be	AUX
ejpam-5509	440	10	considered	consider	VERB
ejpam-5509	440	11	to	to	PART
ejpam-5509	440	12	be	be	AUX
ejpam-5509	440	13	ς	ς	NOUN
ejpam-5509	440	14	=	=	NOUN
ejpam-5509	440	15	1.00	1.00	NUM
ejpam-5509	440	16	,	,	PUNCT
ejpam-5509	440	17	0.95	0.95	NUM
ejpam-5509	440	18	,	,	PUNCT
ejpam-5509	440	19	0.90	0.90	NUM
ejpam-5509	440	20	and	and	CCONJ
ejpam-5509	440	21	0.85	0.85	NUM
ejpam-5509	440	22	while	while	SCONJ
ejpam-5509	440	23	in	in	ADP
ejpam-5509	440	24	figure	figure	NOUN
ejpam-5509	440	25	2	2	NUM
ejpam-5509	440	26	,	,	PUNCT
ejpam-5509	440	27	we	we	PRON
ejpam-5509	440	28	assume	assume	VERB
ejpam-5509	440	29	the	the	DET
ejpam-5509	440	30	value	value	NOUN
ejpam-5509	440	31	of	of	ADP
ejpam-5509	440	32	fractional	fractional	ADJ
ejpam-5509	440	33	order	order	NOUN
ejpam-5509	440	34	ς	ς	NOUN
ejpam-5509	440	35	=	=	PUNCT
ejpam-5509	440	36	0.8	0.8	NUM
ejpam-5509	440	37	,	,	PUNCT
ejpam-5509	440	38	0.7	0.7	NUM
ejpam-5509	440	39	,	,	PUNCT
ejpam-5509	440	40	0.6	0.6	NUM
ejpam-5509	440	41	and	and	CCONJ
ejpam-5509	440	42	0.5	0.5	NUM
ejpam-5509	440	43	.	.	PUNCT
ejpam-5509	441	1	in	in	ADP
ejpam-5509	441	2	these	these	DET
ejpam-5509	441	3	figures	figure	NOUN
ejpam-5509	441	4	,	,	PUNCT
ejpam-5509	441	5	we	we	PRON
ejpam-5509	441	6	noticed	notice	VERB
ejpam-5509	441	7	that	that	SCONJ
ejpam-5509	441	8	decreasing	decrease	VERB
ejpam-5509	441	9	the	the	DET
ejpam-5509	441	10	value	value	NOUN
ejpam-5509	441	11	of	of	ADP
ejpam-5509	441	12	fractional	fractional	ADJ
ejpam-5509	441	13	parameter	parameter	NOUN
ejpam-5509	441	14	can	can	AUX
ejpam-5509	441	15	decrease	decrease	VERB
ejpam-5509	441	16	the	the	DET
ejpam-5509	441	17	infection	infection	NOUN
ejpam-5509	441	18	level	level	NOUN
ejpam-5509	441	19	in	in	ADP
ejpam-5509	441	20	the	the	DET
ejpam-5509	441	21	society	society	NOUN
ejpam-5509	441	22	.	.	PUNCT
ejpam-5509	442	1	this	this	PRON
ejpam-5509	442	2	implies	imply	VERB
ejpam-5509	442	3	that	that	SCONJ
ejpam-5509	442	4	this	this	DET
ejpam-5509	442	5	input	input	NOUN
ejpam-5509	442	6	factor	factor	NOUN
ejpam-5509	442	7	is	be	AUX
ejpam-5509	442	8	fruitful	fruitful	ADJ
ejpam-5509	442	9	and	and	CCONJ
ejpam-5509	442	10	can	can	AUX
ejpam-5509	442	11	control	control	VERB
ejpam-5509	442	12	the	the	DET
ejpam-5509	442	13	infection	infection	NOUN
ejpam-5509	442	14	level	level	NOUN
ejpam-5509	442	15	in	in	ADP
ejpam-5509	442	16	the	the	DET
ejpam-5509	442	17	society	society	NOUN
ejpam-5509	442	18	.	.	PUNCT
ejpam-5509	443	1	in	in	ADP
ejpam-5509	443	2	the	the	DET
ejpam-5509	443	3	second	second	ADJ
ejpam-5509	443	4	simulation	simulation	NOUN
ejpam-5509	443	5	presented	present	VERB
ejpam-5509	443	6	in	in	ADP
ejpam-5509	443	7	figure	figure	NOUN
ejpam-5509	443	8	3	3	NUM
ejpam-5509	443	9	,	,	PUNCT
ejpam-5509	443	10	we	we	PRON
ejpam-5509	443	11	have	have	AUX
ejpam-5509	443	12	shown	show	VERB
ejpam-5509	443	13	the	the	DET
ejpam-5509	443	14	impact	impact	NOUN
ejpam-5509	443	15	of	of	ADP
ejpam-5509	443	16	vaccination	vaccination	NOUN
ejpam-5509	443	17	on	on	ADP
ejpam-5509	443	18	the	the	DET
ejpam-5509	443	19	dynamics	dynamic	NOUN
ejpam-5509	443	20	of	of	ADP
ejpam-5509	443	21	the	the	DET
ejpam-5509	443	22	infection	infection	NOUN
ejpam-5509	443	23	.	.	PUNCT
ejpam-5509	444	1	we	we	PRON
ejpam-5509	444	2	assumed	assume	VERB
ejpam-5509	444	3	the	the	DET
ejpam-5509	444	4	values	value	NOUN
ejpam-5509	444	5	of	of	ADP
ejpam-5509	444	6	φ1	φ1	PROPN
ejpam-5509	444	7	to	to	PART
ejpam-5509	444	8	be	be	AUX
ejpam-5509	444	9	0.25	0.25	NUM
ejpam-5509	444	10	,	,	PUNCT
ejpam-5509	444	11	0.35	0.35	NUM
ejpam-5509	444	12	,	,	PUNCT
ejpam-5509	444	13	0.45	0.45	NUM
ejpam-5509	444	14	and	and	CCONJ
ejpam-5509	444	15	0.55	0.55	NUM
ejpam-5509	444	16	.	.	PUNCT
ejpam-5509	445	1	it	it	PRON
ejpam-5509	445	2	can	can	AUX
ejpam-5509	445	3	be	be	AUX
ejpam-5509	445	4	seen	see	VERB
ejpam-5509	445	5	that	that	SCONJ
ejpam-5509	445	6	vaccination	vaccination	NOUN
ejpam-5509	445	7	is	be	AUX
ejpam-5509	445	8	also	also	ADV
ejpam-5509	445	9	an	an	DET
ejpam-5509	445	10	important	important	ADJ
ejpam-5509	445	11	factor	factor	NOUN
ejpam-5509	445	12	and	and	CCONJ
ejpam-5509	445	13	can	can	AUX
ejpam-5509	445	14	significantly	significantly	ADV
ejpam-5509	445	15	contribute	contribute	VERB
ejpam-5509	445	16	to	to	PART
ejpam-5509	445	17	reduce	reduce	VERB
ejpam-5509	445	18	the	the	DET
ejpam-5509	445	19	burden	burden	NOUN
ejpam-5509	445	20	of	of	ADP
ejpam-5509	445	21	the	the	DET
ejpam-5509	445	22	infection	infection	NOUN
ejpam-5509	445	23	in	in	ADP
ejpam-5509	445	24	the	the	DET
ejpam-5509	445	25	society	society	NOUN
ejpam-5509	445	26	.	.	PUNCT
ejpam-5509	446	1	in	in	ADP
ejpam-5509	446	2	figure	figure	NOUN
ejpam-5509	446	3	4	4	NUM
ejpam-5509	446	4	,	,	PUNCT
ejpam-5509	446	5	we	we	PRON
ejpam-5509	446	6	illustrated	illustrate	VERB
ejpam-5509	446	7	the	the	DET
ejpam-5509	446	8	solution	solution	NOUN
ejpam-5509	446	9	pathways	pathway	NOUN
ejpam-5509	446	10	of	of	ADP
ejpam-5509	446	11	vaccinated	vaccinated	ADJ
ejpam-5509	446	12	,	,	PUNCT
ejpam-5509	446	13	acute	acute	ADJ
ejpam-5509	446	14	,	,	PUNCT
ejpam-5509	446	15	chronic	chronic	ADJ
ejpam-5509	446	16	and	and	CCONJ
ejpam-5509	446	17	recovered	recover	VERB
ejpam-5509	446	18	individuals	individual	NOUN
ejpam-5509	446	19	with	with	ADP
ejpam-5509	446	20	the	the	DET
ejpam-5509	446	21	variation	variation	NOUN
ejpam-5509	446	22	of	of	ADP
ejpam-5509	446	23	the	the	DET
ejpam-5509	446	24	ξ	ξ	PROPN
ejpam-5509	446	25	.	.	PUNCT
ejpam-5509	447	1	in	in	ADP
ejpam-5509	447	2	this	this	DET
ejpam-5509	447	3	simulation	simulation	NOUN
ejpam-5509	447	4	,	,	PUNCT
ejpam-5509	447	5	the	the	DET
ejpam-5509	447	6	values	value	NOUN
ejpam-5509	447	7	of	of	ADP
ejpam-5509	447	8	ξ	ξ	PROPN
ejpam-5509	447	9	are	be	AUX
ejpam-5509	447	10	assumed	assume	VERB
ejpam-5509	447	11	to	to	PART
ejpam-5509	447	12	be	be	AUX
ejpam-5509	447	13	0.45	0.45	NUM
ejpam-5509	447	14	,	,	PUNCT
ejpam-5509	447	15	0.55	0.55	NUM
ejpam-5509	447	16	,	,	PUNCT
ejpam-5509	447	17	0.65	0.65	NUM
ejpam-5509	447	18	and	and	CCONJ
ejpam-5509	447	19	0.75	0.75	NUM
ejpam-5509	447	20	.	.	PUNCT
ejpam-5509	448	1	we	we	PRON
ejpam-5509	448	2	observed	observe	VERB
ejpam-5509	448	3	that	that	SCONJ
ejpam-5509	448	4	the	the	DET
ejpam-5509	448	5	increasing	increase	VERB
ejpam-5509	448	6	value	value	NOUN
ejpam-5509	448	7	of	of	ADP
ejpam-5509	448	8	this	this	DET
ejpam-5509	448	9	parameter	parameter	NOUN
ejpam-5509	448	10	increases	increase	VERB
ejpam-5509	448	11	the	the	DET
ejpam-5509	448	12	infection	infection	NOUN
ejpam-5509	448	13	level	level	NOUN
ejpam-5509	448	14	of	of	ADP
ejpam-5509	448	15	the	the	DET
ejpam-5509	448	16	hepatitis	hepatitis	PROPN
ejpam-5509	448	17	b	b	PROPN
ejpam-5509	448	18	which	which	PRON
ejpam-5509	448	19	means	mean	VERB
ejpam-5509	448	20	that	that	SCONJ
ejpam-5509	448	21	ξ	ξ	PROPN
ejpam-5509	448	22	is	be	AUX
ejpam-5509	448	23	critical	critical	ADJ
ejpam-5509	448	24	parameter	parameter	NOUN
ejpam-5509	448	25	and	and	CCONJ
ejpam-5509	448	26	contribute	contribute	VERB
ejpam-5509	448	27	to	to	ADP
ejpam-5509	448	28	the	the	DET
ejpam-5509	448	29	spread	spread	NOUN
ejpam-5509	448	30	of	of	ADP
ejpam-5509	448	31	hb	hb	PROPN
ejpam-5509	448	32	.	.	PUNCT
ejpam-5509	449	1	in	in	ADP
ejpam-5509	449	2	the	the	DET
ejpam-5509	449	3	last	last	ADJ
ejpam-5509	449	4	simulation	simulation	NOUN
ejpam-5509	449	5	illustrated	illustrate	VERB
ejpam-5509	449	6	in	in	ADP
ejpam-5509	449	7	figure	figure	NOUN
ejpam-5509	449	8	5	5	NUM
ejpam-5509	449	9	,	,	PUNCT
ejpam-5509	449	10	the	the	DET
ejpam-5509	449	11	impact	impact	NOUN
ejpam-5509	449	12	of	of	ADP
ejpam-5509	449	13	δ	δ	PROPN
ejpam-5509	449	14	has	have	AUX
ejpam-5509	449	15	been	be	AUX
ejpam-5509	449	16	conceptualized	conceptualize	VERB
ejpam-5509	449	17	on	on	ADP
ejpam-5509	449	18	the	the	DET
ejpam-5509	449	19	vaccinated	vaccinated	ADJ
ejpam-5509	449	20	,	,	PUNCT
ejpam-5509	449	21	acute	acute	ADJ
ejpam-5509	449	22	,	,	PUNCT
ejpam-5509	449	23	chronic	chronic	ADJ
ejpam-5509	449	24	and	and	CCONJ
ejpam-5509	449	25	recovered	recover	VERB
ejpam-5509	449	26	individuals	individual	NOUN
ejpam-5509	449	27	of	of	ADP
ejpam-5509	449	28	the	the	DET
ejpam-5509	449	29	recommend	recommend	ADJ
ejpam-5509	449	30	fractional	fractional	ADJ
ejpam-5509	449	31	system	system	NOUN
ejpam-5509	449	32	.	.	PUNCT
ejpam-5509	450	1	in	in	ADP
ejpam-5509	450	2	our	our	PRON
ejpam-5509	450	3	increasingly	increasingly	ADV
ejpam-5509	450	4	interconnected	interconnected	ADJ
ejpam-5509	450	5	world	world	NOUN
ejpam-5509	450	6	,	,	PUNCT
ejpam-5509	450	7	accurately	accurately	ADV
ejpam-5509	450	8	modeling	modeling	NOUN
ejpam-5509	450	9	and	and	CCONJ
ejpam-5509	450	10	predicting	predict	VERB
ejpam-5509	450	11	disease	disease	NOUN
ejpam-5509	450	12	transmission	transmission	NOUN
ejpam-5509	450	13	is	be	AUX
ejpam-5509	450	14	essential	essential	ADJ
ejpam-5509	450	15	for	for	ADP
ejpam-5509	450	16	global	global	ADJ
ejpam-5509	450	17	preparedness	preparedness	NOUN
ejpam-5509	450	18	.	.	PUNCT
ejpam-5509	451	1	epidemic	epidemic	NOUN
ejpam-5509	451	2	models	model	NOUN
ejpam-5509	451	3	enable	enable	VERB
ejpam-5509	451	4	early	early	ADJ
ejpam-5509	451	5	detection	detection	NOUN
ejpam-5509	451	6	and	and	CCONJ
ejpam-5509	451	7	guide	guide	VERB
ejpam-5509	451	8	containment	containment	NOUN
ejpam-5509	451	9	strategies	strategy	NOUN
ejpam-5509	451	10	,	,	PUNCT
ejpam-5509	451	11	playing	play	VERB
ejpam-5509	451	12	a	a	DET
ejpam-5509	451	13	crucial	crucial	ADJ
ejpam-5509	451	14	role	role	NOUN
ejpam-5509	451	15	in	in	ADP
ejpam-5509	451	16	preventing	prevent	VERB
ejpam-5509	451	17	the	the	DET
ejpam-5509	451	18	rapid	rapid	ADJ
ejpam-5509	451	19	spread	spread	NOUN
ejpam-5509	451	20	of	of	ADP
ejpam-5509	451	21	infectious	infectious	ADJ
ejpam-5509	451	22	diseases	disease	NOUN
ejpam-5509	451	23	.	.	PUNCT
ejpam-5509	452	1	understanding	understand	VERB
ejpam-5509	452	2	epidemic	epidemic	NOUN
ejpam-5509	452	3	dynamics	dynamic	NOUN
ejpam-5509	452	4	not	not	PART
ejpam-5509	452	5	only	only	ADV
ejpam-5509	452	6	improves	improve	VERB
ejpam-5509	452	7	the	the	DET
ejpam-5509	452	8	communication	communication	NOUN
ejpam-5509	452	9	of	of	ADP
ejpam-5509	452	10	the	the	DET
ejpam-5509	452	11	importance	importance	NOUN
ejpam-5509	452	12	of	of	ADP
ejpam-5509	452	13	preventive	preventive	ADJ
ejpam-5509	452	14	measures	measure	NOUN
ejpam-5509	452	15	to	to	ADP
ejpam-5509	452	16	the	the	DET
ejpam-5509	452	17	public	public	NOUN
ejpam-5509	452	18	but	but	CCONJ
ejpam-5509	452	19	also	also	ADV
ejpam-5509	452	20	promotes	promote	VERB
ejpam-5509	452	21	adherence	adherence	NOUN
ejpam-5509	452	22	to	to	ADP
ejpam-5509	452	23	recommendations	recommendation	NOUN
ejpam-5509	452	24	such	such	ADJ
ejpam-5509	452	25	as	as	ADP
ejpam-5509	452	26	vaccination	vaccination	NOUN
ejpam-5509	452	27	,	,	PUNCT
ejpam-5509	452	28	treatment	treatment	NOUN
ejpam-5509	452	29	,	,	PUNCT
ejpam-5509	452	30	quarantine	quarantine	NOUN
ejpam-5509	452	31	,	,	PUNCT
ejpam-5509	452	32	and	and	CCONJ
ejpam-5509	452	33	other	other	ADJ
ejpam-5509	452	34	preventive	preventive	ADJ
ejpam-5509	452	35	actions	action	NOUN
ejpam-5509	452	36	,	,	PUNCT
ejpam-5509	452	37	ultimately	ultimately	ADV
ejpam-5509	452	38	helping	help	VERB
ejpam-5509	452	39	to	to	PART
ejpam-5509	452	40	mitigate	mitigate	VERB
ejpam-5509	452	41	the	the	DET
ejpam-5509	452	42	impact	impact	NOUN
ejpam-5509	452	43	of	of	ADP
ejpam-5509	452	44	outbreaks	outbreak	NOUN
ejpam-5509	452	45	.	.	PUNCT
ejpam-5509	453	1	6	6	X
ejpam-5509	453	2	.	.	X
ejpam-5509	453	3	conclusion	conclusion	NOUN
ejpam-5509	453	4	hepatitis	hepatitis	PROPN
ejpam-5509	453	5	b	b	PROPN
ejpam-5509	453	6	infection	infection	NOUN
ejpam-5509	453	7	constitutes	constitute	VERB
ejpam-5509	453	8	a	a	DET
ejpam-5509	453	9	severe	severe	ADJ
ejpam-5509	453	10	and	and	CCONJ
ejpam-5509	453	11	potentially	potentially	ADV
ejpam-5509	453	12	fatal	fatal	ADJ
ejpam-5509	453	13	viral	viral	ADJ
ejpam-5509	453	14	disease	disease	NOUN
ejpam-5509	453	15	,	,	PUNCT
ejpam-5509	453	16	necessitating	necessitate	VERB
ejpam-5509	453	17	a	a	DET
ejpam-5509	453	18	thorough	thorough	ADJ
ejpam-5509	453	19	investigation	investigation	NOUN
ejpam-5509	453	20	into	into	ADP
ejpam-5509	453	21	its	its	PRON
ejpam-5509	453	22	transmission	transmission	NOUN
ejpam-5509	453	23	dynamics	dynamic	NOUN
ejpam-5509	453	24	.	.	PUNCT
ejpam-5509	454	1	this	this	DET
ejpam-5509	454	2	research	research	NOUN
ejpam-5509	454	3	has	have	AUX
ejpam-5509	454	4	investigated	investigate	VERB
ejpam-5509	454	5	the	the	DET
ejpam-5509	454	6	dynamics	dynamic	NOUN
ejpam-5509	454	7	of	of	ADP
ejpam-5509	454	8	hepatitis	hepatitis	PROPN
ejpam-5509	454	9	b	b	PROPN
ejpam-5509	454	10	by	by	ADP
ejpam-5509	454	11	introducing	introduce	VERB
ejpam-5509	454	12	a	a	DET
ejpam-5509	454	13	two	two	NUM
ejpam-5509	454	14	-	-	PUNCT
ejpam-5509	454	15	shot	shot	NOUN
ejpam-5509	454	16	vaccination	vaccination	NOUN
ejpam-5509	454	17	series	series	NOUN
ejpam-5509	454	18	and	and	CCONJ
ejpam-5509	454	19	has	have	AUX
ejpam-5509	454	20	employed	employ	VERB
ejpam-5509	454	21	the	the	DET
ejpam-5509	454	22	fractional	fractional	PROPN
ejpam-5509	454	23	caputo	caputo	PROPN
ejpam-5509	454	24	-	-	PUNCT
ejpam-5509	454	25	fabrizio	fabrizio	PROPN
ejpam-5509	454	26	operator	operator	NOUN
ejpam-5509	454	27	to	to	PART
ejpam-5509	454	28	model	model	VERB
ejpam-5509	454	29	the	the	DET
ejpam-5509	454	30	system	system	NOUN
ejpam-5509	454	31	.	.	PUNCT
ejpam-5509	455	1	the	the	DET
ejpam-5509	455	2	fractional	fractional	PROPN
ejpam-5509	455	3	caputo	caputo	PROPN
ejpam-5509	455	4	-	-	PUNCT
ejpam-5509	455	5	fabrizio	fabrizio	PROPN
ejpam-5509	455	6	model	model	NOUN
ejpam-5509	455	7	has	have	AUX
ejpam-5509	455	8	been	be	AUX
ejpam-5509	455	9	derived	derive	VERB
ejpam-5509	455	10	,	,	PUNCT
ejpam-5509	455	11	and	and	CCONJ
ejpam-5509	455	12	key	key	ADJ
ejpam-5509	455	13	findings	finding	NOUN
ejpam-5509	455	14	related	relate	VERB
ejpam-5509	455	15	to	to	ADP
ejpam-5509	455	16	this	this	DET
ejpam-5509	455	17	fractional	fractional	ADJ
ejpam-5509	455	18	model	model	NOUN
ejpam-5509	455	19	have	have	AUX
ejpam-5509	455	20	been	be	AUX
ejpam-5509	455	21	presented	present	VERB
ejpam-5509	455	22	.	.	PUNCT
ejpam-5509	456	1	notably	notably	ADV
ejpam-5509	456	2	,	,	PUNCT
ejpam-5509	456	3	the	the	DET
ejpam-5509	456	4	basic	basic	ADJ
ejpam-5509	456	5	characteristics	characteristic	NOUN
ejpam-5509	456	6	of	of	ADP
ejpam-5509	456	7	the	the	DET
ejpam-5509	456	8	hepatitis	hepatitis	PROPN
ejpam-5509	456	9	b	b	PROPN
ejpam-5509	456	10	disease	disease	NOUN
ejpam-5509	456	11	model	model	NOUN
ejpam-5509	456	12	have	have	AUX
ejpam-5509	456	13	been	be	AUX
ejpam-5509	456	14	determined	determine	VERB
ejpam-5509	456	15	,	,	PUNCT
ejpam-5509	456	16	with	with	SCONJ
ejpam-5509	456	17	the	the	DET
ejpam-5509	456	18	threshold	threshold	NOUN
ejpam-5509	456	19	parameter	parameter	NOUN
ejpam-5509	456	20	r0	r0	NOUN
ejpam-5509	456	21	having	having	AUX
ejpam-5509	456	22	been	be	AUX
ejpam-5509	456	23	determined	determine	VERB
ejpam-5509	456	24	using	use	VERB
ejpam-5509	456	25	the	the	DET
ejpam-5509	456	26	next	next	ADJ
ejpam-5509	456	27	-	-	PUNCT
ejpam-5509	456	28	generation	generation	NOUN
ejpam-5509	456	29	matrix	matrix	NOUN
ejpam-5509	456	30	method	method	NOUN
ejpam-5509	456	31	.	.	PUNCT
ejpam-5509	457	1	stability	stability	NOUN
ejpam-5509	457	2	analysis	analysis	NOUN
ejpam-5509	457	3	of	of	ADP
ejpam-5509	457	4	infection	infection	NOUN
ejpam-5509	457	5	-	-	PUNCT
ejpam-5509	457	6	free	free	ADJ
ejpam-5509	457	7	equilibrium	equilibrium	NOUN
ejpam-5509	457	8	has	have	AUX
ejpam-5509	457	9	been	be	AUX
ejpam-5509	457	10	examined	examine	VERB
ejpam-5509	457	11	,	,	PUNCT
ejpam-5509	457	12	and	and	CCONJ
ejpam-5509	457	13	the	the	DET
ejpam-5509	457	14	uniqueness	uniqueness	NOUN
ejpam-5509	457	15	and	and	CCONJ
ejpam-5509	457	16	existence	existence	NOUN
ejpam-5509	457	17	of	of	ADP
ejpam-5509	457	18	the	the	DET
ejpam-5509	457	19	solution	solution	NOUN
ejpam-5509	457	20	for	for	ADP
ejpam-5509	457	21	the	the	DET
ejpam-5509	457	22	hepatitis	hepatitis	PROPN
ejpam-5509	457	23	b	b	PROPN
ejpam-5509	457	24	disease	disease	NOUN
ejpam-5509	457	25	system	system	NOUN
ejpam-5509	457	26	have	have	AUX
ejpam-5509	457	27	been	be	AUX
ejpam-5509	457	28	investigated	investigate	VERB
ejpam-5509	457	29	.	.	PUNCT
ejpam-5509	458	1	a	a	DET
ejpam-5509	458	2	novel	novel	ADJ
ejpam-5509	458	3	numerical	numerical	ADJ
ejpam-5509	458	4	approach	approach	NOUN
ejpam-5509	458	5	has	have	AUX
ejpam-5509	458	6	been	be	AUX
ejpam-5509	458	7	introduced	introduce	VERB
ejpam-5509	458	8	to	to	PART
ejpam-5509	458	9	explore	explore	VERB
ejpam-5509	458	10	the	the	DET
ejpam-5509	458	11	system	system	NOUN
ejpam-5509	458	12	of	of	ADP
ejpam-5509	458	13	hepatitis	hepatitis	PROPN
ejpam-5509	458	14	b	b	PROPN
ejpam-5509	458	15	disease	disease	NOUN
ejpam-5509	458	16	.	.	PUNCT
ejpam-5509	459	1	the	the	DET
ejpam-5509	459	2	use	use	NOUN
ejpam-5509	459	3	of	of	ADP
ejpam-5509	459	4	different	different	ADJ
ejpam-5509	459	5	orders	order	NOUN
ejpam-5509	459	6	of	of	ADP
ejpam-5509	459	7	derivatives	derivative	NOUN
ejpam-5509	459	8	has	have	AUX
ejpam-5509	459	9	revealed	reveal	VERB
ejpam-5509	459	10	that	that	SCONJ
ejpam-5509	459	11	the	the	DET
ejpam-5509	459	12	hypothesized	hypothesized	ADJ
ejpam-5509	459	13	model	model	NOUN
ejpam-5509	459	14	with	with	ADP
ejpam-5509	459	15	the	the	DET
ejpam-5509	459	16	caputo	caputo	PROPN
ejpam-5509	459	17	-	-	PUNCT
ejpam-5509	459	18	fabrizio	fabrizio	PROPN
ejpam-5509	459	19	derivative	derivative	NOUN
ejpam-5509	459	20	has	have	AUX
ejpam-5509	459	21	yielded	yield	VERB
ejpam-5509	459	22	more	more	ADV
ejpam-5509	459	23	accurate	accurate	ADJ
ejpam-5509	459	24	and	and	CCONJ
ejpam-5509	459	25	efficient	efficient	ADJ
ejpam-5509	459	26	graphical	graphical	ADJ
ejpam-5509	459	27	results	result	NOUN
ejpam-5509	459	28	and	and	CCONJ
ejpam-5509	459	29	analyses	analysis	NOUN
ejpam-5509	459	30	compared	compare	VERB
ejpam-5509	459	31	to	to	ADP
ejpam-5509	459	32	integer	integer	NOUN
ejpam-5509	459	33	-	-	PUNCT
ejpam-5509	459	34	order	order	NOUN
ejpam-5509	459	35	derivatives	derivative	NOUN
ejpam-5509	459	36	.	.	PUNCT
ejpam-5509	460	1	the	the	DET
ejpam-5509	460	2	graphical	graphical	ADJ
ejpam-5509	460	3	representations	representation	NOUN
ejpam-5509	460	4	have	have	AUX
ejpam-5509	460	5	also	also	ADV
ejpam-5509	460	6	highlighted	highlight	VERB
ejpam-5509	460	7	the	the	DET
ejpam-5509	460	8	impact	impact	NOUN
ejpam-5509	460	9	and	and	CCONJ
ejpam-5509	460	10	significance	significance	NOUN
ejpam-5509	460	11	of	of	ADP
ejpam-5509	460	12	i.	i.	PROPN
ejpam-5509	460	13	ahmad	ahmad	PROPN
ejpam-5509	460	14	et	et	PROPN
ejpam-5509	460	15	al	al	PROPN
ejpam-5509	460	16	.	.	PUNCT
ejpam-5509	460	17	/	/	SYM
ejpam-5509	460	18	eur	eur	PROPN
ejpam-5509	460	19	.	.	PUNCT
ejpam-5509	461	1	j.	j.	PROPN
ejpam-5509	461	2	pure	pure	PROPN
ejpam-5509	461	3	appl	appl	PROPN
ejpam-5509	461	4	.	.	PROPN
ejpam-5509	461	5	math	math	PROPN
ejpam-5509	461	6	,	,	PUNCT
ejpam-5509	461	7	18	18	NUM
ejpam-5509	461	8	(	(	PUNCT
ejpam-5509	461	9	1	1	NUM
ejpam-5509	461	10	)	)	PUNCT
ejpam-5509	461	11	(	(	PUNCT
ejpam-5509	461	12	2025	2025	NUM
ejpam-5509	461	13	)	)	PUNCT
ejpam-5509	461	14	,	,	PUNCT
ejpam-5509	461	15	5509	5509	NUM
ejpam-5509	461	16	24	24	NUM
ejpam-5509	461	17	of	of	ADP
ejpam-5509	461	18	27	27	NUM
ejpam-5509	461	19	various	various	ADJ
ejpam-5509	461	20	input	input	NOUN
ejpam-5509	461	21	parameters	parameter	NOUN
ejpam-5509	461	22	and	and	CCONJ
ejpam-5509	461	23	have	have	AUX
ejpam-5509	461	24	visualized	visualize	VERB
ejpam-5509	461	25	the	the	DET
ejpam-5509	461	26	most	most	ADV
ejpam-5509	461	27	important	important	ADJ
ejpam-5509	461	28	factors	factor	NOUN
ejpam-5509	461	29	of	of	ADP
ejpam-5509	461	30	the	the	DET
ejpam-5509	461	31	system	system	NOUN
ejpam-5509	461	32	.	.	PUNCT
ejpam-5509	462	1	the	the	DET
ejpam-5509	462	2	findings	finding	NOUN
ejpam-5509	462	3	of	of	ADP
ejpam-5509	462	4	this	this	DET
ejpam-5509	462	5	study	study	NOUN
ejpam-5509	462	6	are	be	AUX
ejpam-5509	462	7	expected	expect	VERB
ejpam-5509	462	8	to	to	PART
ejpam-5509	462	9	provide	provide	VERB
ejpam-5509	462	10	critical	critical	ADJ
ejpam-5509	462	11	insights	insight	NOUN
ejpam-5509	462	12	for	for	ADP
ejpam-5509	462	13	policymakers	policymaker	NOUN
ejpam-5509	462	14	and	and	CCONJ
ejpam-5509	462	15	healthcare	healthcare	NOUN
ejpam-5509	462	16	authorities	authority	NOUN
ejpam-5509	462	17	working	work	VERB
ejpam-5509	462	18	to	to	PART
ejpam-5509	462	19	control	control	VERB
ejpam-5509	462	20	the	the	DET
ejpam-5509	462	21	spread	spread	NOUN
ejpam-5509	462	22	of	of	ADP
ejpam-5509	462	23	hepatitis	hepatitis	PROPN
ejpam-5509	462	24	b	b	PROPN
ejpam-5509	462	25	within	within	ADP
ejpam-5509	462	26	affected	affected	ADJ
ejpam-5509	462	27	populations	population	NOUN
ejpam-5509	462	28	.	.	PUNCT
ejpam-5509	463	1	additionally	additionally	ADV
ejpam-5509	463	2	,	,	PUNCT
ejpam-5509	463	3	future	future	ADJ
ejpam-5509	463	4	extensions	extension	NOUN
ejpam-5509	463	5	of	of	ADP
ejpam-5509	463	6	this	this	DET
ejpam-5509	463	7	model	model	NOUN
ejpam-5509	463	8	may	may	AUX
ejpam-5509	463	9	incorporate	incorporate	VERB
ejpam-5509	463	10	time	time	NOUN
ejpam-5509	463	11	-	-	PUNCT
ejpam-5509	463	12	dependent	dependent	ADJ
ejpam-5509	463	13	control	control	NOUN
ejpam-5509	463	14	strategies	strategy	NOUN
ejpam-5509	463	15	,	,	PUNCT
ejpam-5509	463	16	grounded	ground	VERB
ejpam-5509	463	17	in	in	ADP
ejpam-5509	463	18	optimal	optimal	ADJ
ejpam-5509	463	19	control	control	NOUN
ejpam-5509	463	20	theory	theory	NOUN
ejpam-5509	463	21	,	,	PUNCT
ejpam-5509	463	22	to	to	PART
ejpam-5509	463	23	further	far	ADV
ejpam-5509	463	24	enhance	enhance	VERB
ejpam-5509	463	25	the	the	DET
ejpam-5509	463	26	effectiveness	effectiveness	NOUN
ejpam-5509	463	27	of	of	ADP
ejpam-5509	463	28	disease	disease	NOUN
ejpam-5509	463	29	management	management	NOUN
ejpam-5509	463	30	and	and	CCONJ
ejpam-5509	463	31	intervention	intervention	NOUN
ejpam-5509	463	32	efforts	effort	NOUN
ejpam-5509	463	33	.	.	PUNCT
ejpam-5509	464	1	declarations	declaration	NOUN
ejpam-5509	464	2	competing	compete	VERB
ejpam-5509	464	3	interests	interest	NOUN
ejpam-5509	464	4	:	:	PUNCT
ejpam-5509	464	5	authors	author	NOUN
ejpam-5509	464	6	declare	declare	VERB
ejpam-5509	464	7	no	no	DET
ejpam-5509	464	8	conflict	conflict	NOUN
ejpam-5509	464	9	of	of	ADP
ejpam-5509	464	10	interest	interest	NOUN
ejpam-5509	464	11	.	.	PUNCT
ejpam-5509	465	1	availability	availability	NOUN
ejpam-5509	465	2	of	of	ADP
ejpam-5509	465	3	data	datum	NOUN
ejpam-5509	465	4	and	and	CCONJ
ejpam-5509	465	5	materials	material	NOUN
ejpam-5509	465	6	:	:	PUNCT
ejpam-5509	465	7	data	datum	NOUN
ejpam-5509	465	8	will	will	AUX
ejpam-5509	465	9	be	be	AUX
ejpam-5509	465	10	provided	provide	VERB
ejpam-5509	465	11	on	on	ADP
ejpam-5509	465	12	request	request	NOUN
ejpam-5509	465	13	to	to	ADP
ejpam-5509	465	14	the	the	DET
ejpam-5509	465	15	corresponding	corresponding	ADJ
ejpam-5509	465	16	author	author	NOUN
ejpam-5509	465	17	.	.	PUNCT
ejpam-5509	466	1	acknowledgments	acknowledgment	NOUN
ejpam-5509	466	2	and	and	CCONJ
ejpam-5509	466	3	funding	fund	VERB
ejpam-5509	466	4	aziz	aziz	PROPN
ejpam-5509	466	5	khan	khan	PROPN
ejpam-5509	466	6	and	and	CCONJ
ejpam-5509	466	7	thabet	thabet	ADJ
ejpam-5509	466	8	abdeljawad	abdeljawad	NOUN
ejpam-5509	466	9	would	would	AUX
ejpam-5509	466	10	like	like	VERB
ejpam-5509	466	11	to	to	PART
ejpam-5509	466	12	thank	thank	VERB
ejpam-5509	466	13	prince	prince	PROPN
ejpam-5509	466	14	sultan	sultan	PROPN
ejpam-5509	466	15	university	university	PROPN
ejpam-5509	466	16	for	for	ADP
ejpam-5509	466	17	paying	pay	VERB
ejpam-5509	466	18	the	the	DET
ejpam-5509	466	19	apc	apc	NOUN
ejpam-5509	466	20	and	and	CCONJ
ejpam-5509	466	21	support	support	VERB
ejpam-5509	466	22	through	through	ADP
ejpam-5509	466	23	tas	ta	NOUN
ejpam-5509	466	24	research	research	NOUN
ejpam-5509	466	25	lab	lab	NOUN
ejpam-5509	466	26	.	.	PUNCT
ejpam-5509	467	1	references	reference	NOUN
ejpam-5509	467	2	[	[	X
ejpam-5509	467	3	1	1	NUM
ejpam-5509	467	4	]	]	PUNCT
ejpam-5509	467	5	sneha	sneha	PROPN
ejpam-5509	467	6	agarwal	agarwal	PROPN
ejpam-5509	467	7	and	and	CCONJ
ejpam-5509	467	8	lakshmi	lakshmi	PROPN
ejpam-5509	467	9	narayan	narayan	PROPN
ejpam-5509	467	10	mishra	mishra	PROPN
ejpam-5509	467	11	.	.	PROPN
ejpam-5509	468	1	attributes	attribute	NOUN
ejpam-5509	468	2	of	of	ADP
ejpam-5509	468	3	residual	residual	ADJ
ejpam-5509	468	4	neural	neural	ADJ
ejpam-5509	468	5	networks	network	NOUN
ejpam-5509	468	6	for	for	ADP
ejpam-5509	468	7	modeling	model	VERB
ejpam-5509	468	8	fractional	fractional	ADJ
ejpam-5509	468	9	differential	differential	ADJ
ejpam-5509	468	10	equations	equation	NOUN
ejpam-5509	468	11	.	.	PUNCT
ejpam-5509	469	1	heliyon	heliyon	NOUN
ejpam-5509	469	2	,	,	PUNCT
ejpam-5509	469	3	10(19	10(19	NUM
ejpam-5509	469	4	)	)	PUNCT
ejpam-5509	469	5	,	,	PUNCT
ejpam-5509	469	6	2024	2024	NUM
ejpam-5509	469	7	.	.	PUNCT
ejpam-5509	470	1	[	[	X
ejpam-5509	470	2	2	2	NUM
ejpam-5509	470	3	]	]	X
ejpam-5509	470	4	imtiaz	imtiaz	PROPN
ejpam-5509	470	5	ahmad	ahmad	PROPN
ejpam-5509	470	6	,	,	PUNCT
ejpam-5509	470	7	ihteram	ihteram	PROPN
ejpam-5509	470	8	ali	ali	PROPN
ejpam-5509	470	9	,	,	PUNCT
ejpam-5509	470	10	rashid	rashid	PROPN
ejpam-5509	470	11	jan	jan	PROPN
ejpam-5509	470	12	,	,	PUNCT
ejpam-5509	470	13	sahar	sahar	PROPN
ejpam-5509	470	14	ahmed	ahmed	PROPN
ejpam-5509	470	15	idris	idris	PROPN
ejpam-5509	470	16	,	,	PUNCT
ejpam-5509	470	17	and	and	CCONJ
ejpam-5509	470	18	mohamed	mohamed	PROPN
ejpam-5509	470	19	mousa	mousa	PROPN
ejpam-5509	470	20	.	.	PUNCT
ejpam-5509	471	1	solutions	solution	NOUN
ejpam-5509	471	2	of	of	ADP
ejpam-5509	471	3	a	a	DET
ejpam-5509	471	4	three	three	NUM
ejpam-5509	471	5	-	-	PUNCT
ejpam-5509	471	6	dimensional	dimensional	ADJ
ejpam-5509	471	7	multi	multi	ADJ
ejpam-5509	471	8	-	-	ADJ
ejpam-5509	471	9	term	term	ADJ
ejpam-5509	471	10	fractional	fractional	ADJ
ejpam-5509	471	11	anomalous	anomalous	ADJ
ejpam-5509	471	12	solute	solute	NOUN
ejpam-5509	471	13	transport	transport	NOUN
ejpam-5509	471	14	model	model	NOUN
ejpam-5509	471	15	for	for	ADP
ejpam-5509	471	16	contamination	contamination	NOUN
ejpam-5509	471	17	in	in	ADP
ejpam-5509	471	18	groundwater	groundwater	NOUN
ejpam-5509	471	19	.	.	PUNCT
ejpam-5509	472	1	plos	plos	PROPN
ejpam-5509	472	2	one	one	NUM
ejpam-5509	472	3	,	,	PUNCT
ejpam-5509	472	4	18(12):e0294348	18(12):e0294348	PROPN
ejpam-5509	472	5	,	,	PUNCT
ejpam-5509	472	6	2023	2023	NUM
ejpam-5509	472	7	.	.	PUNCT
ejpam-5509	473	1	[	[	X
ejpam-5509	473	2	3	3	X
ejpam-5509	473	3	]	]	X
ejpam-5509	473	4	imtiaz	imtiaz	PROPN
ejpam-5509	473	5	ahmad	ahmad	PROPN
ejpam-5509	473	6	,	,	PUNCT
ejpam-5509	473	7	asmidar	asmidar	PROPN
ejpam-5509	473	8	abu	abu	PROPN
ejpam-5509	473	9	bakar	bakar	PROPN
ejpam-5509	473	10	,	,	PUNCT
ejpam-5509	473	11	rashid	rashid	PROPN
ejpam-5509	473	12	jan	jan	PROPN
ejpam-5509	473	13	,	,	PUNCT
ejpam-5509	473	14	and	and	CCONJ
ejpam-5509	473	15	salman	salman	PROPN
ejpam-5509	473	16	yussof	yussof	PROPN
ejpam-5509	473	17	.	.	PUNCT
ejpam-5509	474	1	dynamic	dynamic	ADJ
ejpam-5509	474	2	behaviors	behavior	NOUN
ejpam-5509	474	3	of	of	ADP
ejpam-5509	474	4	a	a	DET
ejpam-5509	474	5	modified	modify	VERB
ejpam-5509	474	6	computer	computer	NOUN
ejpam-5509	474	7	virus	virus	NOUN
ejpam-5509	474	8	model	model	NOUN
ejpam-5509	474	9	:	:	PUNCT
ejpam-5509	474	10	insights	insight	NOUN
ejpam-5509	474	11	into	into	ADP
ejpam-5509	474	12	parameters	parameter	NOUN
ejpam-5509	474	13	and	and	CCONJ
ejpam-5509	474	14	network	network	NOUN
ejpam-5509	474	15	attributes	attribute	NOUN
ejpam-5509	474	16	.	.	PUNCT
ejpam-5509	475	1	alexandria	alexandria	PROPN
ejpam-5509	475	2	engineering	engineering	PROPN
ejpam-5509	475	3	journal	journal	PROPN
ejpam-5509	475	4	,	,	PUNCT
ejpam-5509	475	5	103:266–277	103:266–277	NUM
ejpam-5509	475	6	,	,	PUNCT
ejpam-5509	475	7	2024	2024	NUM
ejpam-5509	475	8	.	.	PUNCT
ejpam-5509	476	1	[	[	X
ejpam-5509	476	2	4	4	X
ejpam-5509	476	3	]	]	X
ejpam-5509	476	4	imtiaz	imtiaz	PROPN
ejpam-5509	476	5	ahmad	ahmad	PROPN
ejpam-5509	476	6	,	,	PUNCT
ejpam-5509	476	7	siraj	siraj	PROPN
ejpam-5509	476	8	-	-	PUNCT
ejpam-5509	476	9	ul	ul	PROPN
ejpam-5509	476	10	-	-	PUNCT
ejpam-5509	476	11	islam	islam	PROPN
ejpam-5509	476	12	,	,	PUNCT
ejpam-5509	476	13	mehnaz	mehnaz	PROPN
ejpam-5509	476	14	,	,	PUNCT
ejpam-5509	476	15	and	and	CCONJ
ejpam-5509	476	16	sakhi	sakhi	PROPN
ejpam-5509	476	17	zaman	zaman	PROPN
ejpam-5509	476	18	.	.	PUNCT
ejpam-5509	476	19	local	local	ADJ
ejpam-5509	476	20	meshless	meshless	ADJ
ejpam-5509	476	21	differential	differential	ADJ
ejpam-5509	476	22	quadrature	quadrature	NOUN
ejpam-5509	476	23	collocation	collocation	NOUN
ejpam-5509	476	24	method	method	NOUN
ejpam-5509	476	25	for	for	ADP
ejpam-5509	476	26	time	time	NOUN
ejpam-5509	476	27	-	-	PUNCT
ejpam-5509	476	28	fractional	fractional	ADJ
ejpam-5509	476	29	pdes	pde	NOUN
ejpam-5509	476	30	.	.	PUNCT
ejpam-5509	477	1	discrete	discrete	ADJ
ejpam-5509	477	2	&	&	CCONJ
ejpam-5509	477	3	continuous	continuous	ADJ
ejpam-5509	477	4	dynamical	dynamical	ADJ
ejpam-5509	477	5	systems	system	NOUN
ejpam-5509	477	6	-	-	PUNCT
ejpam-5509	477	7	series	series	NOUN
ejpam-5509	477	8	s	s	PART
ejpam-5509	477	9	,	,	PUNCT
ejpam-5509	477	10	13(10	13(10	NUM
ejpam-5509	477	11	)	)	PUNCT
ejpam-5509	477	12	,	,	PUNCT
ejpam-5509	477	13	2020	2020	NUM
ejpam-5509	477	14	.	.	PUNCT
ejpam-5509	478	1	[	[	X
ejpam-5509	478	2	5	5	X
ejpam-5509	478	3	]	]	X
ejpam-5509	478	4	mustafa	mustafa	PROPN
ejpam-5509	478	5	ahmed	ahmed	PROPN
ejpam-5509	478	6	and	and	CCONJ
ejpam-5509	478	7	shireen	shireen	PROPN
ejpam-5509	478	8	jawad	jawad	PROPN
ejpam-5509	478	9	.	.	PUNCT
ejpam-5509	479	1	the	the	DET
ejpam-5509	479	2	role	role	NOUN
ejpam-5509	479	3	of	of	ADP
ejpam-5509	479	4	antibiotics	antibiotic	NOUN
ejpam-5509	479	5	and	and	CCONJ
ejpam-5509	479	6	probiotics	probiotic	NOUN
ejpam-5509	479	7	supplements	supplement	NOUN
ejpam-5509	479	8	on	on	ADP
ejpam-5509	479	9	the	the	DET
ejpam-5509	479	10	stability	stability	NOUN
ejpam-5509	479	11	of	of	ADP
ejpam-5509	479	12	gut	gut	NOUN
ejpam-5509	479	13	flora	flora	NOUN
ejpam-5509	479	14	bacteria	bacteria	NOUN
ejpam-5509	479	15	interactions	interaction	NOUN
ejpam-5509	479	16	.	.	PUNCT
ejpam-5509	480	1	commun	commun	PROPN
ejpam-5509	480	2	.	.	PUNCT
ejpam-5509	481	1	math	math	NOUN
ejpam-5509	481	2	.	.	PUNCT
ejpam-5509	482	1	biol	biol	PROPN
ejpam-5509	482	2	.	.	PUNCT
ejpam-5509	483	1	neurosci	neurosci	PROPN
ejpam-5509	483	2	.	.	PUNCT
ejpam-5509	483	3	,	,	PUNCT
ejpam-5509	483	4	2023	2023	NUM
ejpam-5509	483	5	:	:	PUNCT
ejpam-5509	483	6	article	article	NOUN
ejpam-5509	483	7	–	–	PUNCT
ejpam-5509	483	8	id	id	NOUN
ejpam-5509	483	9	,	,	PUNCT
ejpam-5509	483	10	2023	2023	NUM
ejpam-5509	483	11	.	.	PUNCT
ejpam-5509	484	1	[	[	X
ejpam-5509	484	2	6	6	NUM
ejpam-5509	484	3	]	]	X
ejpam-5509	484	4	saim	saim	PROPN
ejpam-5509	484	5	ahmed	ahmed	PROPN
ejpam-5509	484	6	,	,	PUNCT
ejpam-5509	484	7	ahmad	ahmad	PROPN
ejpam-5509	484	8	taher	taher	PROPN
ejpam-5509	484	9	azar	azar	PROPN
ejpam-5509	484	10	,	,	PUNCT
ejpam-5509	484	11	mahmoud	mahmoud	PROPN
ejpam-5509	484	12	abdel	abdel	PROPN
ejpam-5509	484	13	-	-	PUNCT
ejpam-5509	484	14	aty	aty	PROPN
ejpam-5509	484	15	,	,	PUNCT
ejpam-5509	484	16	hasib	hasib	PROPN
ejpam-5509	484	17	khan	khan	PROPN
ejpam-5509	484	18	,	,	PUNCT
ejpam-5509	484	19	and	and	CCONJ
ejpam-5509	484	20	jehad	jehad	PROPN
ejpam-5509	484	21	alzabut	alzabut	PROPN
ejpam-5509	484	22	.	.	PUNCT
ejpam-5509	485	1	a	a	DET
ejpam-5509	485	2	nonlinear	nonlinear	ADJ
ejpam-5509	485	3	system	system	NOUN
ejpam-5509	485	4	of	of	ADP
ejpam-5509	485	5	hybrid	hybrid	ADJ
ejpam-5509	485	6	fractional	fractional	ADJ
ejpam-5509	485	7	differential	differential	ADJ
ejpam-5509	485	8	equations	equation	NOUN
ejpam-5509	485	9	with	with	ADP
ejpam-5509	485	10	application	application	NOUN
ejpam-5509	485	11	to	to	ADP
ejpam-5509	485	12	fixed	fix	VERB
ejpam-5509	485	13	time	time	NOUN
ejpam-5509	485	14	sliding	slide	VERB
ejpam-5509	485	15	mode	mode	NOUN
ejpam-5509	485	16	control	control	NOUN
ejpam-5509	485	17	for	for	ADP
ejpam-5509	485	18	leukemia	leukemia	NOUN
ejpam-5509	485	19	therapy	therapy	NOUN
ejpam-5509	485	20	.	.	PUNCT
ejpam-5509	486	1	ain	ain	PROPN
ejpam-5509	486	2	shams	sham	VERB
ejpam-5509	486	3	engineering	engineering	NOUN
ejpam-5509	486	4	journal	journal	NOUN
ejpam-5509	486	5	,	,	PUNCT
ejpam-5509	486	6	15(4):102566	15(4):102566	NUM
ejpam-5509	486	7	,	,	PUNCT
ejpam-5509	486	8	2024	2024	NUM
ejpam-5509	486	9	.	.	PUNCT
ejpam-5509	487	1	[	[	X
ejpam-5509	487	2	7	7	X
ejpam-5509	487	3	]	]	X
ejpam-5509	487	4	ahmed	ahmed	PROPN
ejpam-5509	487	5	ali	ali	PROPN
ejpam-5509	487	6	,	,	PUNCT
ejpam-5509	487	7	shireen	shireen	PROPN
ejpam-5509	487	8	jawad	jawad	PROPN
ejpam-5509	487	9	,	,	PUNCT
ejpam-5509	487	10	ali	ali	PROPN
ejpam-5509	487	11	hasan	hasan	PROPN
ejpam-5509	487	12	ali	ali	PROPN
ejpam-5509	487	13	,	,	PUNCT
ejpam-5509	487	14	and	and	CCONJ
ejpam-5509	487	15	matthias	matthias	PROPN
ejpam-5509	487	16	winter	winter	NOUN
ejpam-5509	487	17	.	.	PUNCT
ejpam-5509	488	1	stability	stability	NOUN
ejpam-5509	488	2	analysis	analysis	NOUN
ejpam-5509	488	3	for	for	ADP
ejpam-5509	488	4	the	the	DET
ejpam-5509	488	5	phytoplankton	phytoplankton	NOUN
ejpam-5509	488	6	-	-	PUNCT
ejpam-5509	488	7	zooplankton	zooplankton	NOUN
ejpam-5509	488	8	model	model	NOUN
ejpam-5509	488	9	with	with	ADP
ejpam-5509	488	10	depletion	depletion	NOUN
ejpam-5509	488	11	of	of	ADP
ejpam-5509	488	12	dissolved	dissolved	ADJ
ejpam-5509	488	13	oxygen	oxygen	NOUN
ejpam-5509	488	14	and	and	CCONJ
ejpam-5509	488	15	strong	strong	ADJ
ejpam-5509	488	16	allee	allee	NOUN
ejpam-5509	488	17	effects	effect	NOUN
ejpam-5509	488	18	.	.	PUNCT
ejpam-5509	489	1	results	result	NOUN
ejpam-5509	489	2	in	in	ADP
ejpam-5509	489	3	engineering	engineering	NOUN
ejpam-5509	489	4	,	,	PUNCT
ejpam-5509	489	5	22:102190	22:102190	NUM
ejpam-5509	489	6	,	,	PUNCT
ejpam-5509	489	7	2024	2024	NUM
ejpam-5509	489	8	.	.	PUNCT
ejpam-5509	490	1	i.	i.	PROPN
ejpam-5509	490	2	ahmad	ahmad	PROPN
ejpam-5509	490	3	et	et	PROPN
ejpam-5509	490	4	al	al	PROPN
ejpam-5509	490	5	.	.	PUNCT
ejpam-5509	490	6	/	/	SYM
ejpam-5509	490	7	eur	eur	PROPN
ejpam-5509	490	8	.	.	PUNCT
ejpam-5509	491	1	j.	j.	PROPN
ejpam-5509	491	2	pure	pure	PROPN
ejpam-5509	491	3	appl	appl	PROPN
ejpam-5509	491	4	.	.	PROPN
ejpam-5509	491	5	math	math	PROPN
ejpam-5509	491	6	,	,	PUNCT
ejpam-5509	491	7	18	18	NUM
ejpam-5509	491	8	(	(	PUNCT
ejpam-5509	491	9	1	1	NUM
ejpam-5509	491	10	)	)	PUNCT
ejpam-5509	491	11	(	(	PUNCT
ejpam-5509	491	12	2025	2025	NUM
ejpam-5509	491	13	)	)	PUNCT
ejpam-5509	491	14	,	,	PUNCT
ejpam-5509	491	15	5509	5509	NUM
ejpam-5509	491	16	25	25	NUM
ejpam-5509	491	17	of	of	ADP
ejpam-5509	491	18	27	27	NUM
ejpam-5509	491	19	[	[	SYM
ejpam-5509	491	20	8	8	NUM
ejpam-5509	491	21	]	]	X
ejpam-5509	491	22	najat	najat	ADJ
ejpam-5509	491	23	almutairi	almutairi	NOUN
ejpam-5509	491	24	and	and	CCONJ
ejpam-5509	491	25	sayed	say	VERB
ejpam-5509	491	26	saber	saber	PROPN
ejpam-5509	491	27	.	.	PUNCT
ejpam-5509	492	1	on	on	ADP
ejpam-5509	492	2	chaos	chaos	NOUN
ejpam-5509	492	3	control	control	NOUN
ejpam-5509	492	4	of	of	ADP
ejpam-5509	492	5	nonlinear	nonlinear	PROPN
ejpam-5509	492	6	fractional	fractional	PROPN
ejpam-5509	492	7	newton	newton	PROPN
ejpam-5509	492	8	-	-	PUNCT
ejpam-5509	492	9	leipnik	leipnik	NOUN
ejpam-5509	492	10	system	system	NOUN
ejpam-5509	492	11	via	via	ADP
ejpam-5509	492	12	fractional	fractional	PROPN
ejpam-5509	492	13	caputo	caputo	PROPN
ejpam-5509	492	14	-	-	PUNCT
ejpam-5509	492	15	fabrizio	fabrizio	PROPN
ejpam-5509	492	16	derivatives	derivative	NOUN
ejpam-5509	492	17	.	.	PUNCT
ejpam-5509	493	1	scientific	scientific	ADJ
ejpam-5509	493	2	reports	report	NOUN
ejpam-5509	493	3	,	,	PUNCT
ejpam-5509	493	4	13(1):22726	13(1):22726	NUM
ejpam-5509	493	5	,	,	PUNCT
ejpam-5509	493	6	2023	2023	NUM
ejpam-5509	493	7	.	.	PUNCT
ejpam-5509	494	1	[	[	X
ejpam-5509	494	2	9	9	NUM
ejpam-5509	494	3	]	]	X
ejpam-5509	494	4	najat	najat	ADJ
ejpam-5509	494	5	almutairi	almutairi	NOUN
ejpam-5509	494	6	and	and	CCONJ
ejpam-5509	494	7	sayed	sayed	PROPN
ejpam-5509	494	8	saber	saber	PROPN
ejpam-5509	494	9	.	.	PUNCT
ejpam-5509	495	1	existence	existence	NOUN
ejpam-5509	495	2	of	of	ADP
ejpam-5509	495	3	chaos	chaos	NOUN
ejpam-5509	495	4	and	and	CCONJ
ejpam-5509	495	5	the	the	DET
ejpam-5509	495	6	approximate	approximate	ADJ
ejpam-5509	495	7	solution	solution	NOUN
ejpam-5509	495	8	of	of	ADP
ejpam-5509	495	9	the	the	DET
ejpam-5509	495	10	lorenz	lorenz	PROPN
ejpam-5509	495	11	–	–	PUNCT
ejpam-5509	495	12	lü–chen	lü–chen	NOUN
ejpam-5509	495	13	system	system	NOUN
ejpam-5509	495	14	with	with	ADP
ejpam-5509	495	15	the	the	DET
ejpam-5509	495	16	caputo	caputo	PROPN
ejpam-5509	495	17	fractional	fractional	PROPN
ejpam-5509	495	18	operator	operator	NOUN
ejpam-5509	495	19	.	.	PUNCT
ejpam-5509	496	1	aip	aip	PROPN
ejpam-5509	496	2	advances	advance	NOUN
ejpam-5509	496	3	,	,	PUNCT
ejpam-5509	496	4	14(1	14(1	NUM
ejpam-5509	496	5	)	)	PUNCT
ejpam-5509	496	6	,	,	PUNCT
ejpam-5509	496	7	2024	2024	NUM
ejpam-5509	496	8	.	.	PUNCT
ejpam-5509	497	1	[	[	X
ejpam-5509	497	2	10	10	NUM
ejpam-5509	497	3	]	]	X
ejpam-5509	497	4	abdulrahman	abdulrahman	PROPN
ejpam-5509	497	5	obaid	obaid	PROPN
ejpam-5509	497	6	alshammari	alshammari	PROPN
ejpam-5509	497	7	,	,	PUNCT
ejpam-5509	497	8	imtiaz	imtiaz	PROPN
ejpam-5509	497	9	ahmad	ahmad	PROPN
ejpam-5509	497	10	,	,	PUNCT
ejpam-5509	497	11	rashid	rashid	PROPN
ejpam-5509	497	12	jan	jan	PROPN
ejpam-5509	497	13	,	,	PUNCT
ejpam-5509	497	14	and	and	CCONJ
ejpam-5509	497	15	sahar	sahar	PROPN
ejpam-5509	497	16	ahmed	ahmed	PROPN
ejpam-5509	497	17	idris	idris	PROPN
ejpam-5509	497	18	.	.	PUNCT
ejpam-5509	498	1	fractional	fractional	ADJ
ejpam-5509	498	2	-	-	PUNCT
ejpam-5509	498	3	calculus	calculus	NOUN
ejpam-5509	498	4	analysis	analysis	NOUN
ejpam-5509	498	5	of	of	ADP
ejpam-5509	498	6	the	the	DET
ejpam-5509	498	7	dynamics	dynamic	NOUN
ejpam-5509	498	8	of	of	ADP
ejpam-5509	498	9	cd4	cd4	PROPN
ejpam-5509	498	10	+	+	PROPN
ejpam-5509	498	11	t	t	NOUN
ejpam-5509	498	12	cells	cell	NOUN
ejpam-5509	498	13	and	and	CCONJ
ejpam-5509	498	14	human	human	ADJ
ejpam-5509	498	15	immunodeficiency	immunodeficiency	NOUN
ejpam-5509	498	16	viruses	virus	NOUN
ejpam-5509	498	17	.	.	PUNCT
ejpam-5509	499	1	the	the	DET
ejpam-5509	499	2	european	european	PROPN
ejpam-5509	499	3	physical	physical	PROPN
ejpam-5509	499	4	journal	journal	PROPN
ejpam-5509	499	5	special	special	ADJ
ejpam-5509	499	6	topics	topic	NOUN
ejpam-5509	499	7	,	,	PUNCT
ejpam-5509	499	8	pages	page	NOUN
ejpam-5509	499	9	1–13	1–13	NOUN
ejpam-5509	499	10	,	,	PUNCT
ejpam-5509	499	11	2024	2024	NUM
ejpam-5509	499	12	.	.	PUNCT
ejpam-5509	500	1	[	[	X
ejpam-5509	500	2	11	11	NUM
ejpam-5509	500	3	]	]	X
ejpam-5509	500	4	rm	rm	PROPN
ejpam-5509	500	5	anderson	anderson	PROPN
ejpam-5509	500	6	,	,	PUNCT
ejpam-5509	500	7	gf	gf	NOUN
ejpam-5509	500	8	medley	medley	NOUN
ejpam-5509	500	9	,	,	PUNCT
ejpam-5509	500	10	and	and	CCONJ
ejpam-5509	500	11	dj	dj	X
ejpam-5509	500	12	nokes	noke	NOUN
ejpam-5509	500	13	.	.	PUNCT
ejpam-5509	501	1	preliminary	preliminary	ADJ
ejpam-5509	501	2	analyses	analysis	NOUN
ejpam-5509	501	3	of	of	ADP
ejpam-5509	501	4	the	the	DET
ejpam-5509	501	5	predicted	predict	VERB
ejpam-5509	501	6	impacts	impact	NOUN
ejpam-5509	501	7	of	of	ADP
ejpam-5509	501	8	various	various	ADJ
ejpam-5509	501	9	vaccination	vaccination	NOUN
ejpam-5509	501	10	strategies	strategy	NOUN
ejpam-5509	501	11	on	on	ADP
ejpam-5509	501	12	the	the	DET
ejpam-5509	501	13	transmission	transmission	NOUN
ejpam-5509	501	14	of	of	ADP
ejpam-5509	501	15	hepatitis	hepatitis	PROPN
ejpam-5509	501	16	b	b	PROPN
ejpam-5509	501	17	virus	virus	NOUN
ejpam-5509	501	18	.	.	PUNCT
ejpam-5509	502	1	the	the	DET
ejpam-5509	502	2	control	control	NOUN
ejpam-5509	502	3	of	of	ADP
ejpam-5509	502	4	hepatitis	hepatitis	PROPN
ejpam-5509	502	5	b	b	PROPN
ejpam-5509	502	6	:	:	PUNCT
ejpam-5509	502	7	the	the	DET
ejpam-5509	502	8	role	role	NOUN
ejpam-5509	502	9	of	of	ADP
ejpam-5509	502	10	prevention	prevention	NOUN
ejpam-5509	502	11	in	in	ADP
ejpam-5509	502	12	adolescence	adolescence	NOUN
ejpam-5509	502	13	,	,	PUNCT
ejpam-5509	502	14	95130	95130	NUM
ejpam-5509	502	15	,	,	PUNCT
ejpam-5509	502	16	1992	1992	NUM
ejpam-5509	502	17	.	.	PUNCT
ejpam-5509	503	1	[	[	X
ejpam-5509	503	2	12	12	NUM
ejpam-5509	503	3	]	]	PUNCT
ejpam-5509	503	4	abdon	abdon	NOUN
ejpam-5509	503	5	atangana	atangana	PROPN
ejpam-5509	503	6	and	and	CCONJ
ejpam-5509	503	7	kolade	kolade	ADJ
ejpam-5509	503	8	m.	m.	NOUN
ejpam-5509	503	9	owolabi	owolabi	NOUN
ejpam-5509	503	10	.	.	PUNCT
ejpam-5509	504	1	new	new	ADJ
ejpam-5509	504	2	numerical	numerical	ADJ
ejpam-5509	504	3	approach	approach	NOUN
ejpam-5509	504	4	for	for	ADP
ejpam-5509	504	5	fractional	fractional	ADJ
ejpam-5509	504	6	differential	differential	ADJ
ejpam-5509	504	7	equations	equation	NOUN
ejpam-5509	504	8	.	.	PUNCT
ejpam-5509	505	1	mathematical	mathematical	ADJ
ejpam-5509	505	2	modelling	modelling	NOUN
ejpam-5509	505	3	of	of	ADP
ejpam-5509	505	4	natural	natural	ADJ
ejpam-5509	505	5	phenomena	phenomenon	NOUN
ejpam-5509	505	6	,	,	PUNCT
ejpam-5509	505	7	13:3	13:3	NUM
ejpam-5509	505	8	,	,	PUNCT
ejpam-5509	505	9	2018	2018	NUM
ejpam-5509	505	10	.	.	PUNCT
ejpam-5509	506	1	[	[	X
ejpam-5509	506	2	13	13	NUM
ejpam-5509	506	3	]	]	X
ejpam-5509	506	4	m.a	m.a	PROPN
ejpam-5509	506	5	.	.	PROPN
ejpam-5509	506	6	belay	belay	PROPN
ejpam-5509	506	7	,	,	PUNCT
ejpam-5509	506	8	o.j	o.j	PROPN
ejpam-5509	506	9	.	.	PROPN
ejpam-5509	506	10	abonyo	abonyo	PROPN
ejpam-5509	506	11	,	,	PUNCT
ejpam-5509	506	12	and	and	CCONJ
ejpam-5509	507	1	d.m	d.m	PROPN
ejpam-5509	507	2	.	.	PROPN
ejpam-5509	507	3	theuri	theuri	PROPN
ejpam-5509	507	4	.	.	PUNCT
ejpam-5509	508	1	mathematical	mathematical	ADJ
ejpam-5509	508	2	model	model	NOUN
ejpam-5509	508	3	of	of	ADP
ejpam-5509	508	4	hepatitis	hepatitis	PROPN
ejpam-5509	508	5	b	b	PROPN
ejpam-5509	508	6	disease	disease	NOUN
ejpam-5509	508	7	with	with	ADP
ejpam-5509	508	8	optimal	optimal	ADJ
ejpam-5509	508	9	control	control	NOUN
ejpam-5509	508	10	and	and	CCONJ
ejpam-5509	508	11	cost	cost	NOUN
ejpam-5509	508	12	-	-	PUNCT
ejpam-5509	508	13	effectiveness	effectiveness	NOUN
ejpam-5509	508	14	analysis	analysis	NOUN
ejpam-5509	508	15	.	.	PUNCT
ejpam-5509	509	1	computational	computational	ADJ
ejpam-5509	509	2	and	and	CCONJ
ejpam-5509	509	3	mathematical	mathematical	ADJ
ejpam-5509	509	4	methods	method	NOUN
ejpam-5509	509	5	in	in	ADP
ejpam-5509	509	6	medicine	medicine	NOUN
ejpam-5509	509	7	,	,	PUNCT
ejpam-5509	509	8	2023(1):5215494	2023(1):5215494	NUM
ejpam-5509	509	9	,	,	PUNCT
ejpam-5509	509	10	2023	2023	NUM
ejpam-5509	509	11	.	.	PUNCT
ejpam-5509	510	1	[	[	X
ejpam-5509	510	2	14	14	NUM
ejpam-5509	510	3	]	]	X
ejpam-5509	510	4	imtiyaz	imtiyaz	PROPN
ejpam-5509	510	5	ahmad	ahmad	PROPN
ejpam-5509	510	6	bhat	bhat	PROPN
ejpam-5509	510	7	and	and	CCONJ
ejpam-5509	510	8	lakshmi	lakshmi	PROPN
ejpam-5509	510	9	narayan	narayan	PROPN
ejpam-5509	510	10	mishra	mishra	PROPN
ejpam-5509	510	11	.	.	PUNCT
ejpam-5509	511	1	a	a	DET
ejpam-5509	511	2	comparative	comparative	ADJ
ejpam-5509	511	3	study	study	NOUN
ejpam-5509	511	4	of	of	ADP
ejpam-5509	511	5	discretization	discretization	NOUN
ejpam-5509	511	6	techniques	technique	NOUN
ejpam-5509	511	7	for	for	ADP
ejpam-5509	511	8	augmented	augment	VERB
ejpam-5509	511	9	urysohn	urysohn	PROPN
ejpam-5509	511	10	type	type	NOUN
ejpam-5509	511	11	nonlinear	nonlinear	ADJ
ejpam-5509	511	12	functional	functional	ADJ
ejpam-5509	511	13	volterra	volterra	PROPN
ejpam-5509	511	14	integral	integral	ADJ
ejpam-5509	511	15	equations	equation	NOUN
ejpam-5509	511	16	and	and	CCONJ
ejpam-5509	511	17	their	their	PRON
ejpam-5509	511	18	convergence	convergence	NOUN
ejpam-5509	511	19	analysis	analysis	NOUN
ejpam-5509	511	20	.	.	PUNCT
ejpam-5509	512	1	applied	apply	VERB
ejpam-5509	512	2	mathematics	mathematic	NOUN
ejpam-5509	512	3	and	and	CCONJ
ejpam-5509	512	4	computation	computation	NOUN
ejpam-5509	512	5	,	,	PUNCT
ejpam-5509	512	6	470:128555	470:128555	NUM
ejpam-5509	512	7	,	,	PUNCT
ejpam-5509	512	8	2024	2024	NUM
ejpam-5509	512	9	.	.	PUNCT
ejpam-5509	513	1	[	[	X
ejpam-5509	513	2	15	15	NUM
ejpam-5509	513	3	]	]	X
ejpam-5509	513	4	imtiyaz	imtiyaz	PROPN
ejpam-5509	513	5	ahmad	ahmad	PROPN
ejpam-5509	513	6	bhat	bhat	PROPN
ejpam-5509	513	7	,	,	PUNCT
ejpam-5509	513	8	lakshmi	lakshmi	PROPN
ejpam-5509	513	9	narayan	narayan	PROPN
ejpam-5509	513	10	mishra	mishra	PROPN
ejpam-5509	513	11	,	,	PUNCT
ejpam-5509	513	12	vishnu	vishnu	PROPN
ejpam-5509	513	13	narayan	narayan	PROPN
ejpam-5509	513	14	mishra	mishra	PROPN
ejpam-5509	513	15	,	,	PUNCT
ejpam-5509	513	16	mahmoud	mahmoud	PROPN
ejpam-5509	513	17	abdel	abdel	PROPN
ejpam-5509	513	18	-	-	PUNCT
ejpam-5509	513	19	aty	aty	PROPN
ejpam-5509	513	20	,	,	PUNCT
ejpam-5509	513	21	and	and	CCONJ
ejpam-5509	513	22	montasir	montasir	PROPN
ejpam-5509	513	23	qasymeh	qasymeh	NOUN
ejpam-5509	513	24	.	.	PUNCT
ejpam-5509	514	1	a	a	DET
ejpam-5509	514	2	comprehensive	comprehensive	ADJ
ejpam-5509	514	3	analysis	analysis	NOUN
ejpam-5509	514	4	for	for	ADP
ejpam-5509	514	5	weakly	weakly	ADJ
ejpam-5509	514	6	singular	singular	ADJ
ejpam-5509	514	7	nonlinear	nonlinear	PROPN
ejpam-5509	514	8	functional	functional	PROPN
ejpam-5509	514	9	volterra	volterra	PROPN
ejpam-5509	514	10	integral	integral	ADJ
ejpam-5509	514	11	equations	equation	NOUN
ejpam-5509	514	12	using	use	VERB
ejpam-5509	514	13	discretization	discretization	NOUN
ejpam-5509	514	14	techniques	technique	NOUN
ejpam-5509	514	15	.	.	PUNCT
ejpam-5509	515	1	alexandria	alexandria	PROPN
ejpam-5509	515	2	engineering	engineering	PROPN
ejpam-5509	515	3	journal	journal	PROPN
ejpam-5509	515	4	,	,	PUNCT
ejpam-5509	515	5	104:564–575	104:564–575	NUM
ejpam-5509	515	6	,	,	PUNCT
ejpam-5509	515	7	2024	2024	NUM
ejpam-5509	515	8	.	.	PUNCT
ejpam-5509	516	1	[	[	X
ejpam-5509	516	2	16	16	NUM
ejpam-5509	516	3	]	]	X
ejpam-5509	516	4	michele	michele	PROPN
ejpam-5509	516	5	caputo	caputo	PROPN
ejpam-5509	516	6	and	and	CCONJ
ejpam-5509	516	7	mauro	mauro	PROPN
ejpam-5509	516	8	fabrizio	fabrizio	PROPN
ejpam-5509	516	9	.	.	PUNCT
ejpam-5509	517	1	a	a	DET
ejpam-5509	517	2	new	new	ADJ
ejpam-5509	517	3	definition	definition	NOUN
ejpam-5509	517	4	of	of	ADP
ejpam-5509	517	5	fractional	fractional	ADJ
ejpam-5509	517	6	derivative	derivative	NOUN
ejpam-5509	517	7	without	without	ADP
ejpam-5509	517	8	singular	singular	ADJ
ejpam-5509	517	9	kernel	kernel	PROPN
ejpam-5509	517	10	.	.	PUNCT
ejpam-5509	518	1	progress	progress	NOUN
ejpam-5509	518	2	in	in	ADP
ejpam-5509	518	3	fractional	fractional	ADJ
ejpam-5509	518	4	differentiation	differentiation	NOUN
ejpam-5509	518	5	&	&	CCONJ
ejpam-5509	518	6	applications	application	NOUN
ejpam-5509	518	7	,	,	PUNCT
ejpam-5509	518	8	1(2):73–85	1(2):73–85	NUM
ejpam-5509	518	9	,	,	PUNCT
ejpam-5509	518	10	2015	2015	NUM
ejpam-5509	518	11	.	.	PUNCT
ejpam-5509	519	1	[	[	X
ejpam-5509	519	2	17	17	NUM
ejpam-5509	519	3	]	]	X
ejpam-5509	519	4	stanca	stanca	NOUN
ejpam-5509	519	5	m	m	PROPN
ejpam-5509	519	6	ciupe	ciupe	ADJ
ejpam-5509	519	7	,	,	PUNCT
ejpam-5509	519	8	ruy	ruy	PROPN
ejpam-5509	519	9	m	m	PROPN
ejpam-5509	519	10	ribeiro	ribeiro	PROPN
ejpam-5509	519	11	,	,	PUNCT
ejpam-5509	519	12	and	and	CCONJ
ejpam-5509	519	13	alan	alan	PROPN
ejpam-5509	519	14	s	s	PROPN
ejpam-5509	519	15	perelson	perelson	NOUN
ejpam-5509	519	16	.	.	PUNCT
ejpam-5509	520	1	antibody	antibody	NOUN
ejpam-5509	520	2	responses	response	NOUN
ejpam-5509	520	3	during	during	ADP
ejpam-5509	520	4	hepatitis	hepatitis	PROPN
ejpam-5509	520	5	b	b	PROPN
ejpam-5509	520	6	viral	viral	ADJ
ejpam-5509	520	7	infection	infection	NOUN
ejpam-5509	520	8	.	.	PUNCT
ejpam-5509	521	1	plos	plos	PROPN
ejpam-5509	521	2	computational	computational	ADJ
ejpam-5509	521	3	biology	biology	NOUN
ejpam-5509	521	4	,	,	PUNCT
ejpam-5509	521	5	10(7):e1003730	10(7):e1003730	NOUN
ejpam-5509	521	6	,	,	PUNCT
ejpam-5509	521	7	2014	2014	NUM
ejpam-5509	521	8	.	.	PUNCT
ejpam-5509	522	1	[	[	X
ejpam-5509	522	2	18	18	NUM
ejpam-5509	522	3	]	]	PUNCT
ejpam-5509	522	4	anwarud	anwarud	PROPN
ejpam-5509	522	5	din	din	PROPN
ejpam-5509	522	6	and	and	CCONJ
ejpam-5509	522	7	muhammad	muhammad	PROPN
ejpam-5509	522	8	zainul	zainul	PROPN
ejpam-5509	522	9	abidin	abidin	PROPN
ejpam-5509	522	10	.	.	PUNCT
ejpam-5509	523	1	analysis	analysis	NOUN
ejpam-5509	523	2	of	of	ADP
ejpam-5509	523	3	fractional	fractional	ADJ
ejpam-5509	523	4	-	-	PUNCT
ejpam-5509	523	5	order	order	NOUN
ejpam-5509	523	6	vaccinated	vaccinate	VERB
ejpam-5509	523	7	hepatitis	hepatitis	NOUN
ejpam-5509	523	8	-	-	PUNCT
ejpam-5509	523	9	b	b	NOUN
ejpam-5509	523	10	epidemic	epidemic	NOUN
ejpam-5509	523	11	model	model	NOUN
ejpam-5509	523	12	with	with	ADP
ejpam-5509	523	13	mittag	mittag	ADJ
ejpam-5509	523	14	-	-	PUNCT
ejpam-5509	523	15	leffler	leffler	NOUN
ejpam-5509	523	16	kernels	kernel	NOUN
ejpam-5509	523	17	.	.	PUNCT
ejpam-5509	524	1	mathematical	mathematical	ADJ
ejpam-5509	524	2	modelling	modelling	NOUN
ejpam-5509	524	3	and	and	CCONJ
ejpam-5509	524	4	numerical	numerical	PROPN
ejpam-5509	524	5	simulation	simulation	NOUN
ejpam-5509	524	6	with	with	ADP
ejpam-5509	524	7	applications	application	NOUN
ejpam-5509	524	8	,	,	PUNCT
ejpam-5509	524	9	2(2):59–72	2(2):59–72	NUM
ejpam-5509	524	10	,	,	PUNCT
ejpam-5509	524	11	2022	2022	NUM
ejpam-5509	524	12	.	.	PUNCT
ejpam-5509	525	1	[	[	X
ejpam-5509	525	2	19	19	NUM
ejpam-5509	525	3	]	]	X
ejpam-5509	525	4	w	w	PROPN
ejpam-5509	525	5	john	john	PROPN
ejpam-5509	525	6	edmunds	edmunds	PROPN
ejpam-5509	525	7	,	,	PUNCT
ejpam-5509	525	8	gf	gf	NOUN
ejpam-5509	525	9	medley	medley	NOUN
ejpam-5509	525	10	,	,	PUNCT
ejpam-5509	525	11	d	d	PROPN
ejpam-5509	525	12	james	james	PROPN
ejpam-5509	525	13	nokes	nokes	PROPN
ejpam-5509	525	14	,	,	PUNCT
ejpam-5509	525	15	cj	cj	NOUN
ejpam-5509	525	16	o’callaghan	o’callaghan	PROPN
ejpam-5509	525	17	,	,	PUNCT
ejpam-5509	525	18	hc	hc	X
ejpam-5509	525	19	whittle	whittle	NOUN
ejpam-5509	525	20	,	,	PUNCT
ejpam-5509	525	21	and	and	CCONJ
ejpam-5509	525	22	andrew	andrew	PROPN
ejpam-5509	525	23	james	james	PROPN
ejpam-5509	525	24	hall	hall	PROPN
ejpam-5509	525	25	.	.	PUNCT
ejpam-5509	526	1	epidemiological	epidemiological	ADJ
ejpam-5509	526	2	patterns	pattern	NOUN
ejpam-5509	526	3	of	of	ADP
ejpam-5509	526	4	hepatitis	hepatitis	PROPN
ejpam-5509	526	5	b	b	PROPN
ejpam-5509	526	6	virus	virus	NOUN
ejpam-5509	526	7	(	(	PUNCT
ejpam-5509	526	8	hbv	hbv	NOUN
ejpam-5509	526	9	)	)	PUNCT
ejpam-5509	526	10	in	in	ADP
ejpam-5509	526	11	highly	highly	ADV
ejpam-5509	526	12	endemic	endemic	ADJ
ejpam-5509	526	13	areasr	areasr	NOUN
ejpam-5509	526	14	.	.	PUNCT
ejpam-5509	527	1	epidemiology	epidemiology	NOUN
ejpam-5509	527	2	&	&	CCONJ
ejpam-5509	527	3	infection	infection	NOUN
ejpam-5509	527	4	,	,	PUNCT
ejpam-5509	527	5	117(2):313–325	117(2):313–325	PROPN
ejpam-5509	527	6	,	,	PUNCT
ejpam-5509	527	7	1996	1996	NUM
ejpam-5509	527	8	.	.	PUNCT
ejpam-5509	528	1	[	[	X
ejpam-5509	528	2	20	20	NUM
ejpam-5509	528	3	]	]	X
ejpam-5509	528	4	wj	wj	PROPN
ejpam-5509	528	5	edmunds	edmunds	PROPN
ejpam-5509	528	6	,	,	PUNCT
ejpam-5509	528	7	gf	gf	NOUN
ejpam-5509	528	8	medley	medley	NOUN
ejpam-5509	528	9	,	,	PUNCT
ejpam-5509	528	10	and	and	CCONJ
ejpam-5509	528	11	dj	dj	NOUN
ejpam-5509	528	12	nokes	noke	NOUN
ejpam-5509	528	13	.	.	PUNCT
ejpam-5509	529	1	the	the	DET
ejpam-5509	529	2	transmission	transmission	NOUN
ejpam-5509	529	3	dynamics	dynamic	NOUN
ejpam-5509	529	4	and	and	CCONJ
ejpam-5509	529	5	control	control	NOUN
ejpam-5509	529	6	of	of	ADP
ejpam-5509	529	7	hepatitis	hepatitis	PROPN
ejpam-5509	529	8	b	b	PROPN
ejpam-5509	529	9	virus	virus	NOUN
ejpam-5509	529	10	in	in	ADP
ejpam-5509	529	11	the	the	DET
ejpam-5509	529	12	gambia	gambia	NOUN
ejpam-5509	529	13	.	.	PUNCT
ejpam-5509	530	1	statistics	statistic	NOUN
ejpam-5509	530	2	in	in	ADP
ejpam-5509	530	3	medicine	medicine	NOUN
ejpam-5509	530	4	,	,	PUNCT
ejpam-5509	530	5	15(20):2215–2233	15(20):2215–2233	NUM
ejpam-5509	530	6	,	,	PUNCT
ejpam-5509	530	7	1996	1996	NUM
ejpam-5509	530	8	.	.	PUNCT
ejpam-5509	531	1	[	[	X
ejpam-5509	531	2	21	21	NUM
ejpam-5509	531	3	]	]	X
ejpam-5509	531	4	wj	wj	PROPN
ejpam-5509	531	5	edmunds	edmunds	PROPN
ejpam-5509	531	6	,	,	PUNCT
ejpam-5509	531	7	gf	gf	NOUN
ejpam-5509	531	8	medley	medley	NOUN
ejpam-5509	531	9	,	,	PUNCT
ejpam-5509	531	10	dj	dj	NOUN
ejpam-5509	531	11	nokes	noke	NOUN
ejpam-5509	531	12	,	,	PUNCT
ejpam-5509	531	13	aj	aj	PROPN
ejpam-5509	531	14	hall	hall	PROPN
ejpam-5509	531	15	,	,	PUNCT
ejpam-5509	531	16	and	and	CCONJ
ejpam-5509	531	17	hc	hc	AUX
ejpam-5509	531	18	whittle	whittle	NOUN
ejpam-5509	531	19	.	.	PUNCT
ejpam-5509	532	1	the	the	DET
ejpam-5509	532	2	influence	influence	NOUN
ejpam-5509	532	3	of	of	ADP
ejpam-5509	532	4	age	age	NOUN
ejpam-5509	532	5	on	on	ADP
ejpam-5509	532	6	the	the	DET
ejpam-5509	532	7	development	development	NOUN
ejpam-5509	532	8	of	of	ADP
ejpam-5509	532	9	the	the	DET
ejpam-5509	532	10	hepatitis	hepatitis	PROPN
ejpam-5509	532	11	b	b	PROPN
ejpam-5509	532	12	carrier	carrier	NOUN
ejpam-5509	532	13	state	state	NOUN
ejpam-5509	532	14	.	.	PUNCT
ejpam-5509	533	1	proceedings	proceeding	NOUN
ejpam-5509	533	2	of	of	ADP
ejpam-5509	533	3	the	the	DET
ejpam-5509	533	4	royal	royal	ADJ
ejpam-5509	533	5	society	society	NOUN
ejpam-5509	533	6	of	of	ADP
ejpam-5509	533	7	london	london	PROPN
ejpam-5509	533	8	.	.	PUNCT
ejpam-5509	534	1	series	series	PROPN
ejpam-5509	534	2	b	b	PROPN
ejpam-5509	534	3	:	:	PUNCT
ejpam-5509	534	4	biological	biological	ADJ
ejpam-5509	534	5	sciences	science	NOUN
ejpam-5509	534	6	,	,	PUNCT
ejpam-5509	534	7	253(1337):197–201	253(1337):197–201	NUM
ejpam-5509	534	8	,	,	PUNCT
ejpam-5509	534	9	1993	1993	NUM
ejpam-5509	534	10	.	.	PUNCT
ejpam-5509	535	1	[	[	X
ejpam-5509	535	2	22	22	NUM
ejpam-5509	535	3	]	]	X
ejpam-5509	535	4	engida	engida	PROPN
ejpam-5509	535	5	endriyas	endriyas	PROPN
ejpam-5509	535	6	endashaw	endashaw	NOUN
ejpam-5509	535	7	and	and	CCONJ
ejpam-5509	535	8	temesgen	temesgen	NOUN
ejpam-5509	535	9	tibebu	tibebu	NOUN
ejpam-5509	535	10	mekonnen	mekonnen	NOUN
ejpam-5509	535	11	.	.	PUNCT
ejpam-5509	536	1	modeling	model	VERB
ejpam-5509	536	2	the	the	DET
ejpam-5509	536	3	effect	effect	NOUN
ejpam-5509	536	4	i.	i.	PROPN
ejpam-5509	536	5	ahmad	ahmad	PROPN
ejpam-5509	536	6	et	et	PROPN
ejpam-5509	536	7	al	al	PROPN
ejpam-5509	536	8	.	.	PUNCT
ejpam-5509	536	9	/	/	SYM
ejpam-5509	536	10	eur	eur	PROPN
ejpam-5509	536	11	.	.	PUNCT
ejpam-5509	537	1	j.	j.	PROPN
ejpam-5509	537	2	pure	pure	PROPN
ejpam-5509	537	3	appl	appl	PROPN
ejpam-5509	537	4	.	.	PROPN
ejpam-5509	537	5	math	math	PROPN
ejpam-5509	537	6	,	,	PUNCT
ejpam-5509	537	7	18	18	NUM
ejpam-5509	537	8	(	(	PUNCT
ejpam-5509	537	9	1	1	NUM
ejpam-5509	537	10	)	)	PUNCT
ejpam-5509	537	11	(	(	PUNCT
ejpam-5509	537	12	2025	2025	NUM
ejpam-5509	537	13	)	)	PUNCT
ejpam-5509	537	14	,	,	PUNCT
ejpam-5509	537	15	5509	5509	NUM
ejpam-5509	537	16	26	26	NUM
ejpam-5509	537	17	of	of	ADP
ejpam-5509	537	18	27	27	NUM
ejpam-5509	537	19	of	of	ADP
ejpam-5509	537	20	vaccination	vaccination	NOUN
ejpam-5509	537	21	and	and	CCONJ
ejpam-5509	537	22	treatment	treatment	NOUN
ejpam-5509	537	23	on	on	ADP
ejpam-5509	537	24	the	the	DET
ejpam-5509	537	25	transmission	transmission	NOUN
ejpam-5509	537	26	dynamics	dynamic	NOUN
ejpam-5509	537	27	of	of	ADP
ejpam-5509	537	28	hepatitis	hepatitis	PROPN
ejpam-5509	537	29	b	b	PROPN
ejpam-5509	537	30	virus	virus	NOUN
ejpam-5509	537	31	and	and	CCONJ
ejpam-5509	537	32	hiv	hiv	PROPN
ejpam-5509	537	33	/	/	SYM
ejpam-5509	537	34	aids	aids	PROPN
ejpam-5509	537	35	coinfection	coinfection	NOUN
ejpam-5509	537	36	.	.	PUNCT
ejpam-5509	538	1	journal	journal	PROPN
ejpam-5509	538	2	of	of	ADP
ejpam-5509	538	3	applied	apply	VERB
ejpam-5509	538	4	mathematics	mathematic	NOUN
ejpam-5509	538	5	,	,	PUNCT
ejpam-5509	538	6	2022(1):5246762	2022(1):5246762	NOUN
ejpam-5509	538	7	,	,	PUNCT
ejpam-5509	538	8	2022	2022	NUM
ejpam-5509	538	9	.	.	PUNCT
ejpam-5509	539	1	[	[	X
ejpam-5509	539	2	23	23	NUM
ejpam-5509	539	3	]	]	X
ejpam-5509	539	4	stephen	stephen	NOUN
ejpam-5509	539	5	a	a	DET
ejpam-5509	539	6	gourley	gourley	NOUN
ejpam-5509	539	7	,	,	PUNCT
ejpam-5509	539	8	yang	yang	PROPN
ejpam-5509	539	9	kuang	kuang	PROPN
ejpam-5509	539	10	,	,	PUNCT
ejpam-5509	539	11	and	and	CCONJ
ejpam-5509	539	12	john	john	PROPN
ejpam-5509	539	13	d	d	PROPN
ejpam-5509	539	14	nagy	nagy	PROPN
ejpam-5509	539	15	.	.	PUNCT
ejpam-5509	540	1	dynamics	dynamic	NOUN
ejpam-5509	540	2	of	of	ADP
ejpam-5509	540	3	a	a	DET
ejpam-5509	540	4	delay	delay	NOUN
ejpam-5509	540	5	differential	differential	ADJ
ejpam-5509	540	6	equation	equation	NOUN
ejpam-5509	540	7	model	model	NOUN
ejpam-5509	540	8	of	of	ADP
ejpam-5509	540	9	hepatitis	hepatitis	PROPN
ejpam-5509	540	10	b	b	PROPN
ejpam-5509	540	11	virus	virus	NOUN
ejpam-5509	540	12	infection	infection	NOUN
ejpam-5509	540	13	.	.	PUNCT
ejpam-5509	541	1	journal	journal	NOUN
ejpam-5509	541	2	of	of	ADP
ejpam-5509	541	3	biological	biological	ADJ
ejpam-5509	541	4	dynamics	dynamic	NOUN
ejpam-5509	541	5	,	,	PUNCT
ejpam-5509	541	6	2(2):140–153	2(2):140–153	NUM
ejpam-5509	541	7	,	,	PUNCT
ejpam-5509	541	8	2008	2008	NUM
ejpam-5509	541	9	.	.	PUNCT
ejpam-5509	542	1	[	[	X
ejpam-5509	542	2	24	24	NUM
ejpam-5509	542	3	]	]	X
ejpam-5509	542	4	j.h	j.h	PROPN
ejpam-5509	542	5	.	.	PUNCT
ejpam-5509	543	1	he	he	PRON
ejpam-5509	543	2	.	.	PUNCT
ejpam-5509	544	1	a	a	DET
ejpam-5509	544	2	tutorial	tutorial	ADJ
ejpam-5509	544	3	review	review	NOUN
ejpam-5509	544	4	on	on	ADP
ejpam-5509	544	5	fractal	fractal	ADJ
ejpam-5509	544	6	spacetime	spacetime	NOUN
ejpam-5509	544	7	and	and	CCONJ
ejpam-5509	544	8	fractional	fractional	ADJ
ejpam-5509	544	9	calculus	calculus	NOUN
ejpam-5509	544	10	.	.	PUNCT
ejpam-5509	545	1	international	international	ADJ
ejpam-5509	545	2	journal	journal	PROPN
ejpam-5509	545	3	of	of	ADP
ejpam-5509	545	4	theoretical	theoretical	ADJ
ejpam-5509	545	5	physics	physics	NOUN
ejpam-5509	545	6	,	,	PUNCT
ejpam-5509	545	7	53:3698–3718	53:3698–3718	NUM
ejpam-5509	545	8	,	,	PUNCT
ejpam-5509	545	9	2014	2014	NUM
ejpam-5509	545	10	.	.	PUNCT
ejpam-5509	546	1	[	[	X
ejpam-5509	546	2	25	25	NUM
ejpam-5509	546	3	]	]	X
ejpam-5509	546	4	sarah	sarah	PROPN
ejpam-5509	546	5	hews	hew	VERB
ejpam-5509	546	6	,	,	PUNCT
ejpam-5509	546	7	steffen	steffen	PROPN
ejpam-5509	546	8	eikenberry	eikenberry	PROPN
ejpam-5509	546	9	,	,	PUNCT
ejpam-5509	546	10	john	john	PROPN
ejpam-5509	546	11	d	d	PROPN
ejpam-5509	546	12	nagy	nagy	PROPN
ejpam-5509	546	13	,	,	PUNCT
ejpam-5509	546	14	and	and	CCONJ
ejpam-5509	546	15	yang	yang	PROPN
ejpam-5509	546	16	kuang	kuang	PROPN
ejpam-5509	546	17	.	.	PUNCT
ejpam-5509	547	1	rich	rich	ADJ
ejpam-5509	547	2	dynamics	dynamic	NOUN
ejpam-5509	547	3	of	of	ADP
ejpam-5509	547	4	a	a	DET
ejpam-5509	547	5	hepatitis	hepatitis	NOUN
ejpam-5509	547	6	b	b	NOUN
ejpam-5509	547	7	viral	viral	ADJ
ejpam-5509	547	8	infection	infection	NOUN
ejpam-5509	547	9	model	model	NOUN
ejpam-5509	547	10	with	with	ADP
ejpam-5509	547	11	logistic	logistic	ADJ
ejpam-5509	547	12	hepatocyte	hepatocyte	NOUN
ejpam-5509	547	13	growth	growth	NOUN
ejpam-5509	547	14	.	.	PUNCT
ejpam-5509	548	1	journal	journal	PROPN
ejpam-5509	548	2	of	of	ADP
ejpam-5509	548	3	mathematical	mathematical	ADJ
ejpam-5509	548	4	biology	biology	NOUN
ejpam-5509	548	5	,	,	PUNCT
ejpam-5509	548	6	60:573–590	60:573–590	NUM
ejpam-5509	548	7	,	,	PUNCT
ejpam-5509	548	8	2010	2010	NUM
ejpam-5509	548	9	.	.	PUNCT
ejpam-5509	549	1	[	[	X
ejpam-5509	549	2	26	26	NUM
ejpam-5509	549	3	]	]	X
ejpam-5509	549	4	hasib	hasib	PROPN
ejpam-5509	549	5	khan	khan	PROPN
ejpam-5509	549	6	,	,	PUNCT
ejpam-5509	549	7	jehad	jehad	PROPN
ejpam-5509	549	8	alzabut	alzabut	PROPN
ejpam-5509	549	9	,	,	PUNCT
ejpam-5509	549	10	jf	jf	PROPN
ejpam-5509	549	11	gómez	gómez	NOUN
ejpam-5509	549	12	-	-	PUNCT
ejpam-5509	549	13	aguilar	aguilar	ADJ
ejpam-5509	549	14	,	,	PUNCT
ejpam-5509	549	15	and	and	CCONJ
ejpam-5509	549	16	abdulwasea	abdulwasea	NOUN
ejpam-5509	549	17	alkhazan	alkhazan	NOUN
ejpam-5509	549	18	.	.	PUNCT
ejpam-5509	550	1	essential	essential	ADJ
ejpam-5509	550	2	criteria	criterion	NOUN
ejpam-5509	550	3	for	for	ADP
ejpam-5509	550	4	existence	existence	NOUN
ejpam-5509	550	5	of	of	ADP
ejpam-5509	550	6	solution	solution	NOUN
ejpam-5509	550	7	of	of	ADP
ejpam-5509	550	8	a	a	DET
ejpam-5509	550	9	modified	modify	VERB
ejpam-5509	550	10	-	-	PUNCT
ejpam-5509	550	11	abc	abc	NOUN
ejpam-5509	550	12	fractional	fractional	ADJ
ejpam-5509	550	13	order	order	NOUN
ejpam-5509	550	14	smoking	smoking	NOUN
ejpam-5509	550	15	model	model	NOUN
ejpam-5509	550	16	.	.	PUNCT
ejpam-5509	551	1	ain	ain	PROPN
ejpam-5509	551	2	shams	sham	NOUN
ejpam-5509	551	3	engineering	engineering	NOUN
ejpam-5509	551	4	journal	journal	NOUN
ejpam-5509	551	5	,	,	PUNCT
ejpam-5509	551	6	15(5):102646	15(5):102646	NUM
ejpam-5509	551	7	,	,	PUNCT
ejpam-5509	551	8	2024	2024	NUM
ejpam-5509	551	9	.	.	PUNCT
ejpam-5509	552	1	[	[	X
ejpam-5509	552	2	27	27	NUM
ejpam-5509	552	3	]	]	X
ejpam-5509	552	4	hasib	hasib	PROPN
ejpam-5509	552	5	khan	khan	PROPN
ejpam-5509	552	6	,	,	PUNCT
ejpam-5509	552	7	altaf	altaf	PROPN
ejpam-5509	552	8	hussain	hussain	PROPN
ejpam-5509	552	9	rajpar	rajpar	PROPN
ejpam-5509	552	10	,	,	PUNCT
ejpam-5509	552	11	jehad	jehad	PROPN
ejpam-5509	552	12	alzabut	alzabut	PROPN
ejpam-5509	552	13	,	,	PUNCT
ejpam-5509	552	14	muhammad	muhammad	PROPN
ejpam-5509	552	15	aslam	aslam	PROPN
ejpam-5509	552	16	,	,	PUNCT
ejpam-5509	552	17	sina	sina	PROPN
ejpam-5509	552	18	etemad	etemad	PROPN
ejpam-5509	552	19	,	,	PUNCT
ejpam-5509	552	20	and	and	CCONJ
ejpam-5509	552	21	shahram	shahram	PROPN
ejpam-5509	552	22	rezapour	rezapour	PROPN
ejpam-5509	552	23	.	.	PUNCT
ejpam-5509	553	1	on	on	ADP
ejpam-5509	553	2	a	a	DET
ejpam-5509	553	3	fractal	fractal	ADJ
ejpam-5509	553	4	–	–	PUNCT
ejpam-5509	553	5	fractional	fractional	ADJ
ejpam-5509	553	6	-	-	PUNCT
ejpam-5509	553	7	based	base	VERB
ejpam-5509	553	8	modeling	modeling	NOUN
ejpam-5509	553	9	for	for	ADP
ejpam-5509	553	10	influenza	influenza	NOUN
ejpam-5509	553	11	and	and	CCONJ
ejpam-5509	553	12	its	its	PRON
ejpam-5509	553	13	analytical	analytical	ADJ
ejpam-5509	553	14	results	result	NOUN
ejpam-5509	553	15	.	.	PUNCT
ejpam-5509	554	1	qualitative	qualitative	ADJ
ejpam-5509	554	2	theory	theory	NOUN
ejpam-5509	554	3	of	of	ADP
ejpam-5509	554	4	dynamical	dynamical	ADJ
ejpam-5509	554	5	systems	system	NOUN
ejpam-5509	554	6	,	,	PUNCT
ejpam-5509	554	7	23(2):70	23(2):70	NUM
ejpam-5509	554	8	,	,	PUNCT
ejpam-5509	554	9	2024	2024	NUM
ejpam-5509	554	10	.	.	PUNCT
ejpam-5509	555	1	[	[	X
ejpam-5509	555	2	28	28	NUM
ejpam-5509	555	3	]	]	X
ejpam-5509	555	4	jorge	jorge	PROPN
ejpam-5509	555	5	losada	losada	PROPN
ejpam-5509	555	6	and	and	CCONJ
ejpam-5509	555	7	juan	juan	PROPN
ejpam-5509	555	8	j.	j.	PROPN
ejpam-5509	555	9	nieto	nieto	PROPN
ejpam-5509	555	10	.	.	PUNCT
ejpam-5509	556	1	a	a	DET
ejpam-5509	556	2	new	new	ADJ
ejpam-5509	556	3	definition	definition	NOUN
ejpam-5509	556	4	of	of	ADP
ejpam-5509	556	5	fractional	fractional	ADJ
ejpam-5509	556	6	derivative	derivative	NOUN
ejpam-5509	556	7	without	without	ADP
ejpam-5509	556	8	singular	singular	ADJ
ejpam-5509	556	9	kernel	kernel	PROPN
ejpam-5509	556	10	.	.	PUNCT
ejpam-5509	557	1	progr	progr	NOUN
ejpam-5509	557	2	.	.	PUNCT
ejpam-5509	558	1	fract	fract	PROPN
ejpam-5509	558	2	.	.	PUNCT
ejpam-5509	559	1	differ	differ	VERB
ejpam-5509	559	2	.	.	PUNCT
ejpam-5509	560	1	appl	appl	PROPN
ejpam-5509	560	2	,	,	PUNCT
ejpam-5509	560	3	1(2):87–92	1(2):87–92	NUM
ejpam-5509	560	4	,	,	PUNCT
ejpam-5509	560	5	2015	2015	NUM
ejpam-5509	560	6	.	.	PUNCT
ejpam-5509	561	1	[	[	X
ejpam-5509	561	2	29	29	NUM
ejpam-5509	561	3	]	]	SYM
ejpam-5509	561	4	manoochehr	manoochehr	NOUN
ejpam-5509	561	5	makvandi	makvandi	PROPN
ejpam-5509	561	6	.	.	PUNCT
ejpam-5509	561	7	update	update	NOUN
ejpam-5509	561	8	on	on	ADP
ejpam-5509	561	9	occult	occult	NOUN
ejpam-5509	561	10	hepatitis	hepatitis	PROPN
ejpam-5509	561	11	b	b	PROPN
ejpam-5509	561	12	virus	virus	NOUN
ejpam-5509	561	13	infection	infection	NOUN
ejpam-5509	561	14	.	.	PUNCT
ejpam-5509	562	1	world	world	PROPN
ejpam-5509	562	2	journal	journal	PROPN
ejpam-5509	562	3	of	of	ADP
ejpam-5509	562	4	gastroenterology	gastroenterology	NOUN
ejpam-5509	562	5	,	,	PUNCT
ejpam-5509	562	6	22(39):8720	22(39):8720	NUM
ejpam-5509	562	7	,	,	PUNCT
ejpam-5509	562	8	2016	2016	NUM
ejpam-5509	562	9	.	.	PUNCT
ejpam-5509	563	1	[	[	X
ejpam-5509	563	2	30	30	NUM
ejpam-5509	563	3	]	]	X
ejpam-5509	563	4	graham	graham	PROPN
ejpam-5509	563	5	f	f	PROPN
ejpam-5509	563	6	medley	medley	PROPN
ejpam-5509	563	7	,	,	PUNCT
ejpam-5509	563	8	nathan	nathan	PROPN
ejpam-5509	563	9	a	a	DET
ejpam-5509	563	10	lindop	lindop	PROPN
ejpam-5509	563	11	,	,	PUNCT
ejpam-5509	563	12	w	w	PROPN
ejpam-5509	563	13	john	john	PROPN
ejpam-5509	563	14	edmunds	edmunds	PROPN
ejpam-5509	563	15	,	,	PUNCT
ejpam-5509	563	16	and	and	CCONJ
ejpam-5509	563	17	d	d	PROPN
ejpam-5509	563	18	james	james	PROPN
ejpam-5509	563	19	nokes	nokes	PROPN
ejpam-5509	563	20	.	.	PUNCT
ejpam-5509	564	1	hepatitis	hepatitis	NOUN
ejpam-5509	564	2	-	-	PUNCT
ejpam-5509	564	3	b	b	PROPN
ejpam-5509	564	4	virus	virus	NOUN
ejpam-5509	564	5	endemicity	endemicity	NOUN
ejpam-5509	564	6	:	:	PUNCT
ejpam-5509	564	7	heterogeneity	heterogeneity	NOUN
ejpam-5509	564	8	,	,	PUNCT
ejpam-5509	564	9	catastrophic	catastrophic	ADJ
ejpam-5509	564	10	dynamics	dynamic	NOUN
ejpam-5509	564	11	and	and	CCONJ
ejpam-5509	564	12	control	control	NOUN
ejpam-5509	564	13	.	.	PUNCT
ejpam-5509	565	1	nature	nature	NOUN
ejpam-5509	565	2	medicine	medicine	NOUN
ejpam-5509	565	3	,	,	PUNCT
ejpam-5509	565	4	7(5):619–624	7(5):619–624	NOUN
ejpam-5509	565	5	,	,	PUNCT
ejpam-5509	565	6	2001	2001	NUM
ejpam-5509	565	7	.	.	PUNCT
ejpam-5509	566	1	[	[	X
ejpam-5509	566	2	31	31	NUM
ejpam-5509	566	3	]	]	PUNCT
ejpam-5509	566	4	graham	graham	PROPN
ejpam-5509	566	5	f	f	PROPN
ejpam-5509	566	6	medley	medley	PROPN
ejpam-5509	566	7	,	,	PUNCT
ejpam-5509	566	8	nathan	nathan	PROPN
ejpam-5509	566	9	a	a	DET
ejpam-5509	566	10	lindop	lindop	PROPN
ejpam-5509	566	11	,	,	PUNCT
ejpam-5509	566	12	w	w	PROPN
ejpam-5509	566	13	john	john	PROPN
ejpam-5509	566	14	edmunds	edmunds	PROPN
ejpam-5509	566	15	,	,	PUNCT
ejpam-5509	566	16	and	and	CCONJ
ejpam-5509	566	17	d	d	PROPN
ejpam-5509	566	18	james	james	PROPN
ejpam-5509	566	19	nokes	nokes	PROPN
ejpam-5509	566	20	.	.	PUNCT
ejpam-5509	567	1	hepatitis	hepatitis	NOUN
ejpam-5509	567	2	-	-	PUNCT
ejpam-5509	567	3	b	b	PROPN
ejpam-5509	567	4	virus	virus	NOUN
ejpam-5509	567	5	endemicity	endemicity	NOUN
ejpam-5509	567	6	:	:	PUNCT
ejpam-5509	567	7	heterogeneity	heterogeneity	NOUN
ejpam-5509	567	8	,	,	PUNCT
ejpam-5509	567	9	catastrophic	catastrophic	ADJ
ejpam-5509	567	10	dynamics	dynamic	NOUN
ejpam-5509	567	11	and	and	CCONJ
ejpam-5509	567	12	control	control	NOUN
ejpam-5509	567	13	.	.	PUNCT
ejpam-5509	568	1	nature	nature	NOUN
ejpam-5509	568	2	medicine	medicine	NOUN
ejpam-5509	568	3	,	,	PUNCT
ejpam-5509	568	4	7(5):619–624	7(5):619–624	NOUN
ejpam-5509	568	5	,	,	PUNCT
ejpam-5509	568	6	2001	2001	NUM
ejpam-5509	568	7	.	.	PUNCT
ejpam-5509	569	1	[	[	X
ejpam-5509	569	2	32	32	NUM
ejpam-5509	569	3	]	]	PUNCT
ejpam-5509	569	4	douglas	douglas	PROPN
ejpam-5509	569	5	k	k	PROPN
ejpam-5509	569	6	owens	owens	PROPN
ejpam-5509	569	7	,	,	PUNCT
ejpam-5509	569	8	karina	karina	PROPN
ejpam-5509	569	9	w	w	PROPN
ejpam-5509	569	10	davidson	davidson	PROPN
ejpam-5509	569	11	,	,	PUNCT
ejpam-5509	569	12	alex	alex	PROPN
ejpam-5509	569	13	h	h	PROPN
ejpam-5509	569	14	krist	krist	PROPN
ejpam-5509	569	15	,	,	PUNCT
ejpam-5509	569	16	michael	michael	PROPN
ejpam-5509	569	17	j	j	PROPN
ejpam-5509	569	18	barry	barry	PROPN
ejpam-5509	569	19	,	,	PUNCT
ejpam-5509	569	20	michael	michael	PROPN
ejpam-5509	569	21	cabana	cabana	PROPN
ejpam-5509	569	22	,	,	PUNCT
ejpam-5509	569	23	aaron	aaron	PROPN
ejpam-5509	569	24	b	b	PROPN
ejpam-5509	569	25	caughey	caughey	PROPN
ejpam-5509	569	26	,	,	PUNCT
ejpam-5509	569	27	chyke	chyke	VERB
ejpam-5509	569	28	a	a	DET
ejpam-5509	569	29	doubeni	doubeni	NOUN
ejpam-5509	569	30	,	,	PUNCT
ejpam-5509	569	31	john	john	PROPN
ejpam-5509	569	32	w	w	PROPN
ejpam-5509	569	33	epling	epling	PROPN
ejpam-5509	569	34	,	,	PUNCT
ejpam-5509	569	35	alex	alex	PROPN
ejpam-5509	569	36	r	r	PROPN
ejpam-5509	569	37	kemper	kemper	PROPN
ejpam-5509	569	38	,	,	PUNCT
ejpam-5509	569	39	martha	martha	PROPN
ejpam-5509	569	40	kubik	kubik	PROPN
ejpam-5509	569	41	,	,	PUNCT
ejpam-5509	569	42	et	et	PROPN
ejpam-5509	569	43	al	al	PROPN
ejpam-5509	569	44	.	.	PUNCT
ejpam-5509	570	1	screening	screen	VERB
ejpam-5509	570	2	for	for	ADP
ejpam-5509	570	3	hepatitis	hepatitis	PROPN
ejpam-5509	570	4	b	b	PROPN
ejpam-5509	570	5	virus	virus	NOUN
ejpam-5509	570	6	infection	infection	NOUN
ejpam-5509	570	7	in	in	ADP
ejpam-5509	570	8	pregnant	pregnant	ADJ
ejpam-5509	570	9	women	woman	NOUN
ejpam-5509	570	10	:	:	PUNCT
ejpam-5509	570	11	us	us	PROPN
ejpam-5509	570	12	preventive	preventive	ADJ
ejpam-5509	570	13	services	service	NOUN
ejpam-5509	570	14	task	task	PROPN
ejpam-5509	570	15	force	force	PROPN
ejpam-5509	570	16	reaffirmation	reaffirmation	NOUN
ejpam-5509	570	17	recommendation	recommendation	NOUN
ejpam-5509	570	18	statement	statement	NOUN
ejpam-5509	570	19	.	.	PUNCT
ejpam-5509	571	1	jama	jama	PROPN
ejpam-5509	571	2	,	,	PUNCT
ejpam-5509	571	3	322(4):349–354	322(4):349–354	PROPN
ejpam-5509	571	4	,	,	PUNCT
ejpam-5509	571	5	2019	2019	NUM
ejpam-5509	571	6	.	.	PUNCT
ejpam-5509	572	1	[	[	X
ejpam-5509	572	2	33	33	NUM
ejpam-5509	572	3	]	]	X
ejpam-5509	572	4	monica	monica	PROPN
ejpam-5509	572	5	preboth	preboth	PROPN
ejpam-5509	572	6	.	.	PUNCT
ejpam-5509	573	1	phs	phs	NOUN
ejpam-5509	573	2	guidelines	guideline	NOUN
ejpam-5509	573	3	for	for	ADP
ejpam-5509	573	4	management	management	NOUN
ejpam-5509	573	5	of	of	ADP
ejpam-5509	573	6	occupational	occupational	ADJ
ejpam-5509	573	7	exposure	exposure	NOUN
ejpam-5509	573	8	to	to	ADP
ejpam-5509	573	9	hbv	hbv	NOUN
ejpam-5509	573	10	,	,	PUNCT
ejpam-5509	573	11	hcv	hcv	PROPN
ejpam-5509	573	12	and	and	CCONJ
ejpam-5509	573	13	hiv	hiv	PROPN
ejpam-5509	573	14	:	:	PUNCT
ejpam-5509	573	15	management	management	NOUN
ejpam-5509	573	16	of	of	ADP
ejpam-5509	573	17	occupational	occupational	ADJ
ejpam-5509	573	18	blood	blood	NOUN
ejpam-5509	573	19	exposures	exposure	NOUN
ejpam-5509	573	20	.	.	PUNCT
ejpam-5509	574	1	american	american	ADJ
ejpam-5509	574	2	family	family	PROPN
ejpam-5509	574	3	physician	physician	NOUN
ejpam-5509	574	4	,	,	PUNCT
ejpam-5509	574	5	64(12):2012–2014	64(12):2012–2014	NUM
ejpam-5509	574	6	,	,	PUNCT
ejpam-5509	574	7	2001	2001	NUM
ejpam-5509	574	8	.	.	PUNCT
ejpam-5509	575	1	[	[	X
ejpam-5509	575	2	34	34	NUM
ejpam-5509	575	3	]	]	PUNCT
ejpam-5509	575	4	sayed	sayed	PROPN
ejpam-5509	575	5	saber	saber	PROPN
ejpam-5509	575	6	.	.	PUNCT
ejpam-5509	576	1	control	control	NOUN
ejpam-5509	576	2	of	of	ADP
ejpam-5509	576	3	chaos	chaos	NOUN
ejpam-5509	576	4	in	in	ADP
ejpam-5509	576	5	the	the	DET
ejpam-5509	576	6	burke	burke	PROPN
ejpam-5509	576	7	-	-	PUNCT
ejpam-5509	576	8	shaw	shaw	PROPN
ejpam-5509	576	9	system	system	NOUN
ejpam-5509	576	10	of	of	ADP
ejpam-5509	576	11	fractal	fractal	ADJ
ejpam-5509	576	12	-	-	PUNCT
ejpam-5509	576	13	fractional	fractional	ADJ
ejpam-5509	576	14	order	order	NOUN
ejpam-5509	576	15	in	in	ADP
ejpam-5509	576	16	the	the	DET
ejpam-5509	576	17	sense	sense	NOUN
ejpam-5509	576	18	of	of	ADP
ejpam-5509	576	19	caputo	caputo	PROPN
ejpam-5509	576	20	-	-	PUNCT
ejpam-5509	576	21	fabrizio	fabrizio	PROPN
ejpam-5509	576	22	.	.	PUNCT
ejpam-5509	577	1	journal	journal	PROPN
ejpam-5509	577	2	of	of	ADP
ejpam-5509	577	3	applied	apply	VERB
ejpam-5509	577	4	mathematics	mathematic	NOUN
ejpam-5509	577	5	and	and	CCONJ
ejpam-5509	577	6	computational	computational	ADJ
ejpam-5509	577	7	mechanics	mechanic	NOUN
ejpam-5509	577	8	,	,	PUNCT
ejpam-5509	577	9	23(1):83–96	23(1):83–96	NUM
ejpam-5509	577	10	,	,	PUNCT
ejpam-5509	577	11	2024	2024	NUM
ejpam-5509	577	12	.	.	PUNCT
ejpam-5509	578	1	[	[	X
ejpam-5509	578	2	35	35	NUM
ejpam-5509	578	3	]	]	PUNCT
ejpam-5509	578	4	rafel	rafel	PROPN
ejpam-5509	578	5	ibrahim	ibrahim	PROPN
ejpam-5509	578	6	salih	salih	PROPN
ejpam-5509	578	7	,	,	PUNCT
ejpam-5509	578	8	shireen	shireen	PROPN
ejpam-5509	578	9	jawad	jawad	PROPN
ejpam-5509	578	10	,	,	PUNCT
ejpam-5509	578	11	kaushik	kaushik	PROPN
ejpam-5509	578	12	dehingia	dehingia	NOUN
ejpam-5509	578	13	,	,	PUNCT
ejpam-5509	578	14	and	and	CCONJ
ejpam-5509	578	15	anusmita	anusmita	PROPN
ejpam-5509	578	16	das	das	PROPN
ejpam-5509	578	17	.	.	PUNCT
ejpam-5509	579	1	the	the	DET
ejpam-5509	579	2	effect	effect	NOUN
ejpam-5509	579	3	of	of	ADP
ejpam-5509	579	4	a	a	DET
ejpam-5509	579	5	psychological	psychological	ADJ
ejpam-5509	579	6	scare	scare	NOUN
ejpam-5509	579	7	on	on	ADP
ejpam-5509	579	8	the	the	DET
ejpam-5509	579	9	dynamics	dynamic	NOUN
ejpam-5509	579	10	of	of	ADP
ejpam-5509	579	11	the	the	DET
ejpam-5509	579	12	tumor	tumor	NOUN
ejpam-5509	579	13	-	-	PUNCT
ejpam-5509	579	14	immune	immune	ADJ
ejpam-5509	579	15	interaction	interaction	NOUN
ejpam-5509	579	16	with	with	ADP
ejpam-5509	579	17	optimal	optimal	ADJ
ejpam-5509	579	18	control	control	NOUN
ejpam-5509	579	19	strategy	strategy	NOUN
ejpam-5509	579	20	.	.	PUNCT
ejpam-5509	580	1	an	an	DET
ejpam-5509	580	2	international	international	ADJ
ejpam-5509	580	3	journal	journal	NOUN
ejpam-5509	580	4	of	of	ADP
ejpam-5509	580	5	optimization	optimization	NOUN
ejpam-5509	580	6	and	and	CCONJ
ejpam-5509	580	7	control	control	NOUN
ejpam-5509	580	8	:	:	PUNCT
ejpam-5509	580	9	theories	theory	NOUN
ejpam-5509	580	10	&	&	CCONJ
ejpam-5509	580	11	applications	application	NOUN
ejpam-5509	580	12	(	(	PUNCT
ejpam-5509	580	13	ijocta	ijocta	ADJ
ejpam-5509	580	14	)	)	PUNCT
ejpam-5509	580	15	,	,	PUNCT
ejpam-5509	580	16	14(3):276–293	14(3):276–293	NUM
ejpam-5509	580	17	,	,	PUNCT
ejpam-5509	580	18	2024	2024	NUM
ejpam-5509	580	19	.	.	PUNCT
ejpam-5509	581	1	[	[	X
ejpam-5509	581	2	36	36	NUM
ejpam-5509	581	3	]	]	X
ejpam-5509	581	4	sarah	sarah	PROPN
ejpam-5509	581	5	schillie	schillie	PROPN
ejpam-5509	581	6	,	,	PUNCT
ejpam-5509	581	7	trudy	trudy	PROPN
ejpam-5509	581	8	v	v	PROPN
ejpam-5509	581	9	murphy	murphy	PROPN
ejpam-5509	581	10	,	,	PUNCT
ejpam-5509	581	11	mark	mark	PROPN
ejpam-5509	581	12	sawyer	sawyer	PROPN
ejpam-5509	581	13	,	,	PUNCT
ejpam-5509	581	14	kathleen	kathleen	PROPN
ejpam-5509	581	15	ly	ly	PROPN
ejpam-5509	581	16	,	,	PUNCT
ejpam-5509	581	17	elizabeth	elizabeth	PROPN
ejpam-5509	581	18	hughes	hughes	PROPN
ejpam-5509	581	19	,	,	PUNCT
ejpam-5509	581	20	ruth	ruth	PROPN
ejpam-5509	581	21	jiles	jile	NOUN
ejpam-5509	581	22	,	,	PUNCT
ejpam-5509	581	23	marie	marie	PROPN
ejpam-5509	581	24	a	a	DET
ejpam-5509	581	25	de	de	PROPN
ejpam-5509	581	26	perio	perio	PROPN
ejpam-5509	581	27	,	,	PUNCT
ejpam-5509	581	28	meredith	meredith	PROPN
ejpam-5509	581	29	reilly	reilly	PROPN
ejpam-5509	581	30	,	,	PUNCT
ejpam-5509	581	31	kathy	kathy	PROPN
ejpam-5509	581	32	byrd	byrd	PROPN
ejpam-5509	581	33	,	,	PUNCT
ejpam-5509	581	34	john	john	PROPN
ejpam-5509	581	35	w	w	PROPN
ejpam-5509	581	36	ward	ward	PROPN
ejpam-5509	581	37	,	,	PUNCT
ejpam-5509	581	38	et	et	PROPN
ejpam-5509	581	39	al	al	PROPN
ejpam-5509	581	40	.	.	PUNCT
ejpam-5509	582	1	cdc	cdc	PROPN
ejpam-5509	582	2	i.	i.	PROPN
ejpam-5509	582	3	ahmad	ahmad	PROPN
ejpam-5509	582	4	et	et	PROPN
ejpam-5509	582	5	al	al	PROPN
ejpam-5509	582	6	.	.	PUNCT
ejpam-5509	582	7	/	/	SYM
ejpam-5509	582	8	eur	eur	PROPN
ejpam-5509	582	9	.	.	PUNCT
ejpam-5509	583	1	j.	j.	PROPN
ejpam-5509	583	2	pure	pure	PROPN
ejpam-5509	583	3	appl	appl	PROPN
ejpam-5509	583	4	.	.	PROPN
ejpam-5509	583	5	math	math	PROPN
ejpam-5509	583	6	,	,	PUNCT
ejpam-5509	583	7	18	18	NUM
ejpam-5509	583	8	(	(	PUNCT
ejpam-5509	583	9	1	1	NUM
ejpam-5509	583	10	)	)	PUNCT
ejpam-5509	583	11	(	(	PUNCT
ejpam-5509	583	12	2025	2025	NUM
ejpam-5509	583	13	)	)	PUNCT
ejpam-5509	583	14	,	,	PUNCT
ejpam-5509	583	15	5509	5509	NUM
ejpam-5509	583	16	27	27	NUM
ejpam-5509	583	17	of	of	ADP
ejpam-5509	583	18	27	27	NUM
ejpam-5509	583	19	guidance	guidance	NOUN
ejpam-5509	583	20	for	for	ADP
ejpam-5509	583	21	evaluating	evaluate	VERB
ejpam-5509	583	22	health	health	NOUN
ejpam-5509	583	23	-	-	PUNCT
ejpam-5509	583	24	care	care	NOUN
ejpam-5509	583	25	personnel	personnel	NOUN
ejpam-5509	583	26	for	for	ADP
ejpam-5509	583	27	hepatitis	hepatitis	PROPN
ejpam-5509	583	28	b	b	PROPN
ejpam-5509	583	29	virus	virus	NOUN
ejpam-5509	583	30	protection	protection	NOUN
ejpam-5509	583	31	and	and	CCONJ
ejpam-5509	583	32	for	for	ADP
ejpam-5509	583	33	administering	administer	VERB
ejpam-5509	583	34	postexposure	postexposure	NOUN
ejpam-5509	583	35	management	management	NOUN
ejpam-5509	583	36	.	.	PUNCT
ejpam-5509	584	1	mmwr	mmwr	ADJ
ejpam-5509	584	2	recomm	recomm	PROPN
ejpam-5509	584	3	rep	rep	PROPN
ejpam-5509	584	4	,	,	PUNCT
ejpam-5509	584	5	62(10):1–19	62(10):1–19	NOUN
ejpam-5509	584	6	,	,	PUNCT
ejpam-5509	584	7	2013	2013	NUM
ejpam-5509	584	8	.	.	PUNCT
ejpam-5509	585	1	[	[	X
ejpam-5509	585	2	37	37	NUM
ejpam-5509	585	3	]	]	X
ejpam-5509	585	4	siraj	siraj	PROPN
ejpam-5509	585	5	-	-	PUNCT
ejpam-5509	585	6	ul	ul	PROPN
ejpam-5509	585	7	-	-	PUNCT
ejpam-5509	585	8	islam	islam	PROPN
ejpam-5509	585	9	and	and	CCONJ
ejpam-5509	585	10	imtiaz	imtiaz	PROPN
ejpam-5509	585	11	ahmad	ahmad	PROPN
ejpam-5509	585	12	.	.	PUNCT
ejpam-5509	586	1	local	local	ADJ
ejpam-5509	586	2	meshless	meshless	ADJ
ejpam-5509	586	3	method	method	NOUN
ejpam-5509	586	4	for	for	ADP
ejpam-5509	586	5	pdes	pde	NOUN
ejpam-5509	586	6	arising	arise	VERB
ejpam-5509	586	7	from	from	ADP
ejpam-5509	586	8	models	model	NOUN
ejpam-5509	586	9	of	of	ADP
ejpam-5509	586	10	wound	wound	ADJ
ejpam-5509	586	11	healing	healing	NOUN
ejpam-5509	586	12	.	.	PUNCT
ejpam-5509	587	1	applied	apply	VERB
ejpam-5509	587	2	mathematical	mathematical	ADJ
ejpam-5509	587	3	modelling	modelling	NOUN
ejpam-5509	587	4	,	,	PUNCT
ejpam-5509	587	5	48:688–710	48:688–710	PROPN
ejpam-5509	587	6	,	,	PUNCT
ejpam-5509	587	7	2017	2017	NUM
ejpam-5509	587	8	.	.	PUNCT
ejpam-5509	588	1	[	[	X
ejpam-5509	588	2	38	38	NUM
ejpam-5509	588	3	]	]	PUNCT
ejpam-5509	588	4	pauline	pauline	PROPN
ejpam-5509	588	5	van	van	PROPN
ejpam-5509	588	6	den	den	PROPN
ejpam-5509	588	7	driessche	driessche	NOUN
ejpam-5509	588	8	and	and	CCONJ
ejpam-5509	588	9	james	james	PROPN
ejpam-5509	588	10	watmough	watmough	PROPN
ejpam-5509	588	11	.	.	PUNCT
ejpam-5509	589	1	reproduction	reproduction	NOUN
ejpam-5509	589	2	numbers	number	NOUN
ejpam-5509	589	3	and	and	CCONJ
ejpam-5509	589	4	subthreshold	subthreshold	ADJ
ejpam-5509	589	5	endemic	endemic	ADJ
ejpam-5509	589	6	equilibria	equilibrium	NOUN
ejpam-5509	589	7	for	for	ADP
ejpam-5509	589	8	compartmental	compartmental	ADJ
ejpam-5509	589	9	models	model	NOUN
ejpam-5509	589	10	of	of	ADP
ejpam-5509	589	11	disease	disease	NOUN
ejpam-5509	589	12	transmission	transmission	NOUN
ejpam-5509	589	13	.	.	PUNCT
ejpam-5509	590	1	mathematical	mathematical	ADJ
ejpam-5509	590	2	biosciences	bioscience	NOUN
ejpam-5509	590	3	,	,	PUNCT
ejpam-5509	590	4	180(1	180(1	NUM
ejpam-5509	590	5	-	-	SYM
ejpam-5509	590	6	2):29–48	2):29–48	NUM
ejpam-5509	590	7	,	,	PUNCT
ejpam-5509	590	8	2002	2002	NUM
ejpam-5509	590	9	.	.	PUNCT
ejpam-5509	591	1	[	[	X
ejpam-5509	591	2	39	39	NUM
ejpam-5509	591	3	]	]	PUNCT
ejpam-5509	591	4	f.	f.	PROPN
ejpam-5509	591	5	wang	wang	PROPN
ejpam-5509	591	6	,	,	PUNCT
ejpam-5509	591	7	j.	j.	PROPN
ejpam-5509	591	8	zhang	zhang	PROPN
ejpam-5509	591	9	,	,	PUNCT
ejpam-5509	591	10	i.	i.	PROPN
ejpam-5509	591	11	ahmad	ahmad	PROPN
ejpam-5509	591	12	,	,	PUNCT
ejpam-5509	591	13	a.	a.	PROPN
ejpam-5509	591	14	farooq	farooq	PROPN
ejpam-5509	591	15	,	,	PUNCT
ejpam-5509	591	16	and	and	CCONJ
ejpam-5509	591	17	h.	h.	PROPN
ejpam-5509	591	18	ahmad	ahmad	PROPN
ejpam-5509	591	19	.	.	PUNCT
ejpam-5509	592	1	a	a	DET
ejpam-5509	592	2	novel	novel	ADJ
ejpam-5509	592	3	meshfree	meshfree	NOUN
ejpam-5509	592	4	strategy	strategy	NOUN
ejpam-5509	592	5	for	for	ADP
ejpam-5509	592	6	a	a	DET
ejpam-5509	592	7	viscous	viscous	ADJ
ejpam-5509	592	8	wave	wave	NOUN
ejpam-5509	592	9	equation	equation	NOUN
ejpam-5509	592	10	with	with	ADP
ejpam-5509	592	11	variable	variable	ADJ
ejpam-5509	592	12	coefficients	coefficient	NOUN
ejpam-5509	592	13	.	.	PUNCT
ejpam-5509	593	1	frontiers	frontier	NOUN
ejpam-5509	593	2	in	in	ADP
ejpam-5509	593	3	physics	physics	PROPN
ejpam-5509	593	4	,	,	PUNCT
ejpam-5509	593	5	9:701512	9:701512	NUM
ejpam-5509	593	6	,	,	PUNCT
ejpam-5509	593	7	2021	2021	NUM
ejpam-5509	593	8	.	.	PUNCT
ejpam-5509	594	1	[	[	X
ejpam-5509	594	2	40	40	NUM
ejpam-5509	594	3	]	]	X
ejpam-5509	594	4	steven	steven	PROPN
ejpam-5509	594	5	wiersma	wiersma	PROPN
ejpam-5509	594	6	.	.	PUNCT
ejpam-5509	595	1	hepatitis	hepatitis	PROPN
ejpam-5509	595	2	b	b	PROPN
ejpam-5509	595	3	virus	virus	NOUN
ejpam-5509	595	4	:	:	PUNCT
ejpam-5509	595	5	preventing	prevent	VERB
ejpam-5509	595	6	liver	liver	NOUN
ejpam-5509	595	7	disease	disease	NOUN
ejpam-5509	595	8	with	with	ADP
ejpam-5509	595	9	the	the	DET
ejpam-5509	595	10	first	first	ADJ
ejpam-5509	595	11	vaccine	vaccine	NOUN
ejpam-5509	595	12	against	against	ADP
ejpam-5509	595	13	cancer	cancer	NOUN
ejpam-5509	595	14	.	.	PUNCT
ejpam-5509	596	1	protect	protect	NOUN
ejpam-5509	596	2	.	.	PUNCT
ejpam-5509	597	1	against	against	ADP
ejpam-5509	597	2	cancer	cancer	NOUN
ejpam-5509	597	3	-	-	PUNCT
ejpam-5509	597	4	causing	cause	VERB
ejpam-5509	597	5	infect	infect	NOUN
ejpam-5509	597	6	,	,	PUNCT
ejpam-5509	597	7	6	6	NUM
ejpam-5509	597	8	,	,	PUNCT
ejpam-5509	597	9	2010	2010	NUM
ejpam-5509	597	10	.	.	PUNCT
ejpam-5509	598	1	[	[	X
ejpam-5509	598	2	41	41	NUM
ejpam-5509	598	3	]	]	X
ejpam-5509	598	4	jr	jr	PROPN
ejpam-5509	598	5	williams	williams	PROPN
ejpam-5509	598	6	,	,	PUNCT
ejpam-5509	598	7	dj	dj	NOUN
ejpam-5509	598	8	nokes	noke	NOUN
ejpam-5509	598	9	,	,	PUNCT
ejpam-5509	598	10	gf	gf	NOUN
ejpam-5509	598	11	medley	medley	NOUN
ejpam-5509	598	12	,	,	PUNCT
ejpam-5509	598	13	and	and	CCONJ
ejpam-5509	598	14	rm	rm	PROPN
ejpam-5509	598	15	anderson	anderson	PROPN
ejpam-5509	598	16	.	.	PUNCT
ejpam-5509	599	1	the	the	DET
ejpam-5509	599	2	transmission	transmission	NOUN
ejpam-5509	599	3	dynamics	dynamic	NOUN
ejpam-5509	599	4	of	of	ADP
ejpam-5509	599	5	hepatitis	hepatitis	PROPN
ejpam-5509	599	6	b	b	PROPN
ejpam-5509	599	7	in	in	ADP
ejpam-5509	599	8	the	the	DET
ejpam-5509	599	9	uk	uk	PROPN
ejpam-5509	599	10	:	:	PUNCT
ejpam-5509	599	11	a	a	DET
ejpam-5509	599	12	mathematical	mathematical	ADJ
ejpam-5509	599	13	model	model	NOUN
ejpam-5509	599	14	for	for	ADP
ejpam-5509	599	15	evaluating	evaluate	VERB
ejpam-5509	599	16	costs	cost	NOUN
ejpam-5509	599	17	and	and	CCONJ
ejpam-5509	599	18	effectiveness	effectiveness	NOUN
ejpam-5509	599	19	of	of	ADP
ejpam-5509	599	20	immunization	immunization	NOUN
ejpam-5509	599	21	programmes	programme	NOUN
ejpam-5509	599	22	.	.	PUNCT
ejpam-5509	600	1	epidemiology	epidemiology	NOUN
ejpam-5509	600	2	&	&	CCONJ
ejpam-5509	600	3	infection	infection	NOUN
ejpam-5509	600	4	,	,	PUNCT
ejpam-5509	600	5	116(1):71–89	116(1):71–89	NUM
ejpam-5509	600	6	,	,	PUNCT
ejpam-5509	600	7	1996	1996	NUM
ejpam-5509	600	8	.	.	PUNCT