id	sid	tid	token	lemma	pos
ejpam-5687	1	1	european	european	PROPN
ejpam-5687	1	2	journal	journal	PROPN
ejpam-5687	1	3	of	of	ADP
ejpam-5687	1	4	pure	pure	ADJ
ejpam-5687	1	5	and	and	CCONJ
ejpam-5687	1	6	applied	applied	ADJ
ejpam-5687	1	7	mathematics	mathematic	NOUN
ejpam-5687	1	8	2025	2025	NUM
ejpam-5687	1	9	,	,	PUNCT
ejpam-5687	1	10	vol	vol	NOUN
ejpam-5687	1	11	.	.	PROPN
ejpam-5687	1	12	18	18	NUM
ejpam-5687	1	13	,	,	PUNCT
ejpam-5687	1	14	issue	issue	NOUN
ejpam-5687	1	15	2	2	NUM
ejpam-5687	1	16	,	,	PUNCT
ejpam-5687	1	17	article	article	NOUN
ejpam-5687	1	18	number	number	NOUN
ejpam-5687	1	19	5687	5687	NUM
ejpam-5687	1	20	issn	issn	VERB
ejpam-5687	1	21	1307	1307	NUM
ejpam-5687	1	22	-	-	SYM
ejpam-5687	1	23	5543	5543	NUM
ejpam-5687	1	24	–	–	PUNCT
ejpam-5687	1	25	ejpam.com	ejpam.com	X
ejpam-5687	1	26	published	publish	VERB
ejpam-5687	1	27	by	by	ADP
ejpam-5687	1	28	new	new	PROPN
ejpam-5687	1	29	york	york	PROPN
ejpam-5687	1	30	business	business	PROPN
ejpam-5687	1	31	global	global	ADJ
ejpam-5687	1	32	existence	existence	NOUN
ejpam-5687	1	33	and	and	CCONJ
ejpam-5687	1	34	sensitivity	sensitivity	NOUN
ejpam-5687	1	35	analysis	analysis	NOUN
ejpam-5687	1	36	of	of	ADP
ejpam-5687	1	37	a	a	DET
ejpam-5687	1	38	caputo	caputo	PROPN
ejpam-5687	1	39	-	-	PUNCT
ejpam-5687	1	40	fabrizio	fabrizio	PROPN
ejpam-5687	1	41	fractional	fractional	ADJ
ejpam-5687	1	42	order	order	NOUN
ejpam-5687	1	43	vector	vector	NOUN
ejpam-5687	1	44	-	-	PUNCT
ejpam-5687	1	45	borne	bear	VERB
ejpam-5687	1	46	disease	disease	NOUN
ejpam-5687	1	47	model	model	NOUN
ejpam-5687	1	48	nekmat	nekmat	NOUN
ejpam-5687	1	49	ullah1	ullah1	PROPN
ejpam-5687	1	50	,	,	PUNCT
ejpam-5687	1	51	zahir	zahir	PROPN
ejpam-5687	1	52	shah1,∗	shah1,∗	NOUN
ejpam-5687	1	53	,	,	PUNCT
ejpam-5687	1	54	rashid	rashid	PROPN
ejpam-5687	1	55	jan2,3	jan2,3	PROPN
ejpam-5687	1	56	,	,	PUNCT
ejpam-5687	1	57	s.	s.	PROPN
ejpam-5687	1	58	islam4	islam4	PROPN
ejpam-5687	1	59	,	,	PUNCT
ejpam-5687	1	60	narcisa	narcisa	NOUN
ejpam-5687	1	61	vrinceanu5,∗	vrinceanu5,∗	NOUN
ejpam-5687	1	62	,	,	PUNCT
ejpam-5687	1	63	muhammad	muhammad	PROPN
ejpam-5687	1	64	farhan6	farhan6	PROPN
ejpam-5687	1	65	,	,	PUNCT
ejpam-5687	1	66	elisabeta	elisabeta	NOUN
ejpam-5687	1	67	antonescu7	antonescu7	NOUN
ejpam-5687	1	68	1	1	NUM
ejpam-5687	1	69	department	department	NOUN
ejpam-5687	1	70	of	of	ADP
ejpam-5687	1	71	mathematical	mathematical	ADJ
ejpam-5687	1	72	sciences	sciences	PROPN
ejpam-5687	1	73	,	,	PUNCT
ejpam-5687	1	74	university	university	NOUN
ejpam-5687	1	75	of	of	ADP
ejpam-5687	1	76	lakki	lakki	PROPN
ejpam-5687	1	77	marwat	marwat	NOUN
ejpam-5687	1	78	,	,	PUNCT
ejpam-5687	1	79	kpk	kpk	PROPN
ejpam-5687	1	80	,	,	PUNCT
ejpam-5687	1	81	pakistan	pakistan	PROPN
ejpam-5687	1	82	2	2	NUM
ejpam-5687	1	83	department	department	NOUN
ejpam-5687	1	84	of	of	ADP
ejpam-5687	1	85	mathematics	mathematic	NOUN
ejpam-5687	1	86	,	,	PUNCT
ejpam-5687	1	87	saveetha	saveetha	PROPN
ejpam-5687	1	88	school	school	NOUN
ejpam-5687	1	89	of	of	ADP
ejpam-5687	1	90	engineering	engineering	NOUN
ejpam-5687	1	91	(	(	PUNCT
ejpam-5687	1	92	simats	simat	NOUN
ejpam-5687	1	93	)	)	PUNCT
ejpam-5687	1	94	,	,	PUNCT
ejpam-5687	1	95	thandalam	thandalam	PROPN
ejpam-5687	1	96	600124	600124	NUM
ejpam-5687	1	97	,	,	PUNCT
ejpam-5687	1	98	chennai	chennai	PROPN
ejpam-5687	1	99	,	,	PUNCT
ejpam-5687	1	100	tamil	tamil	PROPN
ejpam-5687	1	101	nadu	nadu	PROPN
ejpam-5687	1	102	,	,	PUNCT
ejpam-5687	1	103	india	india	PROPN
ejpam-5687	1	104	3	3	PROPN
ejpam-5687	1	105	institute	institute	PROPN
ejpam-5687	1	106	of	of	ADP
ejpam-5687	1	107	energy	energy	NOUN
ejpam-5687	1	108	infrastructure	infrastructure	NOUN
ejpam-5687	1	109	(	(	PUNCT
ejpam-5687	1	110	iei	iei	PROPN
ejpam-5687	1	111	)	)	PUNCT
ejpam-5687	1	112	,	,	PUNCT
ejpam-5687	1	113	department	department	NOUN
ejpam-5687	1	114	of	of	ADP
ejpam-5687	1	115	civil	civil	ADJ
ejpam-5687	1	116	engineering	engineering	NOUN
ejpam-5687	1	117	,	,	PUNCT
ejpam-5687	1	118	college	college	NOUN
ejpam-5687	1	119	of	of	ADP
ejpam-5687	1	120	engineering	engineering	PROPN
ejpam-5687	1	121	,	,	PUNCT
ejpam-5687	1	122	universiti	universiti	PROPN
ejpam-5687	1	123	tenaga	tenaga	PROPN
ejpam-5687	1	124	nasional	nasional	PROPN
ejpam-5687	1	125	(	(	PUNCT
ejpam-5687	1	126	uniten	uniten	PROPN
ejpam-5687	1	127	)	)	PUNCT
ejpam-5687	1	128	,	,	PUNCT
ejpam-5687	1	129	putrajaya	putrajaya	PROPN
ejpam-5687	1	130	campus	campus	PROPN
ejpam-5687	1	131	,	,	PUNCT
ejpam-5687	1	132	jalan	jalan	PROPN
ejpam-5687	1	133	ikram	ikram	PROPN
ejpam-5687	1	134	-	-	PUNCT
ejpam-5687	1	135	uniten	uniten	VERB
ejpam-5687	1	136	,	,	PUNCT
ejpam-5687	1	137	43000	43000	NUM
ejpam-5687	1	138	kajang	kajang	PROPN
ejpam-5687	1	139	,	,	PUNCT
ejpam-5687	1	140	selangor	selangor	PROPN
ejpam-5687	1	141	,	,	PUNCT
ejpam-5687	1	142	malaysia	malaysia	PROPN
ejpam-5687	1	143	4	4	NUM
ejpam-5687	1	144	department	department	NOUN
ejpam-5687	1	145	of	of	ADP
ejpam-5687	1	146	mechanical	mechanical	ADJ
ejpam-5687	1	147	engineering	engineering	NOUN
ejpam-5687	1	148	,	,	PUNCT
ejpam-5687	1	149	prince	prince	PROPN
ejpam-5687	1	150	mohammad	mohammad	PROPN
ejpam-5687	1	151	bin	bin	PROPN
ejpam-5687	1	152	fahd	fahd	PROPN
ejpam-5687	1	153	university	university	PROPN
ejpam-5687	1	154	,	,	PUNCT
ejpam-5687	1	155	p.o	p.o	PROPN
ejpam-5687	1	156	box	box	PROPN
ejpam-5687	1	157	1664	1664	NUM
ejpam-5687	1	158	,	,	PUNCT
ejpam-5687	1	159	al	al	PROPN
ejpam-5687	1	160	khobar	khobar	PROPN
ejpam-5687	1	161	31952	31952	NUM
ejpam-5687	1	162	,	,	PUNCT
ejpam-5687	1	163	saudi	saudi	PROPN
ejpam-5687	1	164	arabia	arabia	PROPN
ejpam-5687	1	165	5faculty	5faculty	NUM
ejpam-5687	1	166	of	of	ADP
ejpam-5687	1	167	engineering	engineering	NOUN
ejpam-5687	1	168	,	,	PUNCT
ejpam-5687	1	169	“	"	PUNCT
ejpam-5687	1	170	lucian	lucian	PROPN
ejpam-5687	1	171	blaga	blaga	PROPN
ejpam-5687	1	172	”	"	PUNCT
ejpam-5687	1	173	university	university	PROPN
ejpam-5687	1	174	of	of	ADP
ejpam-5687	1	175	sibiu	sibiu	PROPN
ejpam-5687	1	176	,	,	PUNCT
ejpam-5687	1	177	romania	romania	PROPN
ejpam-5687	1	178	6	6	NUM
ejpam-5687	1	179	school	school	NOUN
ejpam-5687	1	180	of	of	ADP
ejpam-5687	1	181	mathematical	mathematical	ADJ
ejpam-5687	1	182	science	science	NOUN
ejpam-5687	1	183	,	,	PUNCT
ejpam-5687	1	184	yangzhou	yangzhou	PROPN
ejpam-5687	1	185	university	university	PROPN
ejpam-5687	1	186	,	,	PUNCT
ejpam-5687	1	187	yangzhou	yangzhou	PROPN
ejpam-5687	1	188	225002	225002	NUM
ejpam-5687	1	189	,	,	PUNCT
ejpam-5687	1	190	china	china	PROPN
ejpam-5687	1	191	7preclinical	7preclinical	PROPN
ejpam-5687	1	192	department	department	PROPN
ejpam-5687	1	193	,	,	PUNCT
ejpam-5687	1	194	faculty	faculty	NOUN
ejpam-5687	1	195	of	of	ADP
ejpam-5687	1	196	medicine	medicine	NOUN
ejpam-5687	1	197	,	,	PUNCT
ejpam-5687	1	198	“	"	PUNCT
ejpam-5687	1	199	lucian	lucian	PROPN
ejpam-5687	1	200	blaga	blaga	PROPN
ejpam-5687	1	201	”	"	PUNCT
ejpam-5687	1	202	university	university	PROPN
ejpam-5687	1	203	,	,	PUNCT
ejpam-5687	1	204	romania	romania	PROPN
ejpam-5687	1	205	abstract	abstract	NOUN
ejpam-5687	1	206	.	.	PUNCT
ejpam-5687	2	1	in	in	ADP
ejpam-5687	2	2	this	this	DET
ejpam-5687	2	3	study	study	NOUN
ejpam-5687	2	4	,	,	PUNCT
ejpam-5687	2	5	we	we	PRON
ejpam-5687	2	6	develop	develop	VERB
ejpam-5687	2	7	a	a	DET
ejpam-5687	2	8	mathematical	mathematical	ADJ
ejpam-5687	2	9	model	model	NOUN
ejpam-5687	2	10	for	for	ADP
ejpam-5687	2	11	vector	vector	NOUN
ejpam-5687	2	12	-	-	PUNCT
ejpam-5687	2	13	borne	bear	VERB
ejpam-5687	2	14	infections	infection	NOUN
ejpam-5687	2	15	within	within	ADP
ejpam-5687	2	16	a	a	DET
ejpam-5687	2	17	fractional	fractional	ADJ
ejpam-5687	2	18	-	-	PUNCT
ejpam-5687	2	19	order	order	NOUN
ejpam-5687	2	20	framework	framework	NOUN
ejpam-5687	2	21	,	,	PUNCT
ejpam-5687	2	22	employing	employ	VERB
ejpam-5687	2	23	the	the	DET
ejpam-5687	2	24	caputo	caputo	PROPN
ejpam-5687	2	25	-	-	PUNCT
ejpam-5687	2	26	fabrizio	fabrizio	PROPN
ejpam-5687	2	27	fractional	fractional	ADJ
ejpam-5687	2	28	derivative	derivative	NOUN
ejpam-5687	2	29	to	to	PART
ejpam-5687	2	30	enhance	enhance	VERB
ejpam-5687	2	31	the	the	DET
ejpam-5687	2	32	analysis	analysis	NOUN
ejpam-5687	2	33	.	.	PUNCT
ejpam-5687	3	1	the	the	DET
ejpam-5687	3	2	steady	steady	ADJ
ejpam-5687	3	3	states	state	NOUN
ejpam-5687	3	4	of	of	ADP
ejpam-5687	3	5	the	the	DET
ejpam-5687	3	6	system	system	NOUN
ejpam-5687	3	7	are	be	AUX
ejpam-5687	3	8	examined	examine	VERB
ejpam-5687	3	9	,	,	PUNCT
ejpam-5687	3	10	and	and	CCONJ
ejpam-5687	3	11	the	the	DET
ejpam-5687	3	12	basic	basic	ADJ
ejpam-5687	3	13	reproduction	reproduction	NOUN
ejpam-5687	3	14	number	number	NOUN
ejpam-5687	3	15	r0	r0	NOUN
ejpam-5687	3	16	is	be	AUX
ejpam-5687	3	17	derived	derive	VERB
ejpam-5687	3	18	using	use	VERB
ejpam-5687	3	19	the	the	DET
ejpam-5687	3	20	next	next	ADJ
ejpam-5687	3	21	-	-	PUNCT
ejpam-5687	3	22	generation	generation	NOUN
ejpam-5687	3	23	matrix	matrix	NOUN
ejpam-5687	3	24	method	method	NOUN
ejpam-5687	3	25	.	.	PUNCT
ejpam-5687	4	1	the	the	DET
ejpam-5687	4	2	existence	existence	NOUN
ejpam-5687	4	3	and	and	CCONJ
ejpam-5687	4	4	uniqueness	uniqueness	NOUN
ejpam-5687	4	5	of	of	ADP
ejpam-5687	4	6	solutions	solution	NOUN
ejpam-5687	4	7	are	be	AUX
ejpam-5687	4	8	established	establish	VERB
ejpam-5687	4	9	through	through	ADP
ejpam-5687	4	10	the	the	DET
ejpam-5687	4	11	application	application	NOUN
ejpam-5687	4	12	of	of	ADP
ejpam-5687	4	13	the	the	DET
ejpam-5687	4	14	banach	banach	ADV
ejpam-5687	4	15	fixed	fix	VERB
ejpam-5687	4	16	-	-	PUNCT
ejpam-5687	4	17	point	point	NOUN
ejpam-5687	4	18	theorem	theorem	VERB
ejpam-5687	4	19	.	.	PUNCT
ejpam-5687	5	1	a	a	DET
ejpam-5687	5	2	detailed	detailed	ADJ
ejpam-5687	5	3	sensitivity	sensitivity	NOUN
ejpam-5687	5	4	analysis	analysis	NOUN
ejpam-5687	5	5	of	of	ADP
ejpam-5687	5	6	r0	r0	NOUN
ejpam-5687	5	7	identifies	identify	VERB
ejpam-5687	5	8	the	the	DET
ejpam-5687	5	9	most	most	ADV
ejpam-5687	5	10	critical	critical	ADJ
ejpam-5687	5	11	parameters	parameter	NOUN
ejpam-5687	5	12	influencing	influence	VERB
ejpam-5687	5	13	the	the	DET
ejpam-5687	5	14	disease	disease	NOUN
ejpam-5687	5	15	dynamics	dynamic	NOUN
ejpam-5687	5	16	.	.	PUNCT
ejpam-5687	6	1	numerical	numerical	ADJ
ejpam-5687	6	2	simulations	simulation	NOUN
ejpam-5687	6	3	are	be	AUX
ejpam-5687	6	4	performed	perform	VERB
ejpam-5687	6	5	to	to	PART
ejpam-5687	6	6	validate	validate	VERB
ejpam-5687	6	7	the	the	DET
ejpam-5687	6	8	theoretical	theoretical	ADJ
ejpam-5687	6	9	findings	finding	NOUN
ejpam-5687	6	10	and	and	CCONJ
ejpam-5687	6	11	highlight	highlight	VERB
ejpam-5687	6	12	key	key	ADJ
ejpam-5687	6	13	factors	factor	NOUN
ejpam-5687	6	14	impacting	impact	VERB
ejpam-5687	6	15	the	the	DET
ejpam-5687	6	16	control	control	NOUN
ejpam-5687	6	17	and	and	CCONJ
ejpam-5687	6	18	prevention	prevention	NOUN
ejpam-5687	6	19	of	of	ADP
ejpam-5687	6	20	the	the	DET
ejpam-5687	6	21	infection	infection	NOUN
ejpam-5687	6	22	.	.	PUNCT
ejpam-5687	7	1	this	this	DET
ejpam-5687	7	2	work	work	NOUN
ejpam-5687	7	3	provides	provide	VERB
ejpam-5687	7	4	insights	insight	NOUN
ejpam-5687	7	5	into	into	ADP
ejpam-5687	7	6	the	the	DET
ejpam-5687	7	7	dynamics	dynamic	NOUN
ejpam-5687	7	8	of	of	ADP
ejpam-5687	7	9	vectorborne	vectorborne	ADJ
ejpam-5687	7	10	infections	infection	NOUN
ejpam-5687	7	11	and	and	CCONJ
ejpam-5687	7	12	offers	offer	VERB
ejpam-5687	7	13	a	a	DET
ejpam-5687	7	14	robust	robust	ADJ
ejpam-5687	7	15	mathematical	mathematical	ADJ
ejpam-5687	7	16	approach	approach	NOUN
ejpam-5687	7	17	for	for	ADP
ejpam-5687	7	18	optimizing	optimize	VERB
ejpam-5687	7	19	intervention	intervention	NOUN
ejpam-5687	7	20	strategies	strategy	NOUN
ejpam-5687	7	21	.	.	PUNCT
ejpam-5687	8	1	2020	2020	NUM
ejpam-5687	8	2	mathematics	mathematic	NOUN
ejpam-5687	8	3	subject	subject	NOUN
ejpam-5687	8	4	classifications	classification	NOUN
ejpam-5687	8	5	:	:	PUNCT
ejpam-5687	8	6	92d25	92d25	NUM
ejpam-5687	8	7	,	,	PUNCT
ejpam-5687	8	8	92d30	92d30	NUM
ejpam-5687	8	9	key	key	ADJ
ejpam-5687	8	10	words	word	NOUN
ejpam-5687	8	11	and	and	CCONJ
ejpam-5687	8	12	phrases	phrase	NOUN
ejpam-5687	8	13	:	:	PUNCT
ejpam-5687	8	14	vector	vector	NOUN
ejpam-5687	8	15	-	-	PUNCT
ejpam-5687	8	16	borne	borne	ADJ
ejpam-5687	8	17	disease	disease	NOUN
ejpam-5687	8	18	,	,	PUNCT
ejpam-5687	8	19	cf	cf	NOUN
ejpam-5687	8	20	fractional	fractional	ADJ
ejpam-5687	8	21	derivative	derivative	ADJ
ejpam-5687	8	22	,	,	PUNCT
ejpam-5687	8	23	mathematical	mathematical	ADJ
ejpam-5687	8	24	modeling	modeling	NOUN
ejpam-5687	8	25	,	,	PUNCT
ejpam-5687	8	26	existence	existence	NOUN
ejpam-5687	8	27	and	and	CCONJ
ejpam-5687	8	28	uniqueness	uniqueness	NOUN
ejpam-5687	8	29	,	,	PUNCT
ejpam-5687	8	30	sensitivity	sensitivity	NOUN
ejpam-5687	8	31	analysis	analysis	NOUN
ejpam-5687	8	32	,	,	PUNCT
ejpam-5687	8	33	numerical	numerical	ADJ
ejpam-5687	8	34	results	result	NOUN
ejpam-5687	8	35	∗corresponding	∗corresponde	VERB
ejpam-5687	8	36	author	author	NOUN
ejpam-5687	8	37	.	.	PUNCT
ejpam-5687	9	1	∗corresponding	∗corresponde	VERB
ejpam-5687	9	2	author	author	NOUN
ejpam-5687	9	3	.	.	PUNCT
ejpam-5687	10	1	doi	doi	NOUN
ejpam-5687	10	2	:	:	PUNCT
ejpam-5687	10	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5687	https://doi.org/10.29020/nybg.ejpam.v18i2.5687	NOUN
ejpam-5687	10	4	email	email	NOUN
ejpam-5687	10	5	addresses	address	NOUN
ejpam-5687	10	6	:	:	PUNCT
ejpam-5687	10	7	zahir@ulm.edu.pk	zahir@ulm.edu.pk	PROPN
ejpam-5687	10	8	(	(	PUNCT
ejpam-5687	10	9	z.	z.	PROPN
ejpam-5687	10	10	shah	shah	PROPN
ejpam-5687	10	11	)	)	PUNCT
ejpam-5687	10	12	,	,	PUNCT
ejpam-5687	10	13	rashid	rashid	PROPN
ejpam-5687	10	14	ash2000@yahoo.com	ash2000@yahoo.com	PROPN
ejpam-5687	10	15	(	(	PUNCT
ejpam-5687	10	16	r.	r.	PROPN
ejpam-5687	10	17	jan	jan	PROPN
ejpam-5687	10	18	)	)	PUNCT
ejpam-5687	10	19	,	,	PUNCT
ejpam-5687	10	20	sislam@pmu.edu.sa	sislam@pmu.edu.sa	PROPN
ejpam-5687	10	21	(	(	PUNCT
ejpam-5687	10	22	s.	s.	PROPN
ejpam-5687	10	23	islam	islam	PROPN
ejpam-5687	10	24	)	)	PUNCT
ejpam-5687	10	25	,	,	PUNCT
ejpam-5687	10	26	vrinceanu.narcisai@ulbsibiu.ro	vrinceanu.narcisai@ulbsibiu.ro	NOUN
ejpam-5687	10	27	(	(	PUNCT
ejpam-5687	10	28	n.	n.	NOUN
ejpam-5687	10	29	vrinceanu	vrinceanu	PROPN
ejpam-5687	10	30	)	)	PUNCT
ejpam-5687	10	31	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5687	11	1	1	1	NUM
ejpam-5687	11	2	copyright	copyright	NOUN
ejpam-5687	11	3	:	:	PUNCT
ejpam-5687	11	4	©	©	PROPN
ejpam-5687	11	5	2025	2025	NUM
ejpam-5687	11	6	the	the	DET
ejpam-5687	11	7	author(s	author(s	NOUN
ejpam-5687	11	8	)	)	PUNCT
ejpam-5687	11	9	.	.	PUNCT
ejpam-5687	12	1	(	(	PUNCT
ejpam-5687	12	2	cc	cc	NOUN
ejpam-5687	12	3	by	by	ADP
ejpam-5687	12	4	-	-	PUNCT
ejpam-5687	12	5	nc	nc	PROPN
ejpam-5687	12	6	4.0	4.0	NUM
ejpam-5687	12	7	)	)	PUNCT
ejpam-5687	12	8	n.	n.	PROPN
ejpam-5687	12	9	ullah	ullah	PROPN
ejpam-5687	12	10	et	et	PROPN
ejpam-5687	12	11	al	al	PROPN
ejpam-5687	12	12	.	.	PUNCT
ejpam-5687	12	13	/	/	SYM
ejpam-5687	12	14	eur	eur	PROPN
ejpam-5687	12	15	.	.	PUNCT
ejpam-5687	13	1	j.	j.	PROPN
ejpam-5687	13	2	pure	pure	PROPN
ejpam-5687	13	3	appl	appl	PROPN
ejpam-5687	13	4	.	.	PROPN
ejpam-5687	13	5	math	math	PROPN
ejpam-5687	13	6	,	,	PUNCT
ejpam-5687	13	7	18	18	NUM
ejpam-5687	13	8	(	(	PUNCT
ejpam-5687	13	9	2	2	NUM
ejpam-5687	13	10	)	)	PUNCT
ejpam-5687	13	11	(	(	PUNCT
ejpam-5687	13	12	2025	2025	NUM
ejpam-5687	13	13	)	)	PUNCT
ejpam-5687	13	14	,	,	PUNCT
ejpam-5687	13	15	5687	5687	NUM
ejpam-5687	13	16	2	2	NUM
ejpam-5687	13	17	of	of	ADP
ejpam-5687	13	18	25	25	NUM
ejpam-5687	13	19	1	1	NUM
ejpam-5687	13	20	.	.	PUNCT
ejpam-5687	14	1	introduction	introduction	NOUN
ejpam-5687	14	2	vector	vector	NOUN
ejpam-5687	14	3	-	-	PUNCT
ejpam-5687	14	4	borne	bear	VERB
ejpam-5687	14	5	diseases	disease	NOUN
ejpam-5687	14	6	are	be	AUX
ejpam-5687	14	7	carried	carry	VERB
ejpam-5687	14	8	through	through	ADP
ejpam-5687	14	9	mosquitoes	mosquito	NOUN
ejpam-5687	14	10	or	or	CCONJ
ejpam-5687	14	11	different	different	ADJ
ejpam-5687	14	12	kinds	kind	NOUN
ejpam-5687	14	13	of	of	ADP
ejpam-5687	14	14	bugs	bug	NOUN
ejpam-5687	14	15	such	such	ADJ
ejpam-5687	14	16	as	as	ADP
ejpam-5687	14	17	houseflies	housefly	NOUN
ejpam-5687	14	18	.	.	PUNCT
ejpam-5687	15	1	vector	vector	NOUN
ejpam-5687	15	2	-	-	PUNCT
ejpam-5687	15	3	borne	bear	VERB
ejpam-5687	15	4	ailments	ailment	NOUN
ejpam-5687	15	5	are	be	AUX
ejpam-5687	15	6	mainly	mainly	ADV
ejpam-5687	15	7	studied	study	VERB
ejpam-5687	15	8	in	in	ADP
ejpam-5687	15	9	vertebrates	vertebrate	NOUN
ejpam-5687	15	10	like	like	ADP
ejpam-5687	15	11	mice	mouse	NOUN
ejpam-5687	15	12	,	,	PUNCT
ejpam-5687	15	13	rats	rat	NOUN
ejpam-5687	15	14	,	,	PUNCT
ejpam-5687	15	15	nonhuman	nonhuman	ADJ
ejpam-5687	15	16	primates	primate	NOUN
ejpam-5687	15	17	(	(	PUNCT
ejpam-5687	15	18	nhps	nhps	NOUN
ejpam-5687	15	19	)	)	PUNCT
ejpam-5687	15	20	,	,	PUNCT
ejpam-5687	15	21	and	and	CCONJ
ejpam-5687	15	22	birds	bird	NOUN
ejpam-5687	15	23	.	.	PUNCT
ejpam-5687	16	1	investigators	investigator	NOUN
ejpam-5687	16	2	want	want	VERB
ejpam-5687	16	3	those	those	DET
ejpam-5687	16	4	animals	animal	NOUN
ejpam-5687	16	5	to	to	PART
ejpam-5687	16	6	assist	assist	VERB
ejpam-5687	16	7	them	they	PRON
ejpam-5687	16	8	explore	explore	VERB
ejpam-5687	16	9	how	how	SCONJ
ejpam-5687	16	10	pathogens	pathogen	NOUN
ejpam-5687	16	11	are	be	AUX
ejpam-5687	16	12	moved	move	VERB
ejpam-5687	16	13	from	from	ADP
ejpam-5687	16	14	one	one	NUM
ejpam-5687	16	15	host	host	NOUN
ejpam-5687	16	16	to	to	ADP
ejpam-5687	16	17	another	another	PRON
ejpam-5687	16	18	in	in	ADP
ejpam-5687	16	19	addition	addition	NOUN
ejpam-5687	16	20	to	to	PART
ejpam-5687	16	21	determine	determine	VERB
ejpam-5687	16	22	the	the	DET
ejpam-5687	16	23	feeding	feeding	NOUN
ejpam-5687	16	24	behaviors	behavior	NOUN
ejpam-5687	16	25	of	of	ADP
ejpam-5687	16	26	immune	immune	ADJ
ejpam-5687	16	27	and	and	CCONJ
ejpam-5687	16	28	non	non	ADJ
ejpam-5687	16	29	-	-	ADJ
ejpam-5687	16	30	immune	immune	ADJ
ejpam-5687	16	31	individuals	individual	NOUN
ejpam-5687	16	32	as	as	ADV
ejpam-5687	16	33	well	well	ADV
ejpam-5687	16	34	as	as	ADP
ejpam-5687	16	35	selectivity	selectivity	NOUN
ejpam-5687	16	36	in	in	ADP
ejpam-5687	16	37	pathogenicity	pathogenicity	NOUN
ejpam-5687	16	38	at	at	ADP
ejpam-5687	16	39	different	different	ADJ
ejpam-5687	16	40	times	time	NOUN
ejpam-5687	16	41	when	when	SCONJ
ejpam-5687	16	42	hosts	host	NOUN
ejpam-5687	16	43	feed[1	feed[1	VERB
ejpam-5687	16	44	]	]	PUNCT
ejpam-5687	16	45	.	.	PUNCT
ejpam-5687	17	1	the	the	DET
ejpam-5687	17	2	[	[	X
ejpam-5687	17	3	2	2	NUM
ejpam-5687	17	4	]	]	PUNCT
ejpam-5687	17	5	talks	talk	NOUN
ejpam-5687	17	6	about	about	ADP
ejpam-5687	17	7	the	the	DET
ejpam-5687	17	8	difficulties	difficulty	NOUN
ejpam-5687	17	9	encountered	encounter	VERB
ejpam-5687	17	10	when	when	SCONJ
ejpam-5687	17	11	trying	try	VERB
ejpam-5687	17	12	to	to	PART
ejpam-5687	17	13	control	control	VERB
ejpam-5687	17	14	vector	vector	NOUN
ejpam-5687	17	15	-	-	PUNCT
ejpam-5687	17	16	borne	bear	VERB
ejpam-5687	17	17	diseases	disease	NOUN
ejpam-5687	17	18	,	,	PUNCT
ejpam-5687	17	19	mainly	mainly	ADV
ejpam-5687	17	20	focusing	focus	VERB
ejpam-5687	17	21	on	on	ADP
ejpam-5687	17	22	mosquitoes	mosquito	NOUN
ejpam-5687	17	23	as	as	ADP
ejpam-5687	17	24	vectors	vector	NOUN
ejpam-5687	17	25	.	.	PUNCT
ejpam-5687	18	1	while	while	SCONJ
ejpam-5687	18	2	there	there	PRON
ejpam-5687	18	3	is	be	VERB
ejpam-5687	18	4	progress	progress	NOUN
ejpam-5687	18	5	in	in	ADP
ejpam-5687	18	6	vaccine	vaccine	NOUN
ejpam-5687	18	7	technology	technology	NOUN
ejpam-5687	18	8	,	,	PUNCT
ejpam-5687	18	9	challenges	challenge	NOUN
ejpam-5687	18	10	such	such	ADJ
ejpam-5687	18	11	as	as	ADP
ejpam-5687	18	12	;	;	PUNCT
ejpam-5687	18	13	resistance	resistance	NOUN
ejpam-5687	18	14	of	of	ADP
ejpam-5687	18	15	vectors	vector	NOUN
ejpam-5687	18	16	to	to	ADP
ejpam-5687	18	17	insecticides	insecticide	NOUN
ejpam-5687	18	18	,	,	PUNCT
ejpam-5687	18	19	altering	alter	VERB
ejpam-5687	18	20	ecosystems	ecosystem	NOUN
ejpam-5687	18	21	and	and	CCONJ
ejpam-5687	18	22	the	the	DET
ejpam-5687	18	23	resurgence	resurgence	NOUN
ejpam-5687	18	24	of	of	ADP
ejpam-5687	18	25	some	some	DET
ejpam-5687	18	26	diseases	disease	NOUN
ejpam-5687	18	27	in	in	ADP
ejpam-5687	18	28	new	new	ADJ
ejpam-5687	18	29	regions	region	NOUN
ejpam-5687	18	30	are	be	AUX
ejpam-5687	18	31	still	still	ADV
ejpam-5687	18	32	present	present	ADJ
ejpam-5687	18	33	.	.	PUNCT
ejpam-5687	19	1	the	the	DET
ejpam-5687	19	2	paper	paper	NOUN
ejpam-5687	19	3	states	state	VERB
ejpam-5687	19	4	that	that	SCONJ
ejpam-5687	19	5	in	in	ADP
ejpam-5687	19	6	order	order	NOUN
ejpam-5687	19	7	to	to	PART
ejpam-5687	19	8	better	well	ADV
ejpam-5687	19	9	handle	handle	VERB
ejpam-5687	19	10	them	they	PRON
ejpam-5687	19	11	,	,	PUNCT
ejpam-5687	19	12	novel	novel	ADJ
ejpam-5687	19	13	surveillance	surveillance	NOUN
ejpam-5687	19	14	mechanisms	mechanism	NOUN
ejpam-5687	19	15	,	,	PUNCT
ejpam-5687	19	16	more	more	ADV
ejpam-5687	19	17	efficient	efficient	ADJ
ejpam-5687	19	18	diagnosis	diagnosis	NOUN
ejpam-5687	19	19	procedures	procedure	NOUN
ejpam-5687	19	20	and	and	CCONJ
ejpam-5687	19	21	new	new	ADJ
ejpam-5687	19	22	ways	way	NOUN
ejpam-5687	19	23	of	of	ADP
ejpam-5687	19	24	controlling	control	VERB
ejpam-5687	19	25	such	such	ADJ
ejpam-5687	19	26	organisms	organism	NOUN
ejpam-5687	19	27	must	must	AUX
ejpam-5687	19	28	be	be	AUX
ejpam-5687	19	29	put	put	VERB
ejpam-5687	19	30	up[3	up[3	NOUN
ejpam-5687	19	31	]	]	PUNCT
ejpam-5687	19	32	.	.	PUNCT
ejpam-5687	20	1	the	the	DET
ejpam-5687	20	2	vector	vector	NOUN
ejpam-5687	20	3	-	-	PUNCT
ejpam-5687	20	4	borne	bear	VERB
ejpam-5687	20	5	diseases	disease	NOUN
ejpam-5687	20	6	explained	explain	VERB
ejpam-5687	20	7	in	in	ADP
ejpam-5687	20	8	[	[	X
ejpam-5687	20	9	4	4	NUM
ejpam-5687	20	10	]	]	PUNCT
ejpam-5687	20	11	indicate	indicate	VERB
ejpam-5687	20	12	how	how	SCONJ
ejpam-5687	20	13	climate	climate	NOUN
ejpam-5687	20	14	change	change	NOUN
ejpam-5687	20	15	is	be	AUX
ejpam-5687	20	16	re	re	VERB
ejpam-5687	20	17	-	-	VERB
ejpam-5687	20	18	resurfacing	resurface	VERB
ejpam-5687	20	19	or	or	CCONJ
ejpam-5687	20	20	emerging	emerge	VERB
ejpam-5687	20	21	their	their	PRON
ejpam-5687	20	22	re	re	NOUN
ejpam-5687	20	23	-	-	NOUN
ejpam-5687	20	24	emergence	emergence	NOUN
ejpam-5687	20	25	.	.	PUNCT
ejpam-5687	21	1	moreover	moreover	ADV
ejpam-5687	21	2	,	,	PUNCT
ejpam-5687	21	3	it	it	PRON
ejpam-5687	21	4	pointed	point	VERB
ejpam-5687	21	5	out	out	ADP
ejpam-5687	21	6	that	that	SCONJ
ejpam-5687	21	7	weather	weather	NOUN
ejpam-5687	21	8	elements	element	NOUN
ejpam-5687	21	9	affect	affect	VERB
ejpam-5687	21	10	vectors	vector	NOUN
ejpam-5687	21	11	such	such	ADJ
ejpam-5687	21	12	as	as	ADP
ejpam-5687	21	13	mosquitoes	mosquito	NOUN
ejpam-5687	21	14	hence	hence	ADV
ejpam-5687	21	15	increasing	increase	VERB
ejpam-5687	21	16	their	their	PRON
ejpam-5687	21	17	numbers	number	NOUN
ejpam-5687	21	18	resulting	result	VERB
ejpam-5687	21	19	into	into	ADP
ejpam-5687	21	20	higher	high	ADJ
ejpam-5687	21	21	chances	chance	NOUN
ejpam-5687	21	22	transmission	transmission	NOUN
ejpam-5687	21	23	.	.	PUNCT
ejpam-5687	22	1	mathematical	mathematical	ADJ
ejpam-5687	22	2	modeling	modeling	NOUN
ejpam-5687	22	3	is	be	AUX
ejpam-5687	22	4	a	a	DET
ejpam-5687	22	5	cornerstone	cornerstone	NOUN
ejpam-5687	22	6	of	of	ADP
ejpam-5687	22	7	modern	modern	ADJ
ejpam-5687	22	8	biology	biology	NOUN
ejpam-5687	22	9	,	,	PUNCT
ejpam-5687	22	10	enabling	enable	VERB
ejpam-5687	22	11	researchers	researcher	NOUN
ejpam-5687	22	12	to	to	PART
ejpam-5687	22	13	explore	explore	VERB
ejpam-5687	22	14	complex	complex	ADJ
ejpam-5687	22	15	systems	system	NOUN
ejpam-5687	22	16	,	,	PUNCT
ejpam-5687	22	17	generate	generate	VERB
ejpam-5687	22	18	new	new	ADJ
ejpam-5687	22	19	hypotheses	hypothesis	NOUN
ejpam-5687	22	20	,	,	PUNCT
ejpam-5687	22	21	and	and	CCONJ
ejpam-5687	22	22	design	design	VERB
ejpam-5687	22	23	efficient	efficient	ADJ
ejpam-5687	22	24	solutions	solution	NOUN
ejpam-5687	22	25	for	for	ADP
ejpam-5687	22	26	real	real	ADJ
ejpam-5687	22	27	-	-	PUNCT
ejpam-5687	22	28	world	world	NOUN
ejpam-5687	22	29	problems	problem	NOUN
ejpam-5687	22	30	[	[	X
ejpam-5687	22	31	5–7	5–7	X
ejpam-5687	22	32	]	]	PUNCT
ejpam-5687	22	33	.	.	PUNCT
ejpam-5687	23	1	in	in	ADP
ejpam-5687	23	2	[	[	X
ejpam-5687	23	3	8	8	NUM
ejpam-5687	23	4	]	]	PUNCT
ejpam-5687	23	5	,	,	PUNCT
ejpam-5687	23	6	the	the	DET
ejpam-5687	23	7	researchers	researcher	NOUN
ejpam-5687	23	8	focussed	focusse	VERB
ejpam-5687	23	9	on	on	ADP
ejpam-5687	23	10	how	how	SCONJ
ejpam-5687	23	11	mathematical	mathematical	ADJ
ejpam-5687	23	12	models	model	NOUN
ejpam-5687	23	13	can	can	AUX
ejpam-5687	23	14	be	be	AUX
ejpam-5687	23	15	used	use	VERB
ejpam-5687	23	16	to	to	PART
ejpam-5687	23	17	estimate	estimate	VERB
ejpam-5687	23	18	how	how	SCONJ
ejpam-5687	23	19	much	much	ADJ
ejpam-5687	23	20	vector	vector	NOUN
ejpam-5687	23	21	-	-	PUNCT
ejpam-5687	23	22	borne	bear	VERB
ejpam-5687	23	23	viral	viral	ADJ
ejpam-5687	23	24	infections	infection	NOUN
ejpam-5687	23	25	will	will	AUX
ejpam-5687	23	26	spread	spread	VERB
ejpam-5687	23	27	out	out	ADP
ejpam-5687	23	28	as	as	ADV
ejpam-5687	23	29	well	well	ADV
ejpam-5687	23	30	as	as	ADP
ejpam-5687	23	31	the	the	DET
ejpam-5687	23	32	speed	speed	NOUN
ejpam-5687	23	33	at	at	ADP
ejpam-5687	23	34	which	which	PRON
ejpam-5687	23	35	they	they	PRON
ejpam-5687	23	36	might	might	AUX
ejpam-5687	23	37	go	go	VERB
ejpam-5687	23	38	ahead	ahead	ADV
ejpam-5687	23	39	thereby	thereby	ADV
ejpam-5687	23	40	creating	create	VERB
ejpam-5687	23	41	an	an	DET
ejpam-5687	23	42	impact	impact	NOUN
ejpam-5687	23	43	.	.	PUNCT
ejpam-5687	24	1	the	the	DET
ejpam-5687	24	2	idea	idea	NOUN
ejpam-5687	24	3	here	here	ADV
ejpam-5687	24	4	is	be	AUX
ejpam-5687	24	5	that	that	SCONJ
ejpam-5687	24	6	through	through	ADP
ejpam-5687	24	7	interventions	intervention	NOUN
ejpam-5687	24	8	aimed	aim	VERB
ejpam-5687	24	9	at	at	ADP
ejpam-5687	24	10	lowering	lower	VERB
ejpam-5687	24	11	r0	r0	NOUN
ejpam-5687	24	12	using	use	VERB
ejpam-5687	24	13	different	different	ADJ
ejpam-5687	24	14	approaches	approach	NOUN
ejpam-5687	24	15	one	one	PRON
ejpam-5687	24	16	can	can	AUX
ejpam-5687	24	17	use	use	VERB
ejpam-5687	24	18	such	such	ADJ
ejpam-5687	24	19	models	model	NOUN
ejpam-5687	24	20	to	to	PART
ejpam-5687	24	21	control	control	VERB
ejpam-5687	24	22	epidemics	epidemic	NOUN
ejpam-5687	24	23	and	and	CCONJ
ejpam-5687	24	24	pandemic	pandemic	ADJ
ejpam-5687	24	25	caused	cause	VERB
ejpam-5687	24	26	by	by	ADP
ejpam-5687	24	27	these	these	DET
ejpam-5687	24	28	viruses	virus	NOUN
ejpam-5687	24	29	.	.	PUNCT
ejpam-5687	25	1	the	the	DET
ejpam-5687	25	2	mathematical	mathematical	ADJ
ejpam-5687	25	3	model	model	NOUN
ejpam-5687	25	4	for	for	ADP
ejpam-5687	25	5	the	the	DET
ejpam-5687	25	6	dynamics	dynamic	NOUN
ejpam-5687	25	7	of	of	ADP
ejpam-5687	25	8	vector	vector	NOUN
ejpam-5687	25	9	-	-	PUNCT
ejpam-5687	25	10	borne	bear	VERB
ejpam-5687	25	11	diseases	disease	NOUN
ejpam-5687	25	12	transmitted	transmit	VERB
ejpam-5687	25	13	by	by	ADP
ejpam-5687	25	14	mosquitoes	mosquito	NOUN
ejpam-5687	25	15	is	be	AUX
ejpam-5687	25	16	presented	present	VERB
ejpam-5687	25	17	in	in	ADP
ejpam-5687	25	18	this	this	DET
ejpam-5687	25	19	paper	paper	NOUN
ejpam-5687	26	1	[	[	X
ejpam-5687	26	2	9	9	NUM
ejpam-5687	26	3	]	]	PUNCT
ejpam-5687	26	4	,	,	PUNCT
ejpam-5687	26	5	integrating	integrate	VERB
ejpam-5687	26	6	aquatic	aquatic	ADJ
ejpam-5687	26	7	stages	stage	NOUN
ejpam-5687	26	8	of	of	ADP
ejpam-5687	26	9	mosquitoes	mosquito	NOUN
ejpam-5687	26	10	as	as	ADV
ejpam-5687	26	11	well	well	ADV
ejpam-5687	26	12	as	as	ADP
ejpam-5687	26	13	the	the	DET
ejpam-5687	26	14	gonotrophic	gonotrophic	ADJ
ejpam-5687	26	15	cycle	cycle	NOUN
ejpam-5687	26	16	.	.	PUNCT
ejpam-5687	27	1	it	it	PRON
ejpam-5687	27	2	is	be	AUX
ejpam-5687	27	3	illustrated	illustrate	VERB
ejpam-5687	27	4	that	that	SCONJ
ejpam-5687	27	5	these	these	DET
ejpam-5687	27	6	elements	element	NOUN
ejpam-5687	27	7	have	have	VERB
ejpam-5687	27	8	an	an	DET
ejpam-5687	27	9	effect	effect	NOUN
ejpam-5687	27	10	on	on	ADP
ejpam-5687	27	11	the	the	DET
ejpam-5687	27	12	spread	spread	NOUN
ejpam-5687	27	13	of	of	ADP
ejpam-5687	27	14	the	the	DET
ejpam-5687	27	15	disease	disease	NOUN
ejpam-5687	27	16	.	.	PUNCT
ejpam-5687	28	1	consequently	consequently	ADV
ejpam-5687	28	2	,	,	PUNCT
ejpam-5687	28	3	mosquito	mosquito	NOUN
ejpam-5687	28	4	-	-	PUNCT
ejpam-5687	28	5	borne	bear	VERB
ejpam-5687	28	6	illnesses	illness	NOUN
ejpam-5687	28	7	can	can	AUX
ejpam-5687	28	8	only	only	ADV
ejpam-5687	28	9	be	be	AUX
ejpam-5687	28	10	treated	treat	VERB
ejpam-5687	28	11	efficiently	efficiently	ADV
ejpam-5687	28	12	if	if	SCONJ
ejpam-5687	28	13	they	they	PRON
ejpam-5687	28	14	aim	aim	VERB
ejpam-5687	28	15	at	at	ADP
ejpam-5687	28	16	these	these	DET
ejpam-5687	28	17	parts	part	NOUN
ejpam-5687	28	18	.	.	PUNCT
ejpam-5687	29	1	in	in	ADP
ejpam-5687	29	2	[	[	X
ejpam-5687	29	3	10	10	NUM
ejpam-5687	29	4	]	]	PUNCT
ejpam-5687	29	5	employs	employ	VERB
ejpam-5687	29	6	fractional	fractional	ADJ
ejpam-5687	29	7	calculus	calculus	NOUN
ejpam-5687	29	8	in	in	ADP
ejpam-5687	29	9	the	the	DET
ejpam-5687	29	10	representation	representation	NOUN
ejpam-5687	29	11	of	of	ADP
ejpam-5687	29	12	malaria	malaria	NOUN
ejpam-5687	29	13	transmission	transmission	NOUN
ejpam-5687	29	14	with	with	ADP
ejpam-5687	29	15	particular	particular	ADJ
ejpam-5687	29	16	reference	reference	NOUN
ejpam-5687	29	17	to	to	ADP
ejpam-5687	29	18	impacts	impact	NOUN
ejpam-5687	29	19	of	of	ADP
ejpam-5687	29	20	treatment	treatment	NOUN
ejpam-5687	29	21	as	as	ADV
ejpam-5687	29	22	well	well	ADV
ejpam-5687	29	23	as	as	ADP
ejpam-5687	29	24	insecticides	insecticide	NOUN
ejpam-5687	29	25	indicating	indicate	VERB
ejpam-5687	29	26	that	that	SCONJ
ejpam-5687	29	27	disease	disease	NOUN
ejpam-5687	29	28	containment	containment	NOUN
ejpam-5687	29	29	can	can	AUX
ejpam-5687	29	30	be	be	AUX
ejpam-5687	29	31	optimally	optimally	ADV
ejpam-5687	29	32	achieved	achieve	VERB
ejpam-5687	29	33	through	through	ADP
ejpam-5687	29	34	fusion	fusion	NOUN
ejpam-5687	29	35	of	of	ADP
ejpam-5687	29	36	these	these	DET
ejpam-5687	29	37	techniques	technique	NOUN
ejpam-5687	29	38	using	use	VERB
ejpam-5687	29	39	nonlinear	nonlinear	ADJ
ejpam-5687	29	40	odes	ode	NOUN
ejpam-5687	29	41	.	.	PUNCT
ejpam-5687	30	1	the	the	DET
ejpam-5687	30	2	fractional	fractional	ADJ
ejpam-5687	30	3	-	-	PUNCT
ejpam-5687	30	4	order	order	NOUN
ejpam-5687	30	5	model	model	NOUN
ejpam-5687	30	6	with	with	ADP
ejpam-5687	30	7	caputo	caputo	PROPN
ejpam-5687	30	8	-	-	PUNCT
ejpam-5687	30	9	fabrizio	fabrizio	PROPN
ejpam-5687	30	10	derivative	derivative	NOUN
ejpam-5687	30	11	is	be	AUX
ejpam-5687	30	12	utilized	utilize	VERB
ejpam-5687	30	13	in	in	ADP
ejpam-5687	30	14	order	order	NOUN
ejpam-5687	30	15	to	to	PART
ejpam-5687	30	16	analyze	analyze	VERB
ejpam-5687	30	17	vector	vector	NOUN
ejpam-5687	30	18	-	-	PUNCT
ejpam-5687	30	19	host	host	NOUN
ejpam-5687	30	20	disease	disease	NOUN
ejpam-5687	30	21	dynamics	dynamic	NOUN
ejpam-5687	30	22	,	,	PUNCT
ejpam-5687	30	23	such	such	ADJ
ejpam-5687	30	24	that	that	DET
ejpam-5687	30	25	memory	memory	NOUN
ejpam-5687	30	26	effects	effect	NOUN
ejpam-5687	30	27	(	(	PUNCT
ejpam-5687	30	28	which	which	PRON
ejpam-5687	30	29	are	be	AUX
ejpam-5687	30	30	important	important	ADJ
ejpam-5687	30	31	for	for	ADP
ejpam-5687	30	32	obtaining	obtain	VERB
ejpam-5687	30	33	better	well	ADJ
ejpam-5687	30	34	predictions	prediction	NOUN
ejpam-5687	30	35	)	)	PUNCT
ejpam-5687	30	36	are	be	AUX
ejpam-5687	30	37	emphasized	emphasize	VERB
ejpam-5687	30	38	.	.	PUNCT
ejpam-5687	31	1	the	the	DET
ejpam-5687	31	2	paper	paper	NOUN
ejpam-5687	31	3	[	[	X
ejpam-5687	31	4	11	11	NUM
ejpam-5687	31	5	]	]	PUNCT
ejpam-5687	31	6	further	far	ADV
ejpam-5687	31	7	provides	provide	VERB
ejpam-5687	31	8	analytical	analytical	ADJ
ejpam-5687	31	9	as	as	ADV
ejpam-5687	31	10	well	well	ADV
ejpam-5687	31	11	as	as	ADP
ejpam-5687	31	12	numerical	numerical	ADJ
ejpam-5687	31	13	analyses	analysis	NOUN
ejpam-5687	31	14	for	for	ADP
ejpam-5687	31	15	exploring	explore	VERB
ejpam-5687	31	16	on	on	ADP
ejpam-5687	31	17	disease	disease	NOUN
ejpam-5687	31	18	behavior	behavior	NOUN
ejpam-5687	31	19	including	include	VERB
ejpam-5687	31	20	control	control	NOUN
ejpam-5687	31	21	strategies.in	strategies.in	PRON
ejpam-5687	31	22	this	this	DET
ejpam-5687	31	23	particular	particular	ADJ
ejpam-5687	31	24	case	case	NOUN
ejpam-5687	31	25	,	,	PUNCT
ejpam-5687	31	26	a	a	DET
ejpam-5687	31	27	nonlinear	nonlinear	ADJ
ejpam-5687	31	28	fractional	fractional	ADJ
ejpam-5687	31	29	-	-	PUNCT
ejpam-5687	31	30	order	order	NOUN
ejpam-5687	31	31	model	model	NOUN
ejpam-5687	31	32	was	be	AUX
ejpam-5687	31	33	applied	apply	VERB
ejpam-5687	31	34	in	in	ADP
ejpam-5687	31	35	order	order	NOUN
ejpam-5687	31	36	to	to	PART
ejpam-5687	31	37	take	take	VERB
ejpam-5687	31	38	a	a	DET
ejpam-5687	31	39	closer	close	ADJ
ejpam-5687	31	40	look	look	NOUN
ejpam-5687	31	41	at	at	ADP
ejpam-5687	31	42	vector	vector	NOUN
ejpam-5687	31	43	-	-	PUNCT
ejpam-5687	31	44	borne	bear	VERB
ejpam-5687	31	45	diseases	disease	NOUN
ejpam-5687	31	46	instead	instead	ADV
ejpam-5687	31	47	of	of	ADP
ejpam-5687	31	48	just	just	ADV
ejpam-5687	31	49	using	use	VERB
ejpam-5687	31	50	traditional	traditional	ADJ
ejpam-5687	31	51	integer	integer	NOUN
ejpam-5687	31	52	-	-	PUNCT
ejpam-5687	31	53	order	order	NOUN
ejpam-5687	31	54	solid	solid	ADJ
ejpam-5687	31	55	-	-	PUNCT
ejpam-5687	31	56	state	state	NOUN
ejpam-5687	31	57	models	model	NOUN
ejpam-5687	31	58	;	;	PUNCT
ejpam-5687	31	59	thus	thus	ADV
ejpam-5687	31	60	making	make	VERB
ejpam-5687	31	61	an	an	DET
ejpam-5687	31	62	improvement	improvement	NOUN
ejpam-5687	31	63	through	through	ADP
ejpam-5687	31	64	incorporating	incorporate	VERB
ejpam-5687	31	65	memory	memory	NOUN
ejpam-5687	31	66	effects	effect	NOUN
ejpam-5687	31	67	.	.	PUNCT
ejpam-5687	32	1	as	as	ADV
ejpam-5687	32	2	far	far	ADV
ejpam-5687	32	3	as	as	SCONJ
ejpam-5687	32	4	stability	stability	NOUN
ejpam-5687	32	5	goes	go	VERB
ejpam-5687	32	6	along	along	ADV
ejpam-5687	32	7	with	with	ADP
ejpam-5687	32	8	following	follow	VERB
ejpam-5687	32	9	pathogenesis	pathogenesis	NOUN
ejpam-5687	32	10	or	or	CCONJ
ejpam-5687	32	11	epidemiology	epidemiology	NOUN
ejpam-5687	32	12	routes	route	NOUN
ejpam-5687	32	13	are	be	AUX
ejpam-5687	32	14	concerned	concern	VERB
ejpam-5687	32	15	which	which	PRON
ejpam-5687	32	16	leads	lead	VERB
ejpam-5687	32	17	us	we	PRON
ejpam-5687	32	18	to	to	PART
ejpam-5687	32	19	know	know	VERB
ejpam-5687	32	20	more	more	ADJ
ejpam-5687	32	21	about	about	ADP
ejpam-5687	32	22	how	how	SCONJ
ejpam-5687	32	23	they	they	PRON
ejpam-5687	32	24	can	can	AUX
ejpam-5687	32	25	affect	affect	VERB
ejpam-5687	32	26	each	each	DET
ejpam-5687	32	27	other	other	ADJ
ejpam-5687	32	28	through	through	ADP
ejpam-5687	32	29	time	time	NOUN
ejpam-5687	32	30	or	or	CCONJ
ejpam-5687	32	31	space[12	space[12	NOUN
ejpam-5687	32	32	]	]	X
ejpam-5687	32	33	.	.	PUNCT
ejpam-5687	33	1	the	the	DET
ejpam-5687	33	2	caputo	caputo	PROPN
ejpam-5687	33	3	-	-	PUNCT
ejpam-5687	33	4	fabrizio	fabrizio	PROPN
ejpam-5687	33	5	fractional	fractional	ADJ
ejpam-5687	33	6	order	order	NOUN
ejpam-5687	33	7	model	model	NOUN
ejpam-5687	33	8	which	which	PRON
ejpam-5687	33	9	captures	capture	VERB
ejpam-5687	33	10	the	the	DET
ejpam-5687	33	11	dynamics	dynamic	NOUN
ejpam-5687	33	12	of	of	ADP
ejpam-5687	33	13	covid-19	covid-19	PROPN
ejpam-5687	33	14	pandemic	pandemic	NOUN
ejpam-5687	33	15	exhibiting	exhibit	VERB
ejpam-5687	33	16	greater	great	ADJ
ejpam-5687	33	17	accuracy	accuracy	NOUN
ejpam-5687	33	18	than	than	ADP
ejpam-5687	33	19	integer	integer	NOUN
ejpam-5687	33	20	-	-	PUNCT
ejpam-5687	33	21	order	order	NOUN
ejpam-5687	33	22	systems	system	NOUN
ejpam-5687	33	23	prevalent	prevalent	ADJ
ejpam-5687	33	24	in	in	ADP
ejpam-5687	33	25	past	past	ADJ
ejpam-5687	33	26	literature	literature	NOUN
ejpam-5687	33	27	by	by	ADP
ejpam-5687	33	28	showing	show	VERB
ejpam-5687	33	29	improved	improved	ADJ
ejpam-5687	33	30	accuracy	accuracy	NOUN
ejpam-5687	34	1	when	when	SCONJ
ejpam-5687	34	2	n.	n.	PROPN
ejpam-5687	34	3	ullah	ullah	PROPN
ejpam-5687	34	4	et	et	PROPN
ejpam-5687	34	5	al	al	PROPN
ejpam-5687	34	6	.	.	PUNCT
ejpam-5687	34	7	/	/	SYM
ejpam-5687	34	8	eur	eur	PROPN
ejpam-5687	34	9	.	.	PUNCT
ejpam-5687	35	1	j.	j.	PROPN
ejpam-5687	35	2	pure	pure	PROPN
ejpam-5687	35	3	appl	appl	PROPN
ejpam-5687	35	4	.	.	PROPN
ejpam-5687	35	5	math	math	PROPN
ejpam-5687	35	6	,	,	PUNCT
ejpam-5687	35	7	18	18	NUM
ejpam-5687	35	8	(	(	PUNCT
ejpam-5687	35	9	2	2	NUM
ejpam-5687	35	10	)	)	PUNCT
ejpam-5687	35	11	(	(	PUNCT
ejpam-5687	35	12	2025	2025	NUM
ejpam-5687	35	13	)	)	PUNCT
ejpam-5687	35	14	,	,	PUNCT
ejpam-5687	35	15	5687	5687	NUM
ejpam-5687	35	16	3	3	NUM
ejpam-5687	35	17	of	of	ADP
ejpam-5687	35	18	25	25	NUM
ejpam-5687	35	19	compared	compare	VERB
ejpam-5687	35	20	against	against	ADP
ejpam-5687	35	21	ordinary	ordinary	ADJ
ejpam-5687	35	22	models	model	NOUN
ejpam-5687	35	23	for	for	ADP
ejpam-5687	35	24	disease	disease	NOUN
ejpam-5687	35	25	spread	spread	VERB
ejpam-5687	35	26	within	within	ADP
ejpam-5687	35	27	community	community	NOUN
ejpam-5687	35	28	settings	setting	NOUN
ejpam-5687	35	29	;	;	PUNCT
ejpam-5687	35	30	moreover	moreover	ADV
ejpam-5687	35	31	it	it	PRON
ejpam-5687	35	32	illustrates	illustrate	VERB
ejpam-5687	35	33	better	well	ADJ
ejpam-5687	35	34	stability	stability	NOUN
ejpam-5687	35	35	and	and	CCONJ
ejpam-5687	35	36	fits	fit	VERB
ejpam-5687	35	37	actual	actual	ADJ
ejpam-5687	35	38	/	/	SYM
ejpam-5687	35	39	empirical	empirical	ADJ
ejpam-5687	35	40	facts	fact	NOUN
ejpam-5687	35	41	as	as	SCONJ
ejpam-5687	35	42	reported	report	VERB
ejpam-5687	35	43	by	by	ADP
ejpam-5687	35	44	[	[	X
ejpam-5687	35	45	13	13	NUM
ejpam-5687	35	46	]	]	PUNCT
ejpam-5687	35	47	.	.	PUNCT
ejpam-5687	36	1	in	in	ADP
ejpam-5687	36	2	[	[	X
ejpam-5687	36	3	14	14	NUM
ejpam-5687	36	4	]	]	PUNCT
ejpam-5687	36	5	,	,	PUNCT
ejpam-5687	36	6	the	the	DET
ejpam-5687	36	7	authors	author	NOUN
ejpam-5687	36	8	utilized	utilize	VERB
ejpam-5687	36	9	a	a	DET
ejpam-5687	36	10	fractional	fractional	ADJ
ejpam-5687	36	11	-	-	PUNCT
ejpam-5687	36	12	order	order	NOUN
ejpam-5687	36	13	caputo	caputo	PROPN
ejpam-5687	36	14	-	-	PUNCT
ejpam-5687	36	15	fabrizio	fabrizio	PROPN
ejpam-5687	36	16	operator	operator	NOUN
ejpam-5687	36	17	for	for	ADP
ejpam-5687	36	18	the	the	DET
ejpam-5687	36	19	modeling	modeling	NOUN
ejpam-5687	36	20	of	of	ADP
ejpam-5687	36	21	covid-19	covid-19	PROPN
ejpam-5687	36	22	spread	spread	NOUN
ejpam-5687	36	23	;	;	PUNCT
ejpam-5687	36	24	it	it	PRON
ejpam-5687	36	25	is	be	AUX
ejpam-5687	36	26	shown	show	VERB
ejpam-5687	36	27	to	to	PART
ejpam-5687	36	28	provide	provide	VERB
ejpam-5687	36	29	better	well	ADJ
ejpam-5687	36	30	descriptions	description	NOUN
ejpam-5687	36	31	of	of	ADP
ejpam-5687	36	32	disease	disease	NOUN
ejpam-5687	36	33	dynamics	dynamic	NOUN
ejpam-5687	36	34	than	than	ADP
ejpam-5687	36	35	those	those	PRON
ejpam-5687	36	36	obtained	obtain	VERB
ejpam-5687	36	37	through	through	ADP
ejpam-5687	36	38	using	use	VERB
ejpam-5687	36	39	integer	integer	NOUN
ejpam-5687	36	40	-	-	PUNCT
ejpam-5687	36	41	order	order	NOUN
ejpam-5687	36	42	models	model	NOUN
ejpam-5687	36	43	.	.	PUNCT
ejpam-5687	37	1	it	it	PRON
ejpam-5687	37	2	improves	improve	VERB
ejpam-5687	37	3	comprehension	comprehension	NOUN
ejpam-5687	37	4	regarding	regard	VERB
ejpam-5687	37	5	how	how	SCONJ
ejpam-5687	37	6	covid-19	covid-19	PROPN
ejpam-5687	37	7	evolves	evolve	VERB
ejpam-5687	37	8	while	while	SCONJ
ejpam-5687	37	9	facilitating	facilitate	VERB
ejpam-5687	37	10	for	for	ADP
ejpam-5687	37	11	better	well	ADJ
ejpam-5687	37	12	policies	policy	NOUN
ejpam-5687	37	13	aimed	aim	VERB
ejpam-5687	37	14	at	at	ADP
ejpam-5687	37	15	curbing	curb	VERB
ejpam-5687	37	16	its	its	PRON
ejpam-5687	37	17	spread	spread	NOUN
ejpam-5687	37	18	.	.	PUNCT
ejpam-5687	38	1	in	in	ADP
ejpam-5687	38	2	[	[	X
ejpam-5687	38	3	15	15	NUM
ejpam-5687	38	4	]	]	PUNCT
ejpam-5687	38	5	created	create	VERB
ejpam-5687	38	6	a	a	DET
ejpam-5687	38	7	broad	broad	ADJ
ejpam-5687	38	8	similitude	similitude	NOUN
ejpam-5687	38	9	model	model	NOUN
ejpam-5687	38	10	of	of	ADP
ejpam-5687	38	11	a	a	DET
ejpam-5687	38	12	fractional	fractional	ADJ
ejpam-5687	38	13	-	-	PUNCT
ejpam-5687	38	14	order	order	NOUN
ejpam-5687	38	15	boost	boost	NOUN
ejpam-5687	38	16	converter	converter	NOUN
ejpam-5687	38	17	applying	apply	VERB
ejpam-5687	38	18	the	the	DET
ejpam-5687	38	19	caputo	caputo	PROPN
ejpam-5687	38	20	-	-	PUNCT
ejpam-5687	38	21	fabrizio	fabrizio	PROPN
ejpam-5687	38	22	principle	principle	NOUN
ejpam-5687	38	23	in	in	ADP
ejpam-5687	38	24	governing	govern	VERB
ejpam-5687	38	25	its	its	PRON
ejpam-5687	38	26	system	system	NOUN
ejpam-5687	38	27	of	of	ADP
ejpam-5687	38	28	operation	operation	NOUN
ejpam-5687	38	29	;	;	PUNCT
ejpam-5687	38	30	this	this	PRON
ejpam-5687	38	31	has	have	AUX
ejpam-5687	38	32	also	also	ADV
ejpam-5687	38	33	led	lead	VERB
ejpam-5687	38	34	to	to	ADP
ejpam-5687	38	35	improvement	improvement	NOUN
ejpam-5687	38	36	thereof	thereof	ADV
ejpam-5687	38	37	by	by	ADP
ejpam-5687	38	38	analysing	analyse	VERB
ejpam-5687	38	39	its	its	PRON
ejpam-5687	38	40	effectiveness	effectiveness	NOUN
ejpam-5687	38	41	and	and	CCONJ
ejpam-5687	38	42	possible	possible	ADJ
ejpam-5687	38	43	ways	way	NOUN
ejpam-5687	38	44	of	of	ADP
ejpam-5687	38	45	operation	operation	NOUN
ejpam-5687	38	46	with	with	ADP
ejpam-5687	38	47	inductors	inductor	NOUN
ejpam-5687	38	48	contained	contain	VERB
ejpam-5687	38	49	therein.the	therein.the	DET
ejpam-5687	38	50	identification	identification	NOUN
ejpam-5687	38	51	of	of	ADP
ejpam-5687	38	52	key	key	ADJ
ejpam-5687	38	53	parameters	parameter	NOUN
ejpam-5687	38	54	influencing	influence	VERB
ejpam-5687	38	55	cholera	cholera	NOUN
ejpam-5687	38	56	’s	’s	PART
ejpam-5687	38	57	basic	basic	ADJ
ejpam-5687	38	58	reproduction	reproduction	NOUN
ejpam-5687	38	59	number	number	NOUN
ejpam-5687	38	60	using	use	VERB
ejpam-5687	38	61	sensitivity	sensitivity	NOUN
ejpam-5687	38	62	analysis	analysis	NOUN
ejpam-5687	38	63	could	could	AUX
ejpam-5687	38	64	assist	assist	VERB
ejpam-5687	38	65	in	in	ADP
ejpam-5687	38	66	the	the	DET
ejpam-5687	38	67	development	development	NOUN
ejpam-5687	38	68	of	of	ADP
ejpam-5687	38	69	intervention	intervention	NOUN
ejpam-5687	38	70	strategies	strategy	NOUN
ejpam-5687	38	71	that	that	PRON
ejpam-5687	38	72	are	be	AUX
ejpam-5687	38	73	more	more	ADV
ejpam-5687	38	74	effective	effective	ADJ
ejpam-5687	38	75	[	[	X
ejpam-5687	38	76	16	16	NUM
ejpam-5687	38	77	]	]	PUNCT
ejpam-5687	38	78	.	.	PUNCT
ejpam-5687	39	1	the	the	DET
ejpam-5687	39	2	spread	spread	NOUN
ejpam-5687	39	3	of	of	ADP
ejpam-5687	39	4	monkeypox	monkeypox	NOUN
ejpam-5687	39	5	in	in	ADP
ejpam-5687	39	6	nigeria	nigeria	PROPN
ejpam-5687	39	7	in	in	ADP
ejpam-5687	39	8	the	the	DET
ejpam-5687	39	9	time	time	NOUN
ejpam-5687	39	10	of	of	ADP
ejpam-5687	39	11	covid-19	covid-19	PROPN
ejpam-5687	39	12	was	be	AUX
ejpam-5687	39	13	examined	examine	VERB
ejpam-5687	39	14	by	by	ADP
ejpam-5687	39	15	the	the	DET
ejpam-5687	39	16	researcher	researcher	NOUN
ejpam-5687	39	17	in	in	ADP
ejpam-5687	39	18	[	[	X
ejpam-5687	39	19	17	17	NUM
ejpam-5687	39	20	]	]	PUNCT
ejpam-5687	39	21	,	,	PUNCT
ejpam-5687	39	22	where	where	SCONJ
ejpam-5687	39	23	they	they	PRON
ejpam-5687	39	24	estimated	estimate	VERB
ejpam-5687	39	25	the	the	DET
ejpam-5687	39	26	effective	effective	ADJ
ejpam-5687	39	27	reproduction	reproduction	NOUN
ejpam-5687	39	28	number	number	NOUN
ejpam-5687	39	29	r0	r0	NOUN
ejpam-5687	39	30	during	during	ADP
ejpam-5687	39	31	the	the	DET
ejpam-5687	39	32	pandemic.using	pandemic.using	ADJ
ejpam-5687	39	33	mathematical	mathematical	ADJ
ejpam-5687	39	34	modeling	modeling	NOUN
ejpam-5687	39	35	,	,	PUNCT
ejpam-5687	39	36	the	the	DET
ejpam-5687	39	37	basic	basic	ADJ
ejpam-5687	39	38	and	and	CCONJ
ejpam-5687	39	39	effective	effective	ADJ
ejpam-5687	39	40	reproduction	reproduction	NOUN
ejpam-5687	39	41	numbers	number	NOUN
ejpam-5687	39	42	of	of	ADP
ejpam-5687	39	43	ebov	ebov	NOUN
ejpam-5687	39	44	during	during	ADP
ejpam-5687	39	45	the	the	DET
ejpam-5687	39	46	2014	2014	NUM
ejpam-5687	39	47	outbreak	outbreak	NOUN
ejpam-5687	39	48	in	in	ADP
ejpam-5687	39	49	west	west	PROPN
ejpam-5687	39	50	africa	africa	PROPN
ejpam-5687	39	51	were	be	AUX
ejpam-5687	39	52	estimated	estimate	VERB
ejpam-5687	39	53	as	as	ADP
ejpam-5687	39	54	in	in	ADP
ejpam-5687	39	55	[	[	X
ejpam-5687	39	56	18	18	NUM
ejpam-5687	39	57	]	]	PUNCT
ejpam-5687	39	58	.	.	PUNCT
ejpam-5687	40	1	in	in	ADP
ejpam-5687	40	2	[	[	X
ejpam-5687	40	3	19	19	NUM
ejpam-5687	40	4	]	]	PUNCT
ejpam-5687	40	5	the	the	DET
ejpam-5687	40	6	transmission	transmission	NOUN
ejpam-5687	40	7	dynamics	dynamic	NOUN
ejpam-5687	40	8	of	of	ADP
ejpam-5687	40	9	ebola	ebola	PROPN
ejpam-5687	40	10	virus	virus	NOUN
ejpam-5687	40	11	using	use	VERB
ejpam-5687	40	12	a	a	DET
ejpam-5687	40	13	caputo	caputo	PROPN
ejpam-5687	40	14	fractional	fractional	PROPN
ejpam-5687	40	15	derivative	derivative	ADJ
ejpam-5687	40	16	model	model	NOUN
ejpam-5687	40	17	are	be	AUX
ejpam-5687	40	18	examined	examine	VERB
ejpam-5687	40	19	,	,	PUNCT
ejpam-5687	40	20	thus	thus	ADV
ejpam-5687	40	21	emphasizing	emphasize	VERB
ejpam-5687	40	22	its	its	PRON
ejpam-5687	40	23	important	important	ADJ
ejpam-5687	40	24	parameters	parameter	NOUN
ejpam-5687	40	25	like	like	ADP
ejpam-5687	40	26	sensitivity	sensitivity	NOUN
ejpam-5687	40	27	for	for	ADP
ejpam-5687	40	28	effective	effective	ADJ
ejpam-5687	40	29	control	control	NOUN
ejpam-5687	40	30	strategies.the	strategies.the	DET
ejpam-5687	40	31	article	article	NOUN
ejpam-5687	40	32	[	[	X
ejpam-5687	40	33	20	20	NUM
ejpam-5687	40	34	]	]	PUNCT
ejpam-5687	40	35	examines	examine	VERB
ejpam-5687	40	36	issues	issue	NOUN
ejpam-5687	40	37	of	of	ADP
ejpam-5687	40	38	the	the	DET
ejpam-5687	40	39	existence	existence	NOUN
ejpam-5687	40	40	of	of	ADP
ejpam-5687	40	41	solutions	solution	NOUN
ejpam-5687	40	42	in	in	ADP
ejpam-5687	40	43	fractional	fractional	ADJ
ejpam-5687	40	44	differential	differential	ADJ
ejpam-5687	40	45	equations	equation	NOUN
ejpam-5687	40	46	,	,	PUNCT
ejpam-5687	40	47	providing	provide	VERB
ejpam-5687	40	48	a	a	DET
ejpam-5687	40	49	number	number	NOUN
ejpam-5687	40	50	of	of	ADP
ejpam-5687	40	51	basic	basic	ADJ
ejpam-5687	40	52	theorems	theorem	NOUN
ejpam-5687	40	53	that	that	PRON
ejpam-5687	40	54	underlie	underlie	VERB
ejpam-5687	40	55	these	these	DET
ejpam-5687	40	56	types	type	NOUN
ejpam-5687	40	57	of	of	ADP
ejpam-5687	40	58	problems	problem	NOUN
ejpam-5687	40	59	.	.	PUNCT
ejpam-5687	41	1	the	the	DET
ejpam-5687	41	2	authors	author	NOUN
ejpam-5687	41	3	employ	employ	VERB
ejpam-5687	41	4	fixed	fix	VERB
ejpam-5687	41	5	point	point	NOUN
ejpam-5687	41	6	theorems	theorem	NOUN
ejpam-5687	41	7	to	to	PART
ejpam-5687	41	8	achieve	achieve	VERB
ejpam-5687	41	9	these	these	DET
ejpam-5687	41	10	ends	end	NOUN
ejpam-5687	41	11	,	,	PUNCT
ejpam-5687	41	12	thereby	thereby	ADV
ejpam-5687	41	13	making	make	VERB
ejpam-5687	41	14	a	a	DET
ejpam-5687	41	15	major	major	ADJ
ejpam-5687	41	16	contribution	contribution	NOUN
ejpam-5687	41	17	to	to	ADP
ejpam-5687	41	18	the	the	DET
ejpam-5687	41	19	discipline	discipline	NOUN
ejpam-5687	41	20	of	of	ADP
ejpam-5687	41	21	fractional	fractional	ADJ
ejpam-5687	41	22	calculus	calculus	NOUN
ejpam-5687	41	23	.	.	PUNCT
ejpam-5687	42	1	the	the	DET
ejpam-5687	42	2	work	work	NOUN
ejpam-5687	42	3	in	in	ADP
ejpam-5687	42	4	[	[	X
ejpam-5687	42	5	21	21	NUM
ejpam-5687	42	6	]	]	PUNCT
ejpam-5687	42	7	examines	examine	VERB
ejpam-5687	42	8	how	how	SCONJ
ejpam-5687	42	9	diphtheria	diphtheria	NOUN
ejpam-5687	42	10	spreads	spread	VERB
ejpam-5687	42	11	in	in	ADP
ejpam-5687	42	12	populations	population	NOUN
ejpam-5687	42	13	by	by	ADP
ejpam-5687	42	14	utilizing	utilize	VERB
ejpam-5687	42	15	caputo	caputo	PROPN
ejpam-5687	42	16	fractional	fractional	ADJ
ejpam-5687	42	17	derivatives	derivative	NOUN
ejpam-5687	42	18	,	,	PUNCT
ejpam-5687	42	19	as	as	SCONJ
ejpam-5687	42	20	it	it	PRON
ejpam-5687	42	21	establishes	establish	VERB
ejpam-5687	42	22	that	that	SCONJ
ejpam-5687	42	23	fixed	fix	VERB
ejpam-5687	42	24	-	-	PUNCT
ejpam-5687	42	25	point	point	NOUN
ejpam-5687	42	26	theorems	theorem	NOUN
ejpam-5687	42	27	result	result	VERB
ejpam-5687	42	28	in	in	ADP
ejpam-5687	42	29	solutions	solution	NOUN
ejpam-5687	42	30	which	which	PRON
ejpam-5687	42	31	are	be	AUX
ejpam-5687	42	32	unique	unique	ADJ
ejpam-5687	42	33	and	and	CCONJ
ejpam-5687	42	34	existent	existent	ADJ
ejpam-5687	42	35	,	,	PUNCT
ejpam-5687	42	36	and	and	CCONJ
ejpam-5687	42	37	in	in	ADP
ejpam-5687	42	38	addition	addition	NOUN
ejpam-5687	42	39	carries	carry	VERB
ejpam-5687	42	40	sensitivity	sensitivity	NOUN
ejpam-5687	42	41	analysis	analysis	NOUN
ejpam-5687	42	42	to	to	PART
ejpam-5687	42	43	comprehend	comprehend	VERB
ejpam-5687	42	44	the	the	DET
ejpam-5687	42	45	parameters	parameter	NOUN
ejpam-5687	42	46	effects	effect	NOUN
ejpam-5687	42	47	towards	towards	ADP
ejpam-5687	42	48	this	this	DET
ejpam-5687	42	49	model.a	model.a	ADJ
ejpam-5687	42	50	fractional	fractional	ADJ
ejpam-5687	42	51	-	-	PUNCT
ejpam-5687	42	52	order	order	NOUN
ejpam-5687	42	53	caputo	caputo	NOUN
ejpam-5687	42	54	operator	operator	NOUN
ejpam-5687	42	55	is	be	AUX
ejpam-5687	42	56	used	use	VERB
ejpam-5687	42	57	in	in	ADP
ejpam-5687	42	58	this	this	DET
ejpam-5687	42	59	study	study	NOUN
ejpam-5687	42	60	to	to	PART
ejpam-5687	42	61	model	model	VERB
ejpam-5687	42	62	the	the	DET
ejpam-5687	42	63	covid-19	covid-19	PROPN
ejpam-5687	42	64	transmission	transmission	NOUN
ejpam-5687	42	65	dynamics	dynamic	NOUN
ejpam-5687	42	66	such	such	ADJ
ejpam-5687	42	67	that	that	SCONJ
ejpam-5687	42	68	both	both	CCONJ
ejpam-5687	42	69	asymptomatic	asymptomatic	ADJ
ejpam-5687	42	70	and	and	CCONJ
ejpam-5687	42	71	symptomatic	symptomatic	ADJ
ejpam-5687	42	72	cases	case	NOUN
ejpam-5687	42	73	can	can	AUX
ejpam-5687	42	74	be	be	AUX
ejpam-5687	42	75	effectively	effectively	ADV
ejpam-5687	42	76	captured	capture	VERB
ejpam-5687	42	77	leading	lead	VERB
ejpam-5687	42	78	to	to	ADP
ejpam-5687	42	79	enhanced	enhanced	ADJ
ejpam-5687	42	80	accuracy[22	accuracy[22	ADP
ejpam-5687	42	81	]	]	PUNCT
ejpam-5687	42	82	.	.	PUNCT
ejpam-5687	43	1	the	the	DET
ejpam-5687	43	2	article	article	NOUN
ejpam-5687	43	3	[	[	X
ejpam-5687	43	4	23	23	NUM
ejpam-5687	43	5	]	]	PUNCT
ejpam-5687	43	6	investigates	investigate	VERB
ejpam-5687	43	7	the	the	DET
ejpam-5687	43	8	role	role	NOUN
ejpam-5687	43	9	of	of	ADP
ejpam-5687	43	10	booster	booster	NOUN
ejpam-5687	43	11	vaccination	vaccination	NOUN
ejpam-5687	43	12	and	and	CCONJ
ejpam-5687	43	13	public	public	ADJ
ejpam-5687	43	14	enlightenment	enlightenment	NOUN
ejpam-5687	43	15	in	in	ADP
ejpam-5687	43	16	tackling	tackle	VERB
ejpam-5687	43	17	infectious	infectious	ADJ
ejpam-5687	43	18	diseases	disease	NOUN
ejpam-5687	43	19	using	use	VERB
ejpam-5687	43	20	a	a	DET
ejpam-5687	43	21	fractional	fractional	ADJ
ejpam-5687	43	22	-	-	PUNCT
ejpam-5687	43	23	order	order	NOUN
ejpam-5687	43	24	epidemic	epidemic	NOUN
ejpam-5687	43	25	model	model	NOUN
ejpam-5687	43	26	(	(	PUNCT
ejpam-5687	43	27	foem	foem	NOUN
ejpam-5687	43	28	)	)	PUNCT
ejpam-5687	43	29	.	.	PUNCT
ejpam-5687	44	1	the	the	DET
ejpam-5687	44	2	necessity	necessity	NOUN
ejpam-5687	44	3	of	of	ADP
ejpam-5687	44	4	booster	booster	NOUN
ejpam-5687	44	5	doses	dose	NOUN
ejpam-5687	44	6	and	and	CCONJ
ejpam-5687	44	7	continuous	continuous	ADJ
ejpam-5687	44	8	awareness	awareness	NOUN
ejpam-5687	44	9	programs	program	NOUN
ejpam-5687	44	10	in	in	ADP
ejpam-5687	44	11	order	order	NOUN
ejpam-5687	44	12	to	to	PART
ejpam-5687	44	13	successfully	successfully	ADV
ejpam-5687	44	14	curb	curb	VERB
ejpam-5687	44	15	outbreaks	outbreak	NOUN
ejpam-5687	44	16	is	be	AUX
ejpam-5687	44	17	underscored	underscore	VERB
ejpam-5687	44	18	by	by	ADP
ejpam-5687	44	19	the	the	DET
ejpam-5687	44	20	model	model	NOUN
ejpam-5687	44	21	that	that	PRON
ejpam-5687	44	22	shows	show	VERB
ejpam-5687	44	23	that	that	SCONJ
ejpam-5687	44	24	even	even	ADV
ejpam-5687	44	25	those	those	PRON
ejpam-5687	44	26	who	who	PRON
ejpam-5687	44	27	have	have	AUX
ejpam-5687	44	28	been	be	AUX
ejpam-5687	44	29	vaccinated	vaccinate	VERB
ejpam-5687	44	30	can	can	AUX
ejpam-5687	44	31	have	have	VERB
ejpam-5687	44	32	the	the	DET
ejpam-5687	44	33	disease	disease	NOUN
ejpam-5687	44	34	.	.	PUNCT
ejpam-5687	45	1	this	this	DET
ejpam-5687	45	2	research	research	NOUN
ejpam-5687	45	3	delves	delve	VERB
ejpam-5687	45	4	into	into	ADP
ejpam-5687	45	5	the	the	DET
ejpam-5687	45	6	study	study	NOUN
ejpam-5687	45	7	of	of	ADP
ejpam-5687	45	8	that	that	DET
ejpam-5687	45	9	pine	pine	ADJ
ejpam-5687	45	10	wilt	wilt	NOUN
ejpam-5687	45	11	disease	disease	NOUN
ejpam-5687	45	12	is	be	AUX
ejpam-5687	45	13	transmitted	transmit	VERB
ejpam-5687	45	14	with	with	ADP
ejpam-5687	45	15	help	help	NOUN
ejpam-5687	45	16	from	from	ADP
ejpam-5687	45	17	a	a	DET
ejpam-5687	45	18	fractional	fractional	ADJ
ejpam-5687	45	19	derivative	derivative	NOUN
ejpam-5687	45	20	by	by	ADP
ejpam-5687	45	21	caputo	caputo	PROPN
ejpam-5687	45	22	.	.	PUNCT
ejpam-5687	46	1	the	the	DET
ejpam-5687	46	2	main	main	ADJ
ejpam-5687	46	3	goal	goal	NOUN
ejpam-5687	46	4	of	of	ADP
ejpam-5687	46	5	this	this	DET
ejpam-5687	46	6	model	model	NOUN
ejpam-5687	46	7	is	be	AUX
ejpam-5687	46	8	to	to	PART
ejpam-5687	46	9	give	give	VERB
ejpam-5687	46	10	insight	insight	NOUN
ejpam-5687	46	11	that	that	SCONJ
ejpam-5687	46	12	the	the	DET
ejpam-5687	46	13	disease	disease	NOUN
ejpam-5687	46	14	can	can	AUX
ejpam-5687	46	15	spread	spread	VERB
ejpam-5687	46	16	across	across	ADP
ejpam-5687	46	17	different	different	ADJ
ejpam-5687	46	18	communities	community	NOUN
ejpam-5687	46	19	while	while	SCONJ
ejpam-5687	46	20	helping	helping	AUX
ejpam-5687	46	21	predict	predict	VERB
ejpam-5687	46	22	what	what	PRON
ejpam-5687	46	23	is	be	AUX
ejpam-5687	46	24	likely	likely	ADV
ejpam-5687	46	25	going	go	VERB
ejpam-5687	46	26	to	to	PART
ejpam-5687	46	27	happen	happen	VERB
ejpam-5687	46	28	next	next	ADV
ejpam-5687	46	29	as	as	ADV
ejpam-5687	46	30	well	well	ADV
ejpam-5687	46	31	as	as	ADP
ejpam-5687	46	32	coming	come	VERB
ejpam-5687	46	33	up	up	ADP
ejpam-5687	46	34	with	with	ADP
ejpam-5687	46	35	appropriate	appropriate	ADJ
ejpam-5687	46	36	measures	measure	NOUN
ejpam-5687	46	37	for	for	ADP
ejpam-5687	46	38	its	its	PRON
ejpam-5687	46	39	containment	containment	NOUN
ejpam-5687	46	40	by	by	ADP
ejpam-5687	46	41	using	use	VERB
ejpam-5687	46	42	fractional	fractional	ADJ
ejpam-5687	46	43	calculus	calculus	NOUN
ejpam-5687	46	44	methods	method	NOUN
ejpam-5687	46	45	that	that	PRON
ejpam-5687	46	46	are	be	AUX
ejpam-5687	46	47	more	more	ADV
ejpam-5687	46	48	efficient	efficient	ADJ
ejpam-5687	46	49	in	in	ADP
ejpam-5687	46	50	representing	represent	VERB
ejpam-5687	46	51	memory	memory	NOUN
ejpam-5687	46	52	and	and	CCONJ
ejpam-5687	46	53	hereditary	hereditary	ADJ
ejpam-5687	46	54	tendencies	tendency	NOUN
ejpam-5687	46	55	during	during	ADP
ejpam-5687	46	56	its	its	PRON
ejpam-5687	46	57	transmission	transmission	NOUN
ejpam-5687	46	58	[	[	X
ejpam-5687	46	59	24	24	NUM
ejpam-5687	46	60	]	]	PUNCT
ejpam-5687	46	61	.	.	PUNCT
ejpam-5687	47	1	caputo	caputo	PROPN
ejpam-5687	47	2	derivatives	derivative	NOUN
ejpam-5687	47	3	in	in	ADP
ejpam-5687	47	4	fractional	fractional	ADJ
ejpam-5687	47	5	-	-	PUNCT
ejpam-5687	47	6	order	order	NOUN
ejpam-5687	47	7	epidemiological	epidemiological	ADJ
ejpam-5687	47	8	models	model	NOUN
ejpam-5687	47	9	help	help	VERB
ejpam-5687	47	10	remember	remember	VERB
ejpam-5687	47	11	that	that	SCONJ
ejpam-5687	47	12	covid-19	covid-19	PROPN
ejpam-5687	47	13	spreads	spread	VERB
ejpam-5687	47	14	remotely[25	remotely[25	NOUN
ejpam-5687	47	15	]	]	PUNCT
ejpam-5687	47	16	.	.	PUNCT
ejpam-5687	48	1	the	the	DET
ejpam-5687	48	2	caputo	caputo	PROPN
ejpam-5687	48	3	hiv	hiv	PROPN
ejpam-5687	48	4	and	and	CCONJ
ejpam-5687	48	5	malaria	malaria	PROPN
ejpam-5687	48	6	co	co	NOUN
ejpam-5687	48	7	-	-	ADJ
ejpam-5687	48	8	infection	infection	ADJ
ejpam-5687	48	9	model	model	NOUN
ejpam-5687	48	10	applies	apply	VERB
ejpam-5687	48	11	fractional	fractional	ADJ
ejpam-5687	48	12	-	-	PUNCT
ejpam-5687	48	13	order	order	NOUN
ejpam-5687	48	14	derivatives	derivative	NOUN
ejpam-5687	48	15	to	to	PART
ejpam-5687	48	16	appropriately	appropriately	ADV
ejpam-5687	48	17	mimic	mimic	VERB
ejpam-5687	48	18	these	these	DET
ejpam-5687	48	19	diseases	disease	NOUN
ejpam-5687	48	20	dynamics	dynamic	NOUN
ejpam-5687	48	21	and	and	CCONJ
ejpam-5687	48	22	relationships[26	relationships[26	NOUN
ejpam-5687	48	23	]	]	PUNCT
ejpam-5687	48	24	.	.	PUNCT
ejpam-5687	49	1	investigating	investigate	VERB
ejpam-5687	49	2	rumor	rumor	NOUN
ejpam-5687	49	3	spread	spread	NOUN
ejpam-5687	49	4	model	model	NOUN
ejpam-5687	49	5	dynamics	dynamic	NOUN
ejpam-5687	49	6	with	with	ADP
ejpam-5687	49	7	fractional	fractional	ADJ
ejpam-5687	49	8	piecewise	piecewise	NOUN
ejpam-5687	49	9	derivative[27	derivative[27	NOUN
ejpam-5687	49	10	]	]	PUNCT
ejpam-5687	49	11	.	.	PUNCT
ejpam-5687	50	1	epidemic	epidemic	NOUN
ejpam-5687	50	2	models	model	NOUN
ejpam-5687	50	3	in	in	ADP
ejpam-5687	50	4	fractions	fraction	NOUN
ejpam-5687	50	5	are	be	AUX
ejpam-5687	50	6	a	a	DET
ejpam-5687	50	7	way	way	NOUN
ejpam-5687	50	8	of	of	ADP
ejpam-5687	50	9	using	use	VERB
ejpam-5687	50	10	half	half	ADJ
ejpam-5687	50	11	calculus	calculus	NOUN
ejpam-5687	50	12	to	to	PART
ejpam-5687	50	13	explain	explain	VERB
ejpam-5687	50	14	better	well	ADV
ejpam-5687	50	15	how	how	SCONJ
ejpam-5687	50	16	certain	certain	ADJ
ejpam-5687	50	17	diseases	disease	NOUN
ejpam-5687	50	18	,	,	PUNCT
ejpam-5687	50	19	which	which	PRON
ejpam-5687	50	20	are	be	AUX
ejpam-5687	50	21	contagious	contagious	ADJ
ejpam-5687	50	22	spread	spread	NOUN
ejpam-5687	50	23	,	,	PUNCT
ejpam-5687	50	24	n.	n.	PROPN
ejpam-5687	50	25	ullah	ullah	PROPN
ejpam-5687	50	26	et	et	PROPN
ejpam-5687	50	27	al	al	PROPN
ejpam-5687	50	28	.	.	PUNCT
ejpam-5687	50	29	/	/	SYM
ejpam-5687	50	30	eur	eur	PROPN
ejpam-5687	50	31	.	.	PUNCT
ejpam-5687	51	1	j.	j.	PROPN
ejpam-5687	51	2	pure	pure	PROPN
ejpam-5687	51	3	appl	appl	PROPN
ejpam-5687	51	4	.	.	PROPN
ejpam-5687	51	5	math	math	PROPN
ejpam-5687	51	6	,	,	PUNCT
ejpam-5687	51	7	18	18	NUM
ejpam-5687	51	8	(	(	PUNCT
ejpam-5687	51	9	2	2	NUM
ejpam-5687	51	10	)	)	PUNCT
ejpam-5687	51	11	(	(	PUNCT
ejpam-5687	51	12	2025	2025	NUM
ejpam-5687	51	13	)	)	PUNCT
ejpam-5687	51	14	,	,	PUNCT
ejpam-5687	51	15	5687	5687	NUM
ejpam-5687	51	16	4	4	NUM
ejpam-5687	51	17	of	of	ADP
ejpam-5687	51	18	25	25	NUM
ejpam-5687	51	19	accounting	account	VERB
ejpam-5687	51	20	for	for	ADP
ejpam-5687	51	21	those	those	DET
ejpam-5687	51	22	times	time	NOUN
ejpam-5687	51	23	-	-	PUNCT
ejpam-5687	51	24	past	past	ADJ
ejpam-5687	51	25	effect	effect	NOUN
ejpam-5687	51	26	and	and	CCONJ
ejpam-5687	51	27	difference	difference	NOUN
ejpam-5687	51	28	in	in	ADP
ejpam-5687	51	29	population	population	NOUN
ejpam-5687	51	30	with	with	ADP
ejpam-5687	51	31	different	different	ADJ
ejpam-5687	51	32	hosts	host	NOUN
ejpam-5687	51	33	[	[	X
ejpam-5687	51	34	28	28	NUM
ejpam-5687	51	35	]	]	PUNCT
ejpam-5687	51	36	.	.	PUNCT
ejpam-5687	52	1	while	while	SCONJ
ejpam-5687	52	2	not	not	PART
ejpam-5687	52	3	all	all	DET
ejpam-5687	52	4	patients	patient	NOUN
ejpam-5687	52	5	receiving	receive	VERB
ejpam-5687	52	6	antibiotic	antibiotic	ADJ
ejpam-5687	52	7	therapy	therapy	NOUN
ejpam-5687	52	8	develop	develop	VERB
ejpam-5687	52	9	diarrhea	diarrhea	NOUN
ejpam-5687	52	10	,	,	PUNCT
ejpam-5687	52	11	ha	ha	INTJ
ejpam-5687	52	12	cdi	cdi	PROPN
ejpam-5687	52	13	is	be	AUX
ejpam-5687	52	14	an	an	DET
ejpam-5687	52	15	important	important	ADJ
ejpam-5687	52	16	and	and	CCONJ
ejpam-5687	52	17	potentially	potentially	ADV
ejpam-5687	52	18	devastating	devastating	ADJ
ejpam-5687	52	19	complication	complication	NOUN
ejpam-5687	52	20	in	in	ADP
ejpam-5687	52	21	hospitalized	hospitalize	VERB
ejpam-5687	52	22	patients	patient	NOUN
ejpam-5687	52	23	who	who	PRON
ejpam-5687	52	24	require	require	VERB
ejpam-5687	52	25	post	post	ADJ
ejpam-5687	52	26	-	-	ADJ
ejpam-5687	52	27	treatment	treatment	NOUN
ejpam-5687	52	28	follow	follow	VERB
ejpam-5687	52	29	up	up	ADP
ejpam-5687	52	30	and	and	CCONJ
ejpam-5687	52	31	therapy[29	therapy[29	NOUN
ejpam-5687	52	32	]	]	X
ejpam-5687	52	33	.	.	PUNCT
ejpam-5687	53	1	since	since	SCONJ
ejpam-5687	53	2	each	each	DET
ejpam-5687	53	3	patient	patient	NOUN
ejpam-5687	53	4	has	have	VERB
ejpam-5687	53	5	their	their	PRON
ejpam-5687	53	6	own	own	ADJ
ejpam-5687	53	7	differences	difference	NOUN
ejpam-5687	53	8	,	,	PUNCT
ejpam-5687	53	9	it	it	PRON
ejpam-5687	53	10	is	be	AUX
ejpam-5687	53	11	a	a	DET
ejpam-5687	53	12	good	good	ADJ
ejpam-5687	53	13	idea	idea	NOUN
ejpam-5687	53	14	to	to	PART
ejpam-5687	53	15	analyze	analyze	VERB
ejpam-5687	53	16	the	the	DET
ejpam-5687	53	17	individual	individual	ADJ
ejpam-5687	53	18	condition	condition	NOUN
ejpam-5687	53	19	study	study	NOUN
ejpam-5687	53	20	and	and	CCONJ
ejpam-5687	53	21	find	find	VERB
ejpam-5687	53	22	the	the	DET
ejpam-5687	53	23	proper	proper	ADJ
ejpam-5687	53	24	method	method	NOUN
ejpam-5687	53	25	for	for	ADP
ejpam-5687	53	26	each	each	DET
ejpam-5687	53	27	patient	patient	NOUN
ejpam-5687	53	28	.	.	PUNCT
ejpam-5687	54	1	the	the	DET
ejpam-5687	54	2	treatment	treatment	NOUN
ejpam-5687	54	3	plan	plan	NOUN
ejpam-5687	54	4	can	can	AUX
ejpam-5687	54	5	be	be	AUX
ejpam-5687	54	6	tailored	tailor	VERB
ejpam-5687	54	7	best	well	ADV
ejpam-5687	54	8	based	base	VERB
ejpam-5687	54	9	on	on	ADP
ejpam-5687	54	10	the	the	DET
ejpam-5687	54	11	factors	factor	NOUN
ejpam-5687	54	12	[	[	X
ejpam-5687	54	13	size	size	NOUN
ejpam-5687	54	14	,	,	PUNCT
ejpam-5687	54	15	type	type	NOUN
ejpam-5687	54	16	]	]	PUNCT
ejpam-5687	54	17	and	and	CCONJ
ejpam-5687	54	18	recovery	recovery	NOUN
ejpam-5687	54	19	time	time	NOUN
ejpam-5687	54	20	patient	patient	NOUN
ejpam-5687	54	21	is	be	AUX
ejpam-5687	54	22	expected	expect	VERB
ejpam-5687	54	23	to	to	PART
ejpam-5687	54	24	have	have	VERB
ejpam-5687	54	25	before	before	ADP
ejpam-5687	54	26	suggesting	suggest	VERB
ejpam-5687	54	27	the	the	DET
ejpam-5687	54	28	treatment	treatment	NOUN
ejpam-5687	54	29	plan	plan	NOUN
ejpam-5687	54	30	.	.	PUNCT
ejpam-5687	55	1	the	the	DET
ejpam-5687	55	2	effective	effective	ADJ
ejpam-5687	55	3	outcome	outcome	NOUN
ejpam-5687	55	4	and	and	CCONJ
ejpam-5687	55	5	fast	fast	ADJ
ejpam-5687	55	6	recovery	recovery	NOUN
ejpam-5687	55	7	can	can	AUX
ejpam-5687	55	8	be	be	AUX
ejpam-5687	55	9	improved	improve	VERB
ejpam-5687	55	10	with	with	ADP
ejpam-5687	55	11	personalized	personalized	ADJ
ejpam-5687	55	12	plan	plan	NOUN
ejpam-5687	55	13	of	of	ADP
ejpam-5687	55	14	care[30	care[30	NOUN
ejpam-5687	55	15	]	]	PUNCT
ejpam-5687	55	16	.	.	PUNCT
ejpam-5687	56	1	advancing	advance	VERB
ejpam-5687	56	2	robotics	robotic	NOUN
ejpam-5687	56	3	have	have	AUX
ejpam-5687	56	4	made	make	VERB
ejpam-5687	56	5	surgery	surgery	NOUN
ejpam-5687	56	6	more	more	ADV
ejpam-5687	56	7	accurate	accurate	ADJ
ejpam-5687	56	8	,	,	PUNCT
ejpam-5687	56	9	but	but	CCONJ
ejpam-5687	56	10	because	because	SCONJ
ejpam-5687	56	11	of	of	ADP
ejpam-5687	56	12	their	their	PRON
ejpam-5687	56	13	prices	price	NOUN
ejpam-5687	56	14	,	,	PUNCT
ejpam-5687	56	15	which	which	PRON
ejpam-5687	56	16	are	be	AUX
ejpam-5687	56	17	prohibitively	prohibitively	ADV
ejpam-5687	56	18	expensive	expensive	ADJ
ejpam-5687	56	19	compared	compare	VERB
ejpam-5687	56	20	to	to	ADP
ejpam-5687	56	21	laparoscopy	laparoscopy	VERB
ejpam-5687	56	22	,	,	PUNCT
ejpam-5687	56	23	the	the	DET
ejpam-5687	56	24	future	future	NOUN
ejpam-5687	56	25	of	of	ADP
ejpam-5687	56	26	surgery	surgery	NOUN
ejpam-5687	56	27	is	be	AUX
ejpam-5687	56	28	these	these	DET
ejpam-5687	56	29	advancements	advancement	NOUN
ejpam-5687	56	30	.	.	PUNCT
ejpam-5687	57	1	however	however	ADV
ejpam-5687	57	2	,	,	PUNCT
ejpam-5687	57	3	robotic	robotic	ADJ
ejpam-5687	57	4	surgery	surgery	NOUN
ejpam-5687	57	5	is	be	AUX
ejpam-5687	57	6	now	now	ADV
ejpam-5687	57	7	being	be	AUX
ejpam-5687	57	8	used	use	VERB
ejpam-5687	57	9	more	more	ADV
ejpam-5687	57	10	often	often	ADV
ejpam-5687	57	11	because	because	SCONJ
ejpam-5687	57	12	of	of	ADP
ejpam-5687	57	13	its	its	PRON
ejpam-5687	57	14	advantages	advantage	NOUN
ejpam-5687	57	15	and	and	CCONJ
ejpam-5687	57	16	we	we	PRON
ejpam-5687	57	17	know	know	VERB
ejpam-5687	57	18	that	that	SCONJ
ejpam-5687	57	19	there	there	PRON
ejpam-5687	57	20	are	be	VERB
ejpam-5687	57	21	benefits	benefit	NOUN
ejpam-5687	57	22	to	to	ADP
ejpam-5687	57	23	the	the	DET
ejpam-5687	57	24	practice	practice	NOUN
ejpam-5687	57	25	,	,	PUNCT
ejpam-5687	57	26	such	such	ADJ
ejpam-5687	57	27	as	as	ADP
ejpam-5687	57	28	using	use	VERB
ejpam-5687	57	29	ultrasound	ultrasound	NOUN
ejpam-5687	57	30	with	with	ADP
ejpam-5687	57	31	contrast	contrast	NOUN
ejpam-5687	57	32	agents	agent	NOUN
ejpam-5687	57	33	during	during	ADP
ejpam-5687	57	34	inoperative	inoperative	ADJ
ejpam-5687	57	35	.	.	PUNCT
ejpam-5687	58	1	these	these	PRON
ejpam-5687	58	2	have	have	AUX
ejpam-5687	58	3	been	be	AUX
ejpam-5687	58	4	followed	follow	VERB
ejpam-5687	58	5	by	by	ADP
ejpam-5687	58	6	many	many	ADJ
ejpam-5687	58	7	novel	novel	NOUN
ejpam-5687	58	8	developed	develop	VERB
ejpam-5687	58	9	surgical	surgical	ADJ
ejpam-5687	58	10	approach	approach	NOUN
ejpam-5687	58	11	allowed	allow	VERB
ejpam-5687	58	12	surgical	surgical	ADJ
ejpam-5687	58	13	outcome	outcome	NOUN
ejpam-5687	58	14	to	to	PART
ejpam-5687	58	15	be	be	AUX
ejpam-5687	58	16	improved[31	improved[31	NOUN
ejpam-5687	58	17	]	]	X
ejpam-5687	58	18	.	.	PUNCT
ejpam-5687	59	1	the	the	DET
ejpam-5687	59	2	factors	factor	NOUN
ejpam-5687	59	3	to	to	PART
ejpam-5687	59	4	consider	consider	VERB
ejpam-5687	59	5	for	for	ADP
ejpam-5687	59	6	selection	selection	NOUN
ejpam-5687	59	7	of	of	ADP
ejpam-5687	59	8	the	the	DET
ejpam-5687	59	9	best	good	ADJ
ejpam-5687	59	10	treatment	treatment	NOUN
ejpam-5687	59	11	approach	approach	NOUN
ejpam-5687	59	12	include	include	VERB
ejpam-5687	59	13	the	the	DET
ejpam-5687	59	14	physician	physician	NOUN
ejpam-5687	59	15	’s	’s	PART
ejpam-5687	59	16	experience	experience	NOUN
ejpam-5687	59	17	,	,	PUNCT
ejpam-5687	59	18	patient	patient	NOUN
ejpam-5687	59	19	’s	’s	PART
ejpam-5687	59	20	characteristics	characteristic	NOUN
ejpam-5687	59	21	and	and	CCONJ
ejpam-5687	59	22	preference[32	preference[32	NOUN
ejpam-5687	59	23	]	]	PUNCT
ejpam-5687	59	24	.	.	PUNCT
ejpam-5687	60	1	the	the	DET
ejpam-5687	60	2	importance	importance	NOUN
ejpam-5687	60	3	of	of	ADP
ejpam-5687	60	4	fractional	fractional	ADJ
ejpam-5687	60	5	epidemic	epidemic	NOUN
ejpam-5687	60	6	models	model	NOUN
ejpam-5687	60	7	lies	lie	VERB
ejpam-5687	60	8	in	in	ADP
ejpam-5687	60	9	their	their	PRON
ejpam-5687	60	10	ability	ability	NOUN
ejpam-5687	60	11	to	to	PART
ejpam-5687	60	12	generalize	generalize	VERB
ejpam-5687	60	13	traditional	traditional	ADJ
ejpam-5687	60	14	approaches	approach	NOUN
ejpam-5687	60	15	,	,	PUNCT
ejpam-5687	60	16	offering	offer	VERB
ejpam-5687	60	17	greater	great	ADJ
ejpam-5687	60	18	flexibility	flexibility	NOUN
ejpam-5687	60	19	in	in	ADP
ejpam-5687	60	20	modeling	model	VERB
ejpam-5687	60	21	various	various	ADJ
ejpam-5687	60	22	disease	disease	NOUN
ejpam-5687	60	23	scenarios	scenario	NOUN
ejpam-5687	60	24	[	[	X
ejpam-5687	60	25	33	33	NUM
ejpam-5687	60	26	,	,	PUNCT
ejpam-5687	60	27	34	34	NUM
ejpam-5687	60	28	]	]	PUNCT
ejpam-5687	60	29	.	.	PUNCT
ejpam-5687	61	1	in	in	ADP
ejpam-5687	61	2	this	this	DET
ejpam-5687	61	3	paper	paper	NOUN
ejpam-5687	61	4	,	,	PUNCT
ejpam-5687	61	5	we	we	PRON
ejpam-5687	61	6	present	present	VERB
ejpam-5687	61	7	a	a	DET
ejpam-5687	61	8	caputo	caputo	PROPN
ejpam-5687	61	9	-	-	PUNCT
ejpam-5687	61	10	fabirizo	fabirizo	ADP
ejpam-5687	61	11	fractional	fractional	ADJ
ejpam-5687	61	12	-	-	PUNCT
ejpam-5687	61	13	order	order	NOUN
ejpam-5687	61	14	vbd	vbd	NOUN
ejpam-5687	61	15	model	model	NOUN
ejpam-5687	61	16	and	and	CCONJ
ejpam-5687	61	17	conduct	conduct	VERB
ejpam-5687	61	18	supplementary	supplementary	ADJ
ejpam-5687	61	19	qualitative	qualitative	ADJ
ejpam-5687	61	20	analysis	analysis	NOUN
ejpam-5687	61	21	.	.	PUNCT
ejpam-5687	62	1	the	the	DET
ejpam-5687	62	2	effects	effect	NOUN
ejpam-5687	62	3	of	of	ADP
ejpam-5687	62	4	parameters	parameter	NOUN
ejpam-5687	62	5	associated	associate	VERB
ejpam-5687	62	6	with	with	ADP
ejpam-5687	62	7	r0	r0	NOUN
ejpam-5687	62	8	were	be	AUX
ejpam-5687	62	9	investigated	investigate	VERB
ejpam-5687	62	10	through	through	ADP
ejpam-5687	62	11	sensitivity	sensitivity	NOUN
ejpam-5687	62	12	analyses	analysis	NOUN
ejpam-5687	62	13	.	.	PUNCT
ejpam-5687	63	1	this	this	PRON
ejpam-5687	63	2	helps	helps	AUX
ejpam-5687	63	3	identify	identify	VERB
ejpam-5687	63	4	key	key	ADJ
ejpam-5687	63	5	elements	element	NOUN
ejpam-5687	63	6	of	of	ADP
ejpam-5687	63	7	the	the	DET
ejpam-5687	63	8	model	model	NOUN
ejpam-5687	63	9	that	that	PRON
ejpam-5687	63	10	should	should	AUX
ejpam-5687	63	11	be	be	AUX
ejpam-5687	63	12	targeted	target	VERB
ejpam-5687	63	13	for	for	ADP
ejpam-5687	63	14	effective	effective	ADJ
ejpam-5687	63	15	control	control	NOUN
ejpam-5687	63	16	strategies	strategy	NOUN
ejpam-5687	63	17	.	.	PUNCT
ejpam-5687	64	1	the	the	DET
ejpam-5687	64	2	theoretical	theoretical	ADJ
ejpam-5687	64	3	results	result	NOUN
ejpam-5687	64	4	of	of	ADP
ejpam-5687	64	5	the	the	DET
ejpam-5687	64	6	vector	vector	NOUN
ejpam-5687	64	7	borne	borne	NOUN
ejpam-5687	64	8	disease	disease	NOUN
ejpam-5687	64	9	model	model	NOUN
ejpam-5687	64	10	were	be	AUX
ejpam-5687	64	11	shown	show	VERB
ejpam-5687	64	12	using	use	VERB
ejpam-5687	64	13	numerical	numerical	ADJ
ejpam-5687	64	14	simulations	simulation	NOUN
ejpam-5687	64	15	,	,	PUNCT
ejpam-5687	64	16	which	which	PRON
ejpam-5687	64	17	provided	provide	VERB
ejpam-5687	64	18	information	information	NOUN
ejpam-5687	64	19	regarding	regard	VERB
ejpam-5687	64	20	the	the	DET
ejpam-5687	64	21	dynamics	dynamic	NOUN
ejpam-5687	64	22	.	.	PUNCT
ejpam-5687	65	1	moreover	moreover	ADV
ejpam-5687	65	2	,	,	PUNCT
ejpam-5687	65	3	we	we	PRON
ejpam-5687	65	4	prefer	prefer	VERB
ejpam-5687	65	5	caputo	caputo	PROPN
ejpam-5687	65	6	-	-	PUNCT
ejpam-5687	65	7	fabrizio	fabrizio	PROPN
ejpam-5687	65	8	derivatives	derivative	NOUN
ejpam-5687	65	9	to	to	ADP
ejpam-5687	65	10	integer	integer	NOUN
ejpam-5687	65	11	order	order	NOUN
ejpam-5687	65	12	derivatives	derivative	NOUN
ejpam-5687	65	13	as	as	SCONJ
ejpam-5687	65	14	described	describe	VERB
ejpam-5687	65	15	by	by	ADP
ejpam-5687	65	16	cf	cf	NOUN
ejpam-5687	65	17	derivatives	derivative	NOUN
ejpam-5687	65	18	because	because	SCONJ
ejpam-5687	65	19	they	they	PRON
ejpam-5687	65	20	address	address	VERB
ejpam-5687	65	21	real	real	ADJ
ejpam-5687	65	22	world	world	NOUN
ejpam-5687	65	23	problems	problem	NOUN
ejpam-5687	65	24	.	.	PUNCT
ejpam-5687	66	1	specifically	specifically	ADV
ejpam-5687	66	2	,	,	PUNCT
ejpam-5687	66	3	the	the	DET
ejpam-5687	66	4	equilibrium	equilibrium	NOUN
ejpam-5687	66	5	points	point	NOUN
ejpam-5687	66	6	,	,	PUNCT
ejpam-5687	66	7	r0	r0	NOUN
ejpam-5687	66	8	,	,	PUNCT
ejpam-5687	66	9	sensitivity	sensitivity	NOUN
ejpam-5687	66	10	as	as	ADV
ejpam-5687	66	11	well	well	ADV
ejpam-5687	66	12	as	as	ADP
ejpam-5687	66	13	its	its	PRON
ejpam-5687	66	14	existence	existence	NOUN
ejpam-5687	66	15	and	and	CCONJ
ejpam-5687	66	16	uniqueness	uniqueness	NOUN
ejpam-5687	66	17	are	be	AUX
ejpam-5687	66	18	the	the	DET
ejpam-5687	66	19	models	model	NOUN
ejpam-5687	66	20	under	under	ADP
ejpam-5687	66	21	consideration	consideration	NOUN
ejpam-5687	66	22	.	.	PUNCT
ejpam-5687	67	1	section	section	NOUN
ejpam-5687	67	2	2	2	NUM
ejpam-5687	67	3	deals	deal	NOUN
ejpam-5687	67	4	with	with	ADP
ejpam-5687	67	5	basics	basic	NOUN
ejpam-5687	67	6	preliminaries	preliminary	NOUN
ejpam-5687	67	7	concept	concept	NOUN
ejpam-5687	67	8	of	of	ADP
ejpam-5687	67	9	fractional	fractional	ADJ
ejpam-5687	67	10	calculus	calculus	NOUN
ejpam-5687	67	11	,	,	PUNCT
ejpam-5687	67	12	in	in	ADP
ejpam-5687	67	13	section	section	NOUN
ejpam-5687	67	14	3	3	NUM
ejpam-5687	67	15	we	we	PRON
ejpam-5687	67	16	formulated	formulate	VERB
ejpam-5687	67	17	cf	cf	NOUN
ejpam-5687	67	18	fractional	fractional	ADJ
ejpam-5687	67	19	-	-	PUNCT
ejpam-5687	67	20	order	order	NOUN
ejpam-5687	67	21	model	model	NOUN
ejpam-5687	67	22	for	for	ADP
ejpam-5687	67	23	vbd	vbd	NOUN
ejpam-5687	67	24	and	and	CCONJ
ejpam-5687	67	25	proved	prove	VERB
ejpam-5687	67	26	the	the	DET
ejpam-5687	67	27	basics	basic	NOUN
ejpam-5687	67	28	results	result	NOUN
ejpam-5687	67	29	from	from	ADP
ejpam-5687	67	30	our	our	PRON
ejpam-5687	67	31	derived	derived	ADJ
ejpam-5687	67	32	model	model	NOUN
ejpam-5687	67	33	.	.	PUNCT
ejpam-5687	68	1	whereas	whereas	SCONJ
ejpam-5687	68	2	in	in	ADP
ejpam-5687	68	3	section	section	NOUN
ejpam-5687	68	4	4	4	NUM
ejpam-5687	68	5	we	we	PRON
ejpam-5687	68	6	present	present	VERB
ejpam-5687	68	7	the	the	DET
ejpam-5687	68	8	sensitivity	sensitivity	NOUN
ejpam-5687	68	9	analysis	analysis	NOUN
ejpam-5687	68	10	.	.	PUNCT
ejpam-5687	69	1	in	in	ADP
ejpam-5687	69	2	section	section	NOUN
ejpam-5687	69	3	5	5	NUM
ejpam-5687	69	4	we	we	PRON
ejpam-5687	69	5	obtain	obtain	VERB
ejpam-5687	69	6	numerical	numerical	ADJ
ejpam-5687	69	7	simulation	simulation	NOUN
ejpam-5687	69	8	from	from	ADP
ejpam-5687	69	9	numerical	numerical	ADJ
ejpam-5687	69	10	scheme	scheme	NOUN
ejpam-5687	69	11	to	to	PART
ejpam-5687	69	12	look	look	VERB
ejpam-5687	69	13	into	into	ADP
ejpam-5687	69	14	the	the	DET
ejpam-5687	69	15	impact	impact	NOUN
ejpam-5687	69	16	of	of	ADP
ejpam-5687	69	17	various	various	ADJ
ejpam-5687	69	18	parameters	parameter	NOUN
ejpam-5687	69	19	governing	govern	VERB
ejpam-5687	69	20	the	the	PRON
ejpam-5687	69	21	in	in	ADP
ejpam-5687	69	22	the	the	DET
ejpam-5687	69	23	dynamics	dynamic	NOUN
ejpam-5687	69	24	of	of	ADP
ejpam-5687	69	25	vbd	vbd	NOUN
ejpam-5687	69	26	transmission	transmission	NOUN
ejpam-5687	69	27	,	,	PUNCT
ejpam-5687	69	28	and	and	CCONJ
ejpam-5687	69	29	finally	finally	ADV
ejpam-5687	69	30	,	,	PUNCT
ejpam-5687	69	31	there	there	PRON
ejpam-5687	69	32	is	be	VERB
ejpam-5687	69	33	the	the	DET
ejpam-5687	69	34	conclusion	conclusion	NOUN
ejpam-5687	69	35	of	of	ADP
ejpam-5687	69	36	our	our	PRON
ejpam-5687	69	37	research	research	NOUN
ejpam-5687	69	38	work	work	NOUN
ejpam-5687	69	39	.	.	PUNCT
ejpam-5687	70	1	2	2	X
ejpam-5687	70	2	.	.	X
ejpam-5687	70	3	preliminaries	preliminary	NOUN
ejpam-5687	70	4	this	this	DET
ejpam-5687	70	5	section	section	NOUN
ejpam-5687	70	6	covered	cover	VERB
ejpam-5687	70	7	some	some	PRON
ejpam-5687	70	8	of	of	ADP
ejpam-5687	70	9	the	the	DET
ejpam-5687	70	10	most	most	ADV
ejpam-5687	70	11	important	important	ADJ
ejpam-5687	70	12	theoretical	theoretical	ADJ
ejpam-5687	70	13	ideas	idea	NOUN
ejpam-5687	70	14	related	relate	VERB
ejpam-5687	70	15	to	to	ADP
ejpam-5687	70	16	fractional	fractional	ADJ
ejpam-5687	70	17	derivatives	derivative	NOUN
ejpam-5687	70	18	,	,	PUNCT
ejpam-5687	70	19	which	which	PRON
ejpam-5687	70	20	are	be	AUX
ejpam-5687	70	21	necessary	necessary	ADJ
ejpam-5687	70	22	for	for	ADP
ejpam-5687	70	23	demonstrating	demonstrate	VERB
ejpam-5687	70	24	the	the	DET
ejpam-5687	70	25	theory	theory	NOUN
ejpam-5687	70	26	analysis	analysis	NOUN
ejpam-5687	70	27	of	of	ADP
ejpam-5687	70	28	the	the	DET
ejpam-5687	70	29	model	model	NOUN
ejpam-5687	70	30	.	.	PUNCT
ejpam-5687	71	1	definition	definition	NOUN
ejpam-5687	71	2	1	1	NUM
ejpam-5687	71	3	.	.	PUNCT
ejpam-5687	72	1	[	[	X
ejpam-5687	72	2	21].the	21].the	DET
ejpam-5687	72	3	order	order	NOUN
ejpam-5687	72	4	of	of	ADP
ejpam-5687	72	5	the	the	DET
ejpam-5687	72	6	cf	cf	NOUN
ejpam-5687	72	7	fractional	fractional	ADJ
ejpam-5687	72	8	derivative	derivative	ADJ
ejpam-5687	72	9	αâ	αâ	PROPN
ejpam-5687	72	10	∈	∈	PROPN
ejpam-5687	72	11	(	(	PUNCT
ejpam-5687	72	12	0	0	NUM
ejpam-5687	72	13	,	,	PUNCT
ejpam-5687	72	14	1	1	NUM
ejpam-5687	72	15	)	)	PUNCT
ejpam-5687	72	16	is	be	AUX
ejpam-5687	72	17	equivalent	equivalent	ADJ
ejpam-5687	72	18	to	to	ADP
ejpam-5687	72	19	:	:	PUNCT
ejpam-5687	72	20	for	for	ADP
ejpam-5687	72	21	the	the	DET
ejpam-5687	72	22	function	function	NOUN
ejpam-5687	72	23	g(s	g(s	NOUN
ejpam-5687	72	24	)	)	PUNCT
ejpam-5687	72	25	cfdγg(s	cfdγg(s	NOUN
ejpam-5687	72	26	)	)	PUNCT
ejpam-5687	72	27	=	=	SYM
ejpam-5687	72	28	1	1	NUM
ejpam-5687	72	29	1−	1−	NUM
ejpam-5687	72	30	γ	γ	PROPN
ejpam-5687	72	31	∫	∫	PROPN
ejpam-5687	72	32	s	s	PART
ejpam-5687	72	33	0	0	NUM
ejpam-5687	73	1	g′(ξ)e	g′(ξ)e	PROPN
ejpam-5687	73	2	−	−	PROPN
ejpam-5687	73	3	γ	γ	X
ejpam-5687	73	4	1−γ	1−γ	NUM
ejpam-5687	73	5	(	(	PUNCT
ejpam-5687	73	6	s−ξ	s−ξ	PROPN
ejpam-5687	73	7	)	)	PUNCT
ejpam-5687	73	8	dξ	dξ	PROPN
ejpam-5687	73	9	.	.	PUNCT
ejpam-5687	74	1	(	(	PUNCT
ejpam-5687	74	2	1	1	X
ejpam-5687	74	3	)	)	PUNCT
ejpam-5687	74	4	n.	n.	PROPN
ejpam-5687	74	5	ullah	ullah	PROPN
ejpam-5687	74	6	et	et	PROPN
ejpam-5687	74	7	al	al	PROPN
ejpam-5687	74	8	.	.	PUNCT
ejpam-5687	74	9	/	/	SYM
ejpam-5687	74	10	eur	eur	PROPN
ejpam-5687	74	11	.	.	PUNCT
ejpam-5687	75	1	j.	j.	PROPN
ejpam-5687	75	2	pure	pure	PROPN
ejpam-5687	75	3	appl	appl	PROPN
ejpam-5687	75	4	.	.	PROPN
ejpam-5687	75	5	math	math	PROPN
ejpam-5687	75	6	,	,	PUNCT
ejpam-5687	75	7	18	18	NUM
ejpam-5687	75	8	(	(	PUNCT
ejpam-5687	75	9	2	2	NUM
ejpam-5687	75	10	)	)	PUNCT
ejpam-5687	75	11	(	(	PUNCT
ejpam-5687	75	12	2025	2025	NUM
ejpam-5687	75	13	)	)	PUNCT
ejpam-5687	75	14	,	,	PUNCT
ejpam-5687	75	15	5687	5687	NUM
ejpam-5687	75	16	5	5	NUM
ejpam-5687	75	17	of	of	ADP
ejpam-5687	75	18	25	25	NUM
ejpam-5687	75	19	the	the	DET
ejpam-5687	75	20	definition	definition	NOUN
ejpam-5687	75	21	includes	include	VERB
ejpam-5687	75	22	a	a	DET
ejpam-5687	75	23	non	non	ADJ
ejpam-5687	75	24	-	-	ADJ
ejpam-5687	75	25	singular	singular	ADJ
ejpam-5687	75	26	exponential	exponential	ADJ
ejpam-5687	75	27	kernel	kernel	NOUN
ejpam-5687	75	28	,	,	PUNCT
ejpam-5687	75	29	which	which	PRON
ejpam-5687	75	30	sets	set	VERB
ejpam-5687	75	31	it	it	PRON
ejpam-5687	75	32	apart	apart	ADV
ejpam-5687	75	33	from	from	ADP
ejpam-5687	75	34	traditional	traditional	ADJ
ejpam-5687	75	35	fractional	fractional	ADJ
ejpam-5687	75	36	derivatives	derivative	NOUN
ejpam-5687	75	37	,	,	PUNCT
ejpam-5687	75	38	and	and	CCONJ
ejpam-5687	75	39	singular	singular	ADJ
ejpam-5687	75	40	kernels	kernel	NOUN
ejpam-5687	75	41	are	be	AUX
ejpam-5687	75	42	typically	typically	ADV
ejpam-5687	75	43	found	find	VERB
ejpam-5687	75	44	in	in	ADP
ejpam-5687	75	45	these	these	DET
ejpam-5687	75	46	definitions	definition	NOUN
ejpam-5687	75	47	.	.	PUNCT
ejpam-5687	76	1	definition	definition	NOUN
ejpam-5687	76	2	2	2	NUM
ejpam-5687	76	3	.	.	PUNCT
ejpam-5687	76	4	a	a	DET
ejpam-5687	76	5	generalized	generalized	ADJ
ejpam-5687	76	6	form	form	NOUN
ejpam-5687	76	7	of	of	ADP
ejpam-5687	76	8	the	the	DET
ejpam-5687	76	9	caputo	caputo	PROPN
ejpam-5687	76	10	-	-	PUNCT
ejpam-5687	76	11	fabrizio	fabrizio	PROPN
ejpam-5687	76	12	fractional	fractional	ADJ
ejpam-5687	76	13	fraction	fraction	NOUN
ejpam-5687	76	14	is	be	AUX
ejpam-5687	76	15	given	give	VERB
ejpam-5687	76	16	as	as	ADP
ejpam-5687	76	17	[	[	X
ejpam-5687	76	18	21	21	NUM
ejpam-5687	76	19	]	]	PUNCT
ejpam-5687	76	20	:	:	PUNCT
ejpam-5687	76	21	cdp	cdp	X
ejpam-5687	76	22	0,t	0,t	PROPN
ejpam-5687	76	23	ψ(t	ψ(t	PROPN
ejpam-5687	76	24	)	)	PUNCT
ejpam-5687	76	25	=	=	SYM
ejpam-5687	76	26	1	1	NUM
ejpam-5687	76	27	γ(1−	γ(1−	NOUN
ejpam-5687	76	28	p	p	X
ejpam-5687	76	29	)	)	PUNCT
ejpam-5687	76	30	∫	∫	PROPN
ejpam-5687	77	1	t	t	PROPN
ejpam-5687	77	2	0	0	NUM
ejpam-5687	77	3	1	1	NUM
ejpam-5687	77	4	(	(	PUNCT
ejpam-5687	77	5	t−	t−	PROPN
ejpam-5687	77	6	y)p	y)p	NOUN
ejpam-5687	78	1	d	d	X
ejpam-5687	78	2	dt	dt	X
ejpam-5687	78	3	ψ(y)dy	ψ(y)dy	PROPN
ejpam-5687	78	4	,	,	PUNCT
ejpam-5687	78	5	t	t	PROPN
ejpam-5687	78	6	>	>	X
ejpam-5687	78	7	0	0	NUM
ejpam-5687	78	8	,	,	PUNCT
ejpam-5687	78	9	(	(	PUNCT
ejpam-5687	78	10	2	2	X
ejpam-5687	78	11	)	)	PUNCT
ejpam-5687	78	12	is	be	AUX
ejpam-5687	78	13	known	know	VERB
ejpam-5687	78	14	as	as	ADP
ejpam-5687	78	15	the	the	DET
ejpam-5687	78	16	cf	cf	NOUN
ejpam-5687	78	17	derivative	derivative	NOUN
ejpam-5687	78	18	of	of	ADP
ejpam-5687	78	19	order	order	NOUN
ejpam-5687	78	20	p	p	NOUN
ejpam-5687	78	21	of	of	ADP
ejpam-5687	78	22	the	the	DET
ejpam-5687	78	23	ψ	ψ	X
ejpam-5687	78	24	function	function	NOUN
ejpam-5687	78	25	.	.	PUNCT
ejpam-5687	79	1	for	for	ADP
ejpam-5687	79	2	this	this	PRON
ejpam-5687	79	3	,	,	PUNCT
ejpam-5687	79	4	if	if	SCONJ
ejpam-5687	79	5	p	p	X
ejpam-5687	79	6	→	→	SYM
ejpam-5687	79	7	1	1	NUM
ejpam-5687	79	8	,	,	PUNCT
ejpam-5687	79	9	then	then	ADV
ejpam-5687	79	10	edp	edp	PROPN
ejpam-5687	79	11	0,tψ(t	0,tψ(t	PROPN
ejpam-5687	79	12	)	)	PUNCT
ejpam-5687	79	13	=	=	PUNCT
ejpam-5687	80	1	d	d	PUNCT
ejpam-5687	80	2	dtψ(t	dtψ(t	PROPN
ejpam-5687	80	3	)	)	PUNCT
ejpam-5687	80	4	.	.	PUNCT
ejpam-5687	81	1	lemma	lemma	PROPN
ejpam-5687	81	2	1	1	NUM
ejpam-5687	81	3	.	.	PUNCT
ejpam-5687	82	1	[	[	X
ejpam-5687	82	2	21	21	NUM
ejpam-5687	82	3	]	]	PUNCT
ejpam-5687	82	4	.	.	PUNCT
ejpam-5687	83	1	assuming	assume	VERB
ejpam-5687	83	2	that	that	SCONJ
ejpam-5687	83	3	ψ	ψ	X
ejpam-5687	83	4	:	:	PUNCT
ejpam-5687	83	5	[	[	X
ejpam-5687	83	6	0	0	NUM
ejpam-5687	83	7	,	,	PUNCT
ejpam-5687	83	8	b	b	NOUN
ejpam-5687	83	9	]	]	X
ejpam-5687	83	10	→	→	PUNCT
ejpam-5687	83	11	r	r	NOUN
ejpam-5687	83	12	is	be	AUX
ejpam-5687	83	13	a	a	DET
ejpam-5687	83	14	continuous	continuous	ADJ
ejpam-5687	83	15	and	and	CCONJ
ejpam-5687	83	16	x	x	SYM
ejpam-5687	83	17	∈	∈	PROPN
ejpam-5687	83	18	c1[0	c1[0	PROPN
ejpam-5687	83	19	,	,	PUNCT
ejpam-5687	83	20	b	b	NOUN
ejpam-5687	83	21	]	]	PUNCT
ejpam-5687	83	22	.	.	PUNCT
ejpam-5687	84	1	consider	consider	VERB
ejpam-5687	84	2	{	{	PUNCT
ejpam-5687	84	3	cdp	cdp	PUNCT
ejpam-5687	84	4	0,t	0,t	PROPN
ejpam-5687	84	5	x(t	x(t	PROPN
ejpam-5687	84	6	)	)	PUNCT
ejpam-5687	84	7	=	=	SYM
ejpam-5687	85	1	ψ(t	ψ(t	PROPN
ejpam-5687	85	2	)	)	PUNCT
ejpam-5687	85	3	,	,	PUNCT
ejpam-5687	85	4	t	t	PROPN
ejpam-5687	85	5	∈	∈	PROPN
ejpam-5687	86	1	[	[	X
ejpam-5687	86	2	0	0	NUM
ejpam-5687	86	3	,	,	PUNCT
ejpam-5687	86	4	b	b	NOUN
ejpam-5687	86	5	]	]	X
ejpam-5687	86	6	,	,	PUNCT
ejpam-5687	86	7	0	0	PUNCT
ejpam-5687	86	8	<	<	X
ejpam-5687	86	9	p	p	X
ejpam-5687	86	10	≤	≤	NUM
ejpam-5687	86	11	1	1	NUM
ejpam-5687	86	12	,	,	PUNCT
ejpam-5687	86	13	x(0	x(0	PROPN
ejpam-5687	86	14	)	)	PUNCT
ejpam-5687	86	15	=	=	PUNCT
ejpam-5687	86	16	x0	x0	PROPN
ejpam-5687	86	17	,	,	PUNCT
ejpam-5687	86	18	x0	x0	PROPN
ejpam-5687	86	19	∈	∈	PROPN
ejpam-5687	86	20	r.	r.	PROPN
ejpam-5687	86	21	(	(	PUNCT
ejpam-5687	86	22	3	3	X
ejpam-5687	86	23	)	)	PUNCT
ejpam-5687	86	24	if	if	SCONJ
ejpam-5687	86	25	x(t	x(t	NOUN
ejpam-5687	86	26	)	)	PUNCT
ejpam-5687	86	27	satisfies	satisfie	NOUN
ejpam-5687	86	28	,	,	PUNCT
ejpam-5687	86	29	then	then	ADV
ejpam-5687	86	30	x(t	x(t	PROPN
ejpam-5687	86	31	)	)	PUNCT
ejpam-5687	86	32	is	be	AUX
ejpam-5687	86	33	a	a	DET
ejpam-5687	86	34	solution	solution	NOUN
ejpam-5687	86	35	of	of	ADP
ejpam-5687	86	36	the	the	DET
ejpam-5687	86	37	problem	problem	NOUN
ejpam-5687	86	38	(	(	PUNCT
ejpam-5687	86	39	3	3	NUM
ejpam-5687	86	40	)	)	PUNCT
ejpam-5687	86	41	.	.	PUNCT
ejpam-5687	87	1	x(t	x(t	PROPN
ejpam-5687	87	2	)	)	PUNCT
ejpam-5687	88	1	=	=	PUNCT
ejpam-5687	89	1	x0	x0	PROPN
ejpam-5687	89	2	+	+	CCONJ
ejpam-5687	89	3	1	1	NUM
ejpam-5687	89	4	γ(q	γ(q	NOUN
ejpam-5687	89	5	)	)	PUNCT
ejpam-5687	89	6	∫	∫	PROPN
ejpam-5687	90	1	t	t	PROPN
ejpam-5687	90	2	0	0	NUM
ejpam-5687	91	1	ψ(y)(t−	ψ(y)(t−	CCONJ
ejpam-5687	92	1	y)p−1dy	y)p−1dy	PRON
ejpam-5687	92	2	.	.	PUNCT
ejpam-5687	93	1	3	3	X
ejpam-5687	93	2	.	.	X
ejpam-5687	93	3	caputo	caputo	PROPN
ejpam-5687	93	4	-	-	PUNCT
ejpam-5687	93	5	fabirizo	fabirizo	PROPN
ejpam-5687	93	6	fractional	fractional	ADJ
ejpam-5687	93	7	vbd	vbd	NOUN
ejpam-5687	93	8	model	model	NOUN
ejpam-5687	93	9	the	the	DET
ejpam-5687	93	10	caputo	caputo	PROPN
ejpam-5687	93	11	-	-	PUNCT
ejpam-5687	93	12	fabrizio	fabrizio	PROPN
ejpam-5687	93	13	fractional	fractional	ADJ
ejpam-5687	93	14	-	-	PUNCT
ejpam-5687	93	15	order	order	NOUN
ejpam-5687	93	16	vector	vector	NOUN
ejpam-5687	93	17	-	-	PUNCT
ejpam-5687	93	18	borne	bear	VERB
ejpam-5687	93	19	disease	disease	NOUN
ejpam-5687	93	20	(	(	PUNCT
ejpam-5687	93	21	vbd	vbd	NOUN
ejpam-5687	93	22	)	)	PUNCT
ejpam-5687	93	23	model	model	NOUN
ejpam-5687	93	24	is	be	AUX
ejpam-5687	93	25	formulated	formulate	VERB
ejpam-5687	93	26	to	to	PART
ejpam-5687	93	27	achieve	achieve	VERB
ejpam-5687	93	28	improved	improved	ADJ
ejpam-5687	93	29	representation	representation	NOUN
ejpam-5687	93	30	of	of	ADP
ejpam-5687	93	31	dynamics	dynamic	NOUN
ejpam-5687	93	32	of	of	ADP
ejpam-5687	93	33	vector	vector	NOUN
ejpam-5687	93	34	-	-	PUNCT
ejpam-5687	93	35	host	host	NOUN
ejpam-5687	93	36	interactions	interaction	NOUN
ejpam-5687	93	37	using	use	VERB
ejpam-5687	93	38	the	the	DET
ejpam-5687	93	39	caputo	caputo	PROPN
ejpam-5687	93	40	-	-	PUNCT
ejpam-5687	93	41	fabrizio	fabrizio	PROPN
ejpam-5687	93	42	derivative	derivative	NOUN
ejpam-5687	93	43	,	,	PUNCT
ejpam-5687	93	44	which	which	PRON
ejpam-5687	93	45	imparts	impart	VERB
ejpam-5687	93	46	a	a	DET
ejpam-5687	93	47	non	non	ADJ
ejpam-5687	93	48	-	-	ADJ
ejpam-5687	93	49	singular	singular	ADJ
ejpam-5687	93	50	kernel	kernel	NOUN
ejpam-5687	93	51	and	and	CCONJ
ejpam-5687	93	52	memory	memory	NOUN
ejpam-5687	93	53	effects	effect	NOUN
ejpam-5687	93	54	into	into	ADP
ejpam-5687	93	55	the	the	DET
ejpam-5687	93	56	model	model	NOUN
ejpam-5687	93	57	.	.	PUNCT
ejpam-5687	94	1	this	this	DET
ejpam-5687	94	2	methodology	methodology	NOUN
ejpam-5687	94	3	enhances	enhance	VERB
ejpam-5687	94	4	fidelity	fidelity	NOUN
ejpam-5687	94	5	in	in	ADP
ejpam-5687	94	6	representing	represent	VERB
ejpam-5687	94	7	the	the	DET
ejpam-5687	94	8	disease	disease	NOUN
ejpam-5687	94	9	transmission	transmission	NOUN
ejpam-5687	94	10	processes	process	NOUN
ejpam-5687	94	11	encompassing	encompass	VERB
ejpam-5687	94	12	host	host	NOUN
ejpam-5687	94	13	and	and	CCONJ
ejpam-5687	94	14	vector	vector	NOUN
ejpam-5687	94	15	populations	population	NOUN
ejpam-5687	94	16	as	as	SCONJ
ejpam-5687	94	17	opposed	oppose	VERB
ejpam-5687	94	18	to	to	ADP
ejpam-5687	94	19	conventional	conventional	ADJ
ejpam-5687	94	20	integer	integer	NOUN
ejpam-5687	94	21	-	-	PUNCT
ejpam-5687	94	22	order	order	NOUN
ejpam-5687	94	23	models[35	models[35	NOUN
ejpam-5687	94	24	]	]	PUNCT
ejpam-5687	94	25	.	.	PUNCT
ejpam-5687	95	1	a	a	DET
ejpam-5687	95	2	vector	vector	NOUN
ejpam-5687	95	3	-	-	PUNCT
ejpam-5687	95	4	borne	bear	VERB
ejpam-5687	95	5	disease	disease	NOUN
ejpam-5687	95	6	transmission	transmission	NOUN
ejpam-5687	95	7	model	model	NOUN
ejpam-5687	95	8	has	have	VERB
ejpam-5687	95	9	humans	human	NOUN
ejpam-5687	95	10	and	and	CCONJ
ejpam-5687	95	11	vectors	vector	NOUN
ejpam-5687	95	12	in	in	ADP
ejpam-5687	95	13	its	its	PRON
ejpam-5687	95	14	population	population	NOUN
ejpam-5687	95	15	,	,	PUNCT
ejpam-5687	95	16	where	where	SCONJ
ejpam-5687	95	17	people	people	NOUN
ejpam-5687	95	18	are	be	AUX
ejpam-5687	95	19	classified	classify	VERB
ejpam-5687	95	20	as	as	ADP
ejpam-5687	95	21	susceptible	susceptible	ADJ
ejpam-5687	95	22	,	,	PUNCT
ejpam-5687	95	23	exposed	expose	VERB
ejpam-5687	95	24	,	,	PUNCT
ejpam-5687	95	25	infected	infected	ADJ
ejpam-5687	95	26	,	,	PUNCT
ejpam-5687	95	27	and	and	CCONJ
ejpam-5687	95	28	recovered	recover	VERB
ejpam-5687	95	29	(	(	PUNCT
ejpam-5687	95	30	sh	sh	INTJ
ejpam-5687	95	31	,	,	PUNCT
ejpam-5687	95	32	eh	eh	INTJ
ejpam-5687	95	33	,	,	PUNCT
ejpam-5687	95	34	ih	ih	X
ejpam-5687	95	35	,	,	PUNCT
ejpam-5687	95	36	rh	rh	PROPN
ejpam-5687	95	37	)	)	PUNCT
ejpam-5687	95	38	,	,	PUNCT
ejpam-5687	95	39	while	while	SCONJ
ejpam-5687	95	40	vectors	vector	NOUN
ejpam-5687	95	41	are	be	AUX
ejpam-5687	95	42	classified	classify	VERB
ejpam-5687	95	43	as	as	ADP
ejpam-5687	95	44	susceptible	susceptible	ADJ
ejpam-5687	95	45	,	,	PUNCT
ejpam-5687	95	46	exposed	expose	VERB
ejpam-5687	95	47	,	,	PUNCT
ejpam-5687	95	48	and	and	CCONJ
ejpam-5687	95	49	infected	infected	ADJ
ejpam-5687	95	50	(	(	PUNCT
ejpam-5687	95	51	sv	sv	PROPN
ejpam-5687	95	52	,	,	PUNCT
ejpam-5687	95	53	ev	ev	PROPN
ejpam-5687	95	54	,	,	PUNCT
ejpam-5687	95	55	iv	iv	NUM
ejpam-5687	95	56	)	)	PUNCT
ejpam-5687	95	57	.	.	PUNCT
ejpam-5687	96	1	the	the	DET
ejpam-5687	96	2	population	population	NOUN
ejpam-5687	96	3	is	be	AUX
ejpam-5687	96	4	susceptible	susceptible	ADJ
ejpam-5687	96	5	to	to	ADP
ejpam-5687	96	6	natural	natural	ADJ
ejpam-5687	96	7	mortality	mortality	NOUN
ejpam-5687	96	8	rates	rate	NOUN
ejpam-5687	96	9	,	,	PUNCT
ejpam-5687	96	10	and	and	CCONJ
ejpam-5687	96	11	the	the	DET
ejpam-5687	96	12	model	model	NOUN
ejpam-5687	96	13	implies	imply	VERB
ejpam-5687	96	14	that	that	SCONJ
ejpam-5687	96	15	humans	human	NOUN
ejpam-5687	96	16	who	who	PRON
ejpam-5687	96	17	have	have	AUX
ejpam-5687	96	18	recovered	recover	VERB
ejpam-5687	96	19	are	be	AUX
ejpam-5687	96	20	immune	immune	ADJ
ejpam-5687	96	21	.	.	PUNCT
ejpam-5687	97	1	the	the	DET
ejpam-5687	97	2	paper	paper	NOUN
ejpam-5687	97	3	analyzes	analyze	VERB
ejpam-5687	97	4	the	the	DET
ejpam-5687	97	5	dynamics	dynamic	NOUN
ejpam-5687	97	6	of	of	ADP
ejpam-5687	97	7	disease	disease	NOUN
ejpam-5687	97	8	propagation	propagation	NOUN
ejpam-5687	97	9	with	with	ADP
ejpam-5687	97	10	fractional	fractional	ADJ
ejpam-5687	97	11	calculus	calculus	NOUN
ejpam-5687	97	12	using	use	VERB
ejpam-5687	97	13	caputo	caputo	PROPN
ejpam-5687	97	14	-	-	PUNCT
ejpam-5687	97	15	fabirizo	fabirizo	PROPN
ejpam-5687	97	16	derivatives	derivative	NOUN
ejpam-5687	97	17	,	,	PUNCT
ejpam-5687	97	18	showing	show	VERB
ejpam-5687	97	19	the	the	DET
ejpam-5687	97	20	improved	improved	ADJ
ejpam-5687	97	21	accuracy	accuracy	NOUN
ejpam-5687	97	22	of	of	ADP
ejpam-5687	97	23	fractional	fractional	ADJ
ejpam-5687	97	24	-	-	PUNCT
ejpam-5687	97	25	order	order	NOUN
ejpam-5687	97	26	models	model	NOUN
ejpam-5687	97	27	.	.	PUNCT
ejpam-5687	98	1	the	the	DET
ejpam-5687	98	2	caputo	caputo	PROPN
ejpam-5687	98	3	-	-	PUNCT
ejpam-5687	98	4	fabirizo	fabirizo	PROPN
ejpam-5687	98	5	fractional	fractional	ADJ
ejpam-5687	98	6	model	model	NOUN
ejpam-5687	98	7	for	for	ADP
ejpam-5687	98	8	vbd	vbd	NOUN
ejpam-5687	98	9	is	be	AUX
ejpam-5687	98	10	as	as	ADP
ejpam-5687	98	11	follow	follow	VERB
ejpam-5687	98	12	:	:	PUNCT
ejpam-5687	98	13			PROPN
ejpam-5687	98	14	dαsh	dαsh	PROPN
ejpam-5687	98	15	duα	duα	NOUN
ejpam-5687	98	16	=	=	SYM
ejpam-5687	98	17	λh	λh	ADP
ejpam-5687	98	18	−	−	PROPN
ejpam-5687	98	19	β1sh	β1sh	PUNCT
ejpam-5687	98	20	iv	iv	NUM
ejpam-5687	98	21	nv	nv	PROPN
ejpam-5687	98	22	−	−	PROPN
ejpam-5687	98	23	µhsh	µhsh	NOUN
ejpam-5687	98	24	,	,	PUNCT
ejpam-5687	98	25	dαeh	dαeh	NOUN
ejpam-5687	98	26	duα	duα	NOUN
ejpam-5687	98	27	=	=	SYM
ejpam-5687	98	28	β1sh	β1sh	PUNCT
ejpam-5687	98	29	iv	iv	NUM
ejpam-5687	98	30	nv	nv	PROPN
ejpam-5687	98	31	−	−	PROPN
ejpam-5687	98	32	(	(	PUNCT
ejpam-5687	98	33	σh	σh	PROPN
ejpam-5687	98	34	+	+	SYM
ejpam-5687	98	35	µh)eh	µh)eh	NUM
ejpam-5687	98	36	,	,	PUNCT
ejpam-5687	98	37	dαih	dαih	NOUN
ejpam-5687	98	38	duα	duα	NOUN
ejpam-5687	98	39	=	=	PUNCT
ejpam-5687	98	40	σheh	σheh	ADJ
ejpam-5687	98	41	−	−	PROPN
ejpam-5687	98	42	(	(	PUNCT
ejpam-5687	98	43	γ	γ	X
ejpam-5687	98	44	+	+	SYM
ejpam-5687	98	45	µh)ih	µh)ih	PROPN
ejpam-5687	98	46	,	,	PUNCT
ejpam-5687	98	47	dαrh	dαrh	INTJ
ejpam-5687	98	48	duα	duα	PROPN
ejpam-5687	98	49	=	=	SYM
ejpam-5687	98	50	γih	γih	NOUN
ejpam-5687	98	51	−	−	PROPN
ejpam-5687	98	52	µhrh	µhrh	NOUN
ejpam-5687	98	53	,	,	PUNCT
ejpam-5687	98	54	dαsv	dαsv	ADJ
ejpam-5687	98	55	duα	duα	PROPN
ejpam-5687	98	56	=	=	SYM
ejpam-5687	99	1	λv	λv	ADP
ejpam-5687	99	2	−	−	PROPN
ejpam-5687	99	3	β2sv	β2sv	PUNCT
ejpam-5687	99	4	ih	ih	PROPN
ejpam-5687	99	5	nh	nh	PROPN
ejpam-5687	100	1	−	−	NOUN
ejpam-5687	100	2	µvsv	µvsv	ADJ
ejpam-5687	100	3	,	,	PUNCT
ejpam-5687	100	4	dαev	dαev	NOUN
ejpam-5687	100	5	duα	duα	NOUN
ejpam-5687	100	6	=	=	X
ejpam-5687	100	7	β2sv	β2sv	PUNCT
ejpam-5687	100	8	ih	ih	X
ejpam-5687	100	9	nh	nh	PROPN
ejpam-5687	100	10	−	−	PROPN
ejpam-5687	101	1	(	(	PUNCT
ejpam-5687	101	2	σv	σv	PROPN
ejpam-5687	101	3	+	+	CCONJ
ejpam-5687	101	4	µv)ev	µv)ev	NUM
ejpam-5687	101	5	,	,	PUNCT
ejpam-5687	101	6	dαiv	dαiv	VERB
ejpam-5687	101	7	duα	duα	NOUN
ejpam-5687	101	8	=	=	SYM
ejpam-5687	101	9	σvev	σvev	PROPN
ejpam-5687	101	10	−	−	PROPN
ejpam-5687	101	11	µviv	µviv	PROPN
ejpam-5687	101	12	.	.	PUNCT
ejpam-5687	102	1	(	(	PUNCT
ejpam-5687	102	2	4	4	X
ejpam-5687	102	3	)	)	PUNCT
ejpam-5687	102	4	n.	n.	PROPN
ejpam-5687	102	5	ullah	ullah	PROPN
ejpam-5687	102	6	et	et	PROPN
ejpam-5687	102	7	al	al	PROPN
ejpam-5687	102	8	.	.	PUNCT
ejpam-5687	102	9	/	/	SYM
ejpam-5687	102	10	eur	eur	PROPN
ejpam-5687	102	11	.	.	PUNCT
ejpam-5687	103	1	j.	j.	PROPN
ejpam-5687	103	2	pure	pure	PROPN
ejpam-5687	103	3	appl	appl	PROPN
ejpam-5687	103	4	.	.	PROPN
ejpam-5687	103	5	math	math	PROPN
ejpam-5687	103	6	,	,	PUNCT
ejpam-5687	103	7	18	18	NUM
ejpam-5687	103	8	(	(	PUNCT
ejpam-5687	103	9	2	2	NUM
ejpam-5687	103	10	)	)	PUNCT
ejpam-5687	103	11	(	(	PUNCT
ejpam-5687	103	12	2025	2025	NUM
ejpam-5687	103	13	)	)	PUNCT
ejpam-5687	103	14	,	,	PUNCT
ejpam-5687	103	15	5687	5687	NUM
ejpam-5687	103	16	6	6	NUM
ejpam-5687	103	17	of	of	ADP
ejpam-5687	103	18	25	25	NUM
ejpam-5687	103	19	the	the	DET
ejpam-5687	103	20	definition	definition	NOUN
ejpam-5687	103	21	of	of	ADP
ejpam-5687	103	22	its	its	PRON
ejpam-5687	103	23	cf	cf	NOUN
ejpam-5687	103	24	derivative	derivative	ADJ
ejpam-5687	103	25	operator	operator	NOUN
ejpam-5687	103	26	is	be	AUX
ejpam-5687	103	27	as	as	SCONJ
ejpam-5687	103	28	follows	follow	VERB
ejpam-5687	103	29	:	:	PUNCT
ejpam-5687	104	1	dαf	dαf	NOUN
ejpam-5687	104	2	dtα	dtα	NOUN
ejpam-5687	104	3	=	=	NOUN
ejpam-5687	104	4	1	1	NUM
ejpam-5687	104	5	γ(1−	γ(1−	NOUN
ejpam-5687	104	6	α	α	NUM
ejpam-5687	104	7	)	)	PUNCT
ejpam-5687	104	8	∫	∫	PROPN
ejpam-5687	104	9	t	t	PROPN
ejpam-5687	104	10	0	0	NUM
ejpam-5687	104	11	(	(	PUNCT
ejpam-5687	104	12	t−	t−	PROPN
ejpam-5687	104	13	s)−αf	s)−αf	PROPN
ejpam-5687	104	14	′(s	′(s	NOUN
ejpam-5687	104	15	)	)	PUNCT
ejpam-5687	104	16	ds	ds	PROPN
ejpam-5687	104	17	,	,	PUNCT
ejpam-5687	104	18	(	(	PUNCT
ejpam-5687	104	19	5	5	NUM
ejpam-5687	104	20	)	)	PUNCT
ejpam-5687	104	21	and	and	CCONJ
ejpam-5687	104	22	γ(1−	γ(1−	PROPN
ejpam-5687	104	23	α	α	X
ejpam-5687	104	24	)	)	PUNCT
ejpam-5687	104	25	is	be	AUX
ejpam-5687	104	26	the	the	DET
ejpam-5687	104	27	gamma	gamma	PROPN
ejpam-5687	104	28	function	function	NOUN
ejpam-5687	104	29	.	.	PUNCT
ejpam-5687	105	1	with	with	ADP
ejpam-5687	105	2	i.c	i.c	PROPN
ejpam-5687	105	3	:	:	PUNCT
ejpam-5687	105	4	sh(0	sh(0	PROPN
ejpam-5687	105	5	)	)	PUNCT
ejpam-5687	105	6	≥	≥	NOUN
ejpam-5687	105	7	0	0	NUM
ejpam-5687	105	8	,	,	PUNCT
ejpam-5687	105	9	eh(0	eh(0	NOUN
ejpam-5687	105	10	)	)	PUNCT
ejpam-5687	105	11	≥	≥	NOUN
ejpam-5687	105	12	0	0	NUM
ejpam-5687	105	13	,	,	PUNCT
ejpam-5687	105	14	ih(0	ih(0	NOUN
ejpam-5687	105	15	)	)	PUNCT
ejpam-5687	105	16	≥	≥	NOUN
ejpam-5687	105	17	0	0	NUM
ejpam-5687	105	18	,	,	PUNCT
ejpam-5687	105	19	rh(0	rh(0	NOUN
ejpam-5687	105	20	)	)	PUNCT
ejpam-5687	105	21	≥	≥	NOUN
ejpam-5687	105	22	0	0	NUM
ejpam-5687	105	23	,	,	PUNCT
ejpam-5687	105	24	sv(0	sv(0	NOUN
ejpam-5687	105	25	)	)	PUNCT
ejpam-5687	105	26	≥	≥	NOUN
ejpam-5687	105	27	0	0	NUM
ejpam-5687	105	28	,	,	PUNCT
ejpam-5687	105	29	ev(0	ev(0	PROPN
ejpam-5687	105	30	)	)	PUNCT
ejpam-5687	105	31	≥	≥	NOUN
ejpam-5687	105	32	0	0	NUM
ejpam-5687	105	33	,	,	PUNCT
ejpam-5687	105	34	iv(0	iv(0	PROPN
ejpam-5687	105	35	)	)	PUNCT
ejpam-5687	105	36	≥	≥	NOUN
ejpam-5687	105	37	0	0	NUM
ejpam-5687	105	38	.	.	PUNCT
ejpam-5687	105	39	table	table	NOUN
ejpam-5687	105	40	1	1	NUM
ejpam-5687	105	41	explains	explain	VERB
ejpam-5687	105	42	each	each	DET
ejpam-5687	105	43	state	state	NOUN
ejpam-5687	105	44	variable	variable	NOUN
ejpam-5687	105	45	and	and	CCONJ
ejpam-5687	105	46	parameter	parameter	NOUN
ejpam-5687	105	47	associated	associate	VERB
ejpam-5687	105	48	with	with	ADP
ejpam-5687	105	49	the	the	DET
ejpam-5687	105	50	model	model	NOUN
ejpam-5687	105	51	(	(	PUNCT
ejpam-5687	105	52	4	4	NUM
ejpam-5687	105	53	)	)	PUNCT
ejpam-5687	105	54	.	.	PUNCT
ejpam-5687	106	1	table	table	NOUN
ejpam-5687	106	2	1	1	NUM
ejpam-5687	106	3	:	:	PUNCT
ejpam-5687	106	4	meaning	meaning	NOUN
ejpam-5687	106	5	of	of	ADP
ejpam-5687	106	6	variable	variable	ADJ
ejpam-5687	106	7	and	and	CCONJ
ejpam-5687	106	8	parameter	parameter	NOUN
ejpam-5687	106	9	variable	variable	ADJ
ejpam-5687	106	10	/	/	SYM
ejpam-5687	106	11	parameter	parameter	NOUN
ejpam-5687	106	12	meaning	mean	VERB
ejpam-5687	106	13	sh(t	sh(t	X
ejpam-5687	106	14	)	)	PUNCT
ejpam-5687	106	15	susceptible	susceptible	ADJ
ejpam-5687	106	16	population	population	NOUN
ejpam-5687	106	17	of	of	ADP
ejpam-5687	106	18	human	human	NOUN
ejpam-5687	106	19	eh(t	eh(t	PUNCT
ejpam-5687	106	20	)	)	PUNCT
ejpam-5687	106	21	exposed	expose	VERB
ejpam-5687	106	22	population	population	NOUN
ejpam-5687	106	23	of	of	ADP
ejpam-5687	106	24	human	human	NOUN
ejpam-5687	106	25	ih(t	ih(t	PUNCT
ejpam-5687	106	26	)	)	PUNCT
ejpam-5687	106	27	infected	infected	ADJ
ejpam-5687	106	28	population	population	NOUN
ejpam-5687	106	29	of	of	ADP
ejpam-5687	106	30	human	human	NOUN
ejpam-5687	106	31	rh(t	rh(t	PUNCT
ejpam-5687	106	32	)	)	PUNCT
ejpam-5687	106	33	recovered	recover	VERB
ejpam-5687	106	34	population	population	NOUN
ejpam-5687	106	35	of	of	ADP
ejpam-5687	106	36	human	human	ADJ
ejpam-5687	106	37	sv(t	sv(t	NOUN
ejpam-5687	106	38	)	)	PUNCT
ejpam-5687	106	39	susceptible	susceptible	ADJ
ejpam-5687	106	40	population	population	NOUN
ejpam-5687	106	41	of	of	ADP
ejpam-5687	106	42	vector	vector	NOUN
ejpam-5687	106	43	ev(t	ev(t	NOUN
ejpam-5687	106	44	)	)	PUNCT
ejpam-5687	106	45	exposed	expose	VERB
ejpam-5687	106	46	population	population	NOUN
ejpam-5687	106	47	of	of	ADP
ejpam-5687	106	48	vector	vector	NOUN
ejpam-5687	106	49	iv(t	iv(t	PUNCT
ejpam-5687	106	50	)	)	PUNCT
ejpam-5687	106	51	infected	infect	VERB
ejpam-5687	106	52	population	population	NOUN
ejpam-5687	106	53	of	of	ADP
ejpam-5687	106	54	vector	vector	NOUN
ejpam-5687	106	55	α	α	PROPN
ejpam-5687	106	56	fractional	fractional	ADJ
ejpam-5687	106	57	derivative	derivative	ADJ
ejpam-5687	106	58	order	order	NOUN
ejpam-5687	106	59	,	,	PUNCT
ejpam-5687	106	60	0	0	NUM
ejpam-5687	106	61	<	<	X
ejpam-5687	106	62	α	α	PROPN
ejpam-5687	106	63	≤	≤	NUM
ejpam-5687	106	64	1	1	NUM
ejpam-5687	106	65	λh	λh	ADP
ejpam-5687	106	66	birth	birth	NOUN
ejpam-5687	106	67	rate	rate	NOUN
ejpam-5687	106	68	for	for	ADP
ejpam-5687	106	69	humans	human	NOUN
ejpam-5687	106	70	λv	λv	INTJ
ejpam-5687	106	71	birth	birth	NOUN
ejpam-5687	106	72	rate	rate	NOUN
ejpam-5687	106	73	for	for	ADP
ejpam-5687	106	74	vectors	vector	NOUN
ejpam-5687	106	75	β1	β1	NOUN
ejpam-5687	106	76	transmission	transmission	NOUN
ejpam-5687	106	77	rate	rate	NOUN
ejpam-5687	106	78	from	from	ADP
ejpam-5687	106	79	vectors	vector	NOUN
ejpam-5687	106	80	to	to	ADP
ejpam-5687	106	81	humans	human	NOUN
ejpam-5687	106	82	β2	β2	NOUN
ejpam-5687	106	83	transmission	transmission	NOUN
ejpam-5687	106	84	rate	rate	NOUN
ejpam-5687	106	85	from	from	ADP
ejpam-5687	106	86	humans	human	NOUN
ejpam-5687	106	87	to	to	ADP
ejpam-5687	106	88	vectors	vector	NOUN
ejpam-5687	106	89	σh	σh	ADP
ejpam-5687	106	90	progression	progression	NOUN
ejpam-5687	106	91	rate	rate	NOUN
ejpam-5687	106	92	from	from	ADP
ejpam-5687	106	93	exposed	expose	VERB
ejpam-5687	106	94	to	to	ADP
ejpam-5687	106	95	infected	infect	VERB
ejpam-5687	106	96	for	for	ADP
ejpam-5687	106	97	humans	human	NOUN
ejpam-5687	106	98	σv	σv	ADP
ejpam-5687	106	99	progression	progression	NOUN
ejpam-5687	106	100	rate	rate	NOUN
ejpam-5687	106	101	from	from	ADP
ejpam-5687	106	102	exposed	expose	VERB
ejpam-5687	106	103	to	to	ADP
ejpam-5687	106	104	infected	infect	VERB
ejpam-5687	106	105	for	for	ADP
ejpam-5687	106	106	vectors	vector	NOUN
ejpam-5687	106	107	γ	γ	PROPN
ejpam-5687	106	108	recovery	recovery	NOUN
ejpam-5687	106	109	rate	rate	NOUN
ejpam-5687	106	110	for	for	ADP
ejpam-5687	106	111	humans	human	NOUN
ejpam-5687	106	112	µh	µh	ADP
ejpam-5687	106	113	mortality	mortality	NOUN
ejpam-5687	106	114	rate	rate	NOUN
ejpam-5687	106	115	for	for	ADP
ejpam-5687	106	116	humans	human	NOUN
ejpam-5687	106	117	µv	µv	VERB
ejpam-5687	106	118	mortality	mortality	NOUN
ejpam-5687	106	119	rate	rate	NOUN
ejpam-5687	106	120	for	for	ADP
ejpam-5687	106	121	vectors	vector	NOUN
ejpam-5687	106	122	nh	nh	PROPN
ejpam-5687	107	1	total	total	ADJ
ejpam-5687	107	2	human	human	ADJ
ejpam-5687	107	3	population	population	NOUN
ejpam-5687	107	4	nv	nv	PROPN
ejpam-5687	107	5	total	total	ADJ
ejpam-5687	107	6	vector	vector	NOUN
ejpam-5687	107	7	population	population	NOUN
ejpam-5687	107	8	3.1	3.1	NUM
ejpam-5687	107	9	.	.	PUNCT
ejpam-5687	108	1	analysis	analysis	NOUN
ejpam-5687	108	2	of	of	ADP
ejpam-5687	108	3	the	the	DET
ejpam-5687	108	4	caputo	caputo	PROPN
ejpam-5687	108	5	-	-	PUNCT
ejpam-5687	108	6	fabrizio	fabrizio	PROPN
ejpam-5687	108	7	fractional	fractional	ADJ
ejpam-5687	108	8	model	model	NOUN
ejpam-5687	108	9	in	in	ADP
ejpam-5687	108	10	this	this	DET
ejpam-5687	108	11	section	section	NOUN
ejpam-5687	108	12	,	,	PUNCT
ejpam-5687	108	13	we	we	PRON
ejpam-5687	108	14	analyze	analyze	VERB
ejpam-5687	108	15	the	the	DET
ejpam-5687	108	16	and	and	CCONJ
ejpam-5687	108	17	existence	existence	NOUN
ejpam-5687	108	18	uniqueness	uniqueness	NOUN
ejpam-5687	108	19	results	result	NOUN
ejpam-5687	108	20	of	of	ADP
ejpam-5687	108	21	the(4	the(4	NOUN
ejpam-5687	108	22	)	)	PUNCT
ejpam-5687	108	23	model	model	NOUN
ejpam-5687	108	24	by	by	ADP
ejpam-5687	108	25	using	use	VERB
ejpam-5687	108	26	the	the	DET
ejpam-5687	108	27	banach	banach	ADV
ejpam-5687	108	28	fixed	fix	VERB
ejpam-5687	108	29	point	point	NOUN
ejpam-5687	108	30	theorem	theorem	VERB
ejpam-5687	108	31	.	.	PUNCT
ejpam-5687	109	1	note	note	VERB
ejpam-5687	109	2	that	that	SCONJ
ejpam-5687	109	3	in	in	ADP
ejpam-5687	109	4	q	q	PROPN
ejpam-5687	109	5	=	=	PUNCT
ejpam-5687	110	1	[	[	X
ejpam-5687	110	2	0	0	NUM
ejpam-5687	110	3	,	,	PUNCT
ejpam-5687	110	4	b	b	NOUN
ejpam-5687	110	5	]	]	PUNCT
ejpam-5687	110	6	and	and	CCONJ
ejpam-5687	110	7	sup	sup	NOUN
ejpam-5687	110	8	norm	norm	VERB
ejpam-5687	110	9	all	all	DET
ejpam-5687	110	10	continuous	continuous	ADJ
ejpam-5687	110	11	real	real	ADJ
ejpam-5687	110	12	value	value	NOUN
ejpam-5687	110	13	functions	function	NOUN
ejpam-5687	110	14	and	and	CCONJ
ejpam-5687	110	15	y(q	y(q	NOUN
ejpam-5687	110	16	)	)	PUNCT
ejpam-5687	110	17	represent	represent	VERB
ejpam-5687	110	18	banach	banach	NOUN
ejpam-5687	110	19	spaces	space	NOUN
ejpam-5687	110	20	n	n	NOUN
ejpam-5687	110	21	=	=	SYM
ejpam-5687	110	22	y(q)×	y(q)×	NOUN
ejpam-5687	111	1	y(q)×	y(q)×	NOUN
ejpam-5687	111	2	y(q)×	y(q)×	NOUN
ejpam-5687	112	1	y(q)×	y(q)×	NOUN
ejpam-5687	112	2	y(q)×	y(q)×	PROPN
ejpam-5687	112	3	y(q)×	y(q)×	PROPN
ejpam-5687	112	4	y(q	y(q	PROPN
ejpam-5687	112	5	)	)	PUNCT
ejpam-5687	112	6	,	,	PUNCT
ejpam-5687	112	7	with	with	ADP
ejpam-5687	112	8	norm	norm	NOUN
ejpam-5687	112	9	∥(sh	∥(sh	ADV
ejpam-5687	112	10	,	,	PUNCT
ejpam-5687	112	11	eh	eh	INTJ
ejpam-5687	112	12	,	,	PUNCT
ejpam-5687	112	13	ih	ih	X
ejpam-5687	112	14	,	,	PUNCT
ejpam-5687	112	15	rh	rh	PROPN
ejpam-5687	112	16	,	,	PUNCT
ejpam-5687	112	17	sv	sv	PROPN
ejpam-5687	112	18	,	,	PUNCT
ejpam-5687	112	19	ev	ev	INTJ
ejpam-5687	112	20	,	,	PUNCT
ejpam-5687	112	21	iv)∥	iv)∥	PROPN
ejpam-5687	112	22	=	=	SYM
ejpam-5687	112	23	∥sh∥+	∥sh∥+	PROPN
ejpam-5687	112	24	∥eh∥+	∥eh∥+	PUNCT
ejpam-5687	112	25	∥ih∥+	∥ih∥+	NOUN
ejpam-5687	112	26	∥rh∥+	∥rh∥+	PROPN
ejpam-5687	112	27	∥sv∥+	∥sv∥+	PROPN
ejpam-5687	112	28	∥ev∥+	∥ev∥+	NOUN
ejpam-5687	112	29	∥iv∥	∥iv∥	NOUN
ejpam-5687	112	30	,	,	PUNCT
ejpam-5687	113	1	n.	n.	PROPN
ejpam-5687	113	2	ullah	ullah	PROPN
ejpam-5687	113	3	et	et	PROPN
ejpam-5687	113	4	al	al	PROPN
ejpam-5687	113	5	.	.	PUNCT
ejpam-5687	113	6	/	/	SYM
ejpam-5687	113	7	eur	eur	PROPN
ejpam-5687	113	8	.	.	PUNCT
ejpam-5687	114	1	j.	j.	PROPN
ejpam-5687	114	2	pure	pure	PROPN
ejpam-5687	114	3	appl	appl	PROPN
ejpam-5687	114	4	.	.	PROPN
ejpam-5687	114	5	math	math	PROPN
ejpam-5687	114	6	,	,	PUNCT
ejpam-5687	114	7	18	18	NUM
ejpam-5687	114	8	(	(	PUNCT
ejpam-5687	114	9	2	2	NUM
ejpam-5687	114	10	)	)	PUNCT
ejpam-5687	114	11	(	(	PUNCT
ejpam-5687	114	12	2025	2025	NUM
ejpam-5687	114	13	)	)	PUNCT
ejpam-5687	114	14	,	,	PUNCT
ejpam-5687	114	15	5687	5687	NUM
ejpam-5687	114	16	7	7	NUM
ejpam-5687	114	17	of	of	ADP
ejpam-5687	114	18	25	25	NUM
ejpam-5687	114	19	where	where	SCONJ
ejpam-5687	114	20	∥sh∥	∥sh∥	NUM
ejpam-5687	114	21	=	=	SYM
ejpam-5687	114	22	max	max	PROPN
ejpam-5687	114	23	u∈q	u∈q	ADJ
ejpam-5687	114	24	|sh(u)|	|sh(u)|	PROPN
ejpam-5687	114	25	,	,	PUNCT
ejpam-5687	114	26	∥eh∥	∥eh∥	VERB
ejpam-5687	114	27	=	=	PUNCT
ejpam-5687	114	28	max	max	PROPN
ejpam-5687	114	29	u∈q	u∈q	PROPN
ejpam-5687	114	30	|eh(u)|	|eh(u)|	PROPN
ejpam-5687	114	31	,	,	PUNCT
ejpam-5687	114	32	∥ih∥	∥ih∥	PUNCT
ejpam-5687	115	1	=	=	SYM
ejpam-5687	115	2	max	max	PROPN
ejpam-5687	115	3	u∈q	u∈q	PROPN
ejpam-5687	115	4	|ih(u)|	|ih(u)|	PROPN
ejpam-5687	115	5	,	,	PUNCT
ejpam-5687	115	6	∥rh∥	∥rh∥	ADV
ejpam-5687	115	7	=	=	SYM
ejpam-5687	115	8	max	max	PROPN
ejpam-5687	115	9	u∈q	u∈q	PROPN
ejpam-5687	115	10	|rh(u)|	|rh(u)|	PROPN
ejpam-5687	115	11	,	,	PUNCT
ejpam-5687	115	12	∥sv∥	∥sv∥	NOUN
ejpam-5687	115	13	=	=	SYM
ejpam-5687	115	14	max	max	PROPN
ejpam-5687	115	15	u∈q	u∈q	PROPN
ejpam-5687	115	16	|sv(u)|	|sv(u)|	PROPN
ejpam-5687	115	17	,	,	PUNCT
ejpam-5687	115	18	∥ev∥	∥ev∥	PUNCT
ejpam-5687	115	19	=	=	SYM
ejpam-5687	116	1	max	max	PROPN
ejpam-5687	116	2	u∈q	u∈q	PROPN
ejpam-5687	116	3	|ev(u)|	|ev(u)|	PROPN
ejpam-5687	116	4	,	,	PUNCT
ejpam-5687	116	5	∥iv∥	∥iv∥	ADJ
ejpam-5687	116	6	=	=	SYM
ejpam-5687	116	7	max	max	PROPN
ejpam-5687	116	8	u∈q	u∈q	VERB
ejpam-5687	116	9	|iv(u)|	|iv(u)|	NOUN
ejpam-5687	116	10	.	.	PUNCT
ejpam-5687	117	1	for	for	ADP
ejpam-5687	117	2	each	each	DET
ejpam-5687	117	3	equation	equation	NOUN
ejpam-5687	117	4	in	in	ADP
ejpam-5687	117	5	the(4	the(4	NOUN
ejpam-5687	117	6	)	)	PUNCT
ejpam-5687	117	7	system	system	NOUN
ejpam-5687	117	8	,	,	PUNCT
ejpam-5687	117	9	apply	apply	VERB
ejpam-5687	117	10	hp	hp	PROPN
ejpam-5687	117	11	0	0	NUM
ejpam-5687	117	12	obtained	obtain	VERB
ejpam-5687	117	13	:	:	PUNCT
ejpam-5687	117	14			PROPN
ejpam-5687	117	15	sh(u	sh(u	X
ejpam-5687	117	16	)	)	PUNCT
ejpam-5687	118	1	=	=	PUNCT
ejpam-5687	118	2	sh(0	sh(0	NOUN
ejpam-5687	118	3	)	)	PUNCT
ejpam-5687	118	4	+	+	NOUN
ejpam-5687	118	5	hp	hp	NOUN
ejpam-5687	118	6	0[λh	0[λh	NUM
ejpam-5687	118	7	−	−	NOUN
ejpam-5687	118	8	β1sh	β1sh	SYM
ejpam-5687	118	9	iv	iv	NUM
ejpam-5687	118	10	nv	nv	PROPN
ejpam-5687	118	11	−	−	PROPN
ejpam-5687	118	12	µhsh	µhsh	NOUN
ejpam-5687	118	13	]	]	PUNCT
ejpam-5687	118	14	,	,	PUNCT
ejpam-5687	118	15	eh(u	eh(u	NUM
ejpam-5687	118	16	)	)	PUNCT
ejpam-5687	118	17	=	=	SYM
ejpam-5687	118	18	eh(0	eh(0	NOUN
ejpam-5687	118	19	)	)	PUNCT
ejpam-5687	119	1	+	+	NOUN
ejpam-5687	119	2	hp	hp	NOUN
ejpam-5687	119	3	0[β1sh	0[β1sh	NUM
ejpam-5687	119	4	iv	iv	NUM
ejpam-5687	119	5	nv	nv	PROPN
ejpam-5687	119	6	−	−	PROPN
ejpam-5687	119	7	(	(	PUNCT
ejpam-5687	119	8	σh	σh	PROPN
ejpam-5687	119	9	+	+	PUNCT
ejpam-5687	119	10	µh)eh	µh)eh	X
ejpam-5687	119	11	]	]	X
ejpam-5687	119	12	,	,	PUNCT
ejpam-5687	119	13	ih(u	ih(u	X
ejpam-5687	119	14	)	)	PUNCT
ejpam-5687	119	15	=	=	SYM
ejpam-5687	119	16	ih(0	ih(0	NOUN
ejpam-5687	119	17	)	)	PUNCT
ejpam-5687	120	1	+	+	NOUN
ejpam-5687	120	2	hp	hp	ADJ
ejpam-5687	120	3	0[σheh	0[σheh	NUM
ejpam-5687	120	4	−	−	PROPN
ejpam-5687	121	1	(	(	PUNCT
ejpam-5687	121	2	γ	γ	X
ejpam-5687	121	3	+	+	X
ejpam-5687	121	4	µh)ih	µh)ih	PROPN
ejpam-5687	121	5	]	]	PUNCT
ejpam-5687	121	6	,	,	PUNCT
ejpam-5687	121	7	rh(u	rh(u	X
ejpam-5687	121	8	)	)	PUNCT
ejpam-5687	121	9	=	=	SYM
ejpam-5687	121	10	rh(0	rh(0	PROPN
ejpam-5687	121	11	)	)	PUNCT
ejpam-5687	122	1	+	+	NOUN
ejpam-5687	122	2	hp	hp	ADJ
ejpam-5687	122	3	0[γih	0[γih	ADJ
ejpam-5687	122	4	−	−	PROPN
ejpam-5687	122	5	µhrh	µhrh	NOUN
ejpam-5687	122	6	]	]	PUNCT
ejpam-5687	122	7	,	,	PUNCT
ejpam-5687	122	8	sv(u	sv(u	ADJ
ejpam-5687	122	9	)	)	PUNCT
ejpam-5687	122	10	=	=	SYM
ejpam-5687	122	11	sv(0	sv(0	NOUN
ejpam-5687	122	12	)	)	PUNCT
ejpam-5687	122	13	+	+	PROPN
ejpam-5687	122	14	hp	hp	NOUN
ejpam-5687	122	15	0[λv	0[λv	NOUN
ejpam-5687	122	16	−	−	NOUN
ejpam-5687	122	17	β2sv	β2sv	PUNCT
ejpam-5687	122	18	ih	ih	PROPN
ejpam-5687	122	19	nh	nh	PROPN
ejpam-5687	122	20	−	−	PROPN
ejpam-5687	122	21	µvsv	µvsv	ADJ
ejpam-5687	122	22	]	]	X
ejpam-5687	122	23	,	,	PUNCT
ejpam-5687	122	24	ev(u	ev(u	PUNCT
ejpam-5687	122	25	)	)	PUNCT
ejpam-5687	122	26	=	=	SYM
ejpam-5687	122	27	ev(0	ev(0	PROPN
ejpam-5687	122	28	)	)	PUNCT
ejpam-5687	122	29	+	+	NOUN
ejpam-5687	122	30	hp	hp	NOUN
ejpam-5687	122	31	0[β2sv	0[β2sv	X
ejpam-5687	122	32	ih	ih	PROPN
ejpam-5687	122	33	nh	nh	PROPN
ejpam-5687	122	34	−	−	PROPN
ejpam-5687	122	35	(	(	PUNCT
ejpam-5687	122	36	σv	σv	ADP
ejpam-5687	122	37	+	+	PUNCT
ejpam-5687	122	38	µv)ev	µv)ev	NOUN
ejpam-5687	122	39	]	]	X
ejpam-5687	122	40	,	,	PUNCT
ejpam-5687	122	41	iv(u	iv(u	NUM
ejpam-5687	122	42	)	)	PUNCT
ejpam-5687	122	43	=	=	SYM
ejpam-5687	122	44	iv(0	iv(0	NOUN
ejpam-5687	122	45	)	)	PUNCT
ejpam-5687	123	1	+	+	NOUN
ejpam-5687	123	2	hp	hp	ADJ
ejpam-5687	123	3	0[σvev	0[σvev	NOUN
ejpam-5687	123	4	−	−	PROPN
ejpam-5687	123	5	µviv	µviv	NOUN
ejpam-5687	123	6	]	]	PUNCT
ejpam-5687	123	7	.	.	PUNCT
ejpam-5687	124	1	(	(	PUNCT
ejpam-5687	124	2	6	6	X
ejpam-5687	124	3	)	)	PUNCT
ejpam-5687	124	4	setting	set	VERB
ejpam-5687	124	5	the	the	DET
ejpam-5687	124	6	(	(	PUNCT
ejpam-5687	124	7	6	6	NUM
ejpam-5687	124	8	)	)	PUNCT
ejpam-5687	124	9			NUM
ejpam-5687	124	10	ψ1(u	ψ1(u	NOUN
ejpam-5687	124	11	,	,	PUNCT
ejpam-5687	124	12	sh	sh	NOUN
ejpam-5687	124	13	)	)	PUNCT
ejpam-5687	124	14	=	=	NOUN
ejpam-5687	124	15	λh	λh	ADP
ejpam-5687	124	16	−	−	PROPN
ejpam-5687	124	17	β1sh	β1sh	PUNCT
ejpam-5687	124	18	iv	iv	NUM
ejpam-5687	124	19	nv	nv	PROPN
ejpam-5687	124	20	−	−	PROPN
ejpam-5687	124	21	µhsh	µhsh	NOUN
ejpam-5687	124	22	,	,	PUNCT
ejpam-5687	124	23	ψ2(u	ψ2(u	NOUN
ejpam-5687	124	24	,	,	PUNCT
ejpam-5687	124	25	eh	eh	INTJ
ejpam-5687	124	26	)	)	PUNCT
ejpam-5687	124	27	=	=	SYM
ejpam-5687	124	28	β1sh	β1sh	PUNCT
ejpam-5687	124	29	iv	iv	NUM
ejpam-5687	124	30	nv	nv	PROPN
ejpam-5687	124	31	−	−	PROPN
ejpam-5687	124	32	(	(	PUNCT
ejpam-5687	124	33	σh	σh	PROPN
ejpam-5687	124	34	+	+	X
ejpam-5687	124	35	µh)eh	µh)eh	NUM
ejpam-5687	124	36	,	,	PUNCT
ejpam-5687	124	37	ψ3(u	ψ3(u	PROPN
ejpam-5687	124	38	,	,	PUNCT
ejpam-5687	124	39	ih	ih	NOUN
ejpam-5687	124	40	)	)	PUNCT
ejpam-5687	124	41	=	=	VERB
ejpam-5687	125	1	σheh	σheh	ADJ
ejpam-5687	125	2	−	−	PROPN
ejpam-5687	125	3	(	(	PUNCT
ejpam-5687	125	4	γ	γ	X
ejpam-5687	125	5	+	+	X
ejpam-5687	125	6	µh)ih	µh)ih	PROPN
ejpam-5687	125	7	,	,	PUNCT
ejpam-5687	125	8	ψ4(u	ψ4(u	PROPN
ejpam-5687	125	9	,	,	PUNCT
ejpam-5687	125	10	rh	rh	PROPN
ejpam-5687	125	11	)	)	PUNCT
ejpam-5687	125	12	=	=	PROPN
ejpam-5687	125	13	γih	γih	NOUN
ejpam-5687	125	14	−	−	PROPN
ejpam-5687	125	15	µhrh	µhrh	NOUN
ejpam-5687	125	16	,	,	PUNCT
ejpam-5687	125	17	ψ5(u	ψ5(u	PROPN
ejpam-5687	125	18	,	,	PUNCT
ejpam-5687	125	19	sv	sv	NOUN
ejpam-5687	125	20	)	)	PUNCT
ejpam-5687	125	21	=	=	SYM
ejpam-5687	126	1	λv	λv	ADP
ejpam-5687	126	2	−	−	NOUN
ejpam-5687	126	3	β2sv	β2sv	PUNCT
ejpam-5687	126	4	ih	ih	PROPN
ejpam-5687	126	5	nh	nh	PROPN
ejpam-5687	126	6	−	−	PROPN
ejpam-5687	126	7	µvsv	µvsv	ADJ
ejpam-5687	126	8	,	,	PUNCT
ejpam-5687	126	9	ψ6(u	ψ6(u	NOUN
ejpam-5687	126	10	,	,	PUNCT
ejpam-5687	126	11	ev	ev	ADJ
ejpam-5687	126	12	)	)	PUNCT
ejpam-5687	126	13	=	=	X
ejpam-5687	126	14	β2sv	β2sv	PUNCT
ejpam-5687	126	15	ih	ih	X
ejpam-5687	126	16	nh	nh	PROPN
ejpam-5687	126	17	−	−	PROPN
ejpam-5687	127	1	(	(	PUNCT
ejpam-5687	127	2	σv	σv	PROPN
ejpam-5687	127	3	+	+	CCONJ
ejpam-5687	127	4	µv)ev	µv)ev	X
ejpam-5687	127	5	,	,	PUNCT
ejpam-5687	127	6	ψ7(u	ψ7(u	PROPN
ejpam-5687	127	7	,	,	PUNCT
ejpam-5687	127	8	iv	iv	X
ejpam-5687	127	9	)	)	PUNCT
ejpam-5687	127	10	=	=	SYM
ejpam-5687	127	11	σvev	σvev	PROPN
ejpam-5687	127	12	−	−	PROPN
ejpam-5687	127	13	µviv	µviv	PROPN
ejpam-5687	127	14	.	.	PUNCT
ejpam-5687	128	1	(	(	PUNCT
ejpam-5687	128	2	7	7	X
ejpam-5687	128	3	)	)	PUNCT
ejpam-5687	128	4	the	the	DET
ejpam-5687	128	5	lipschitz	lipschitz	NOUN
ejpam-5687	128	6	condition	condition	NOUN
ejpam-5687	128	7	is	be	AUX
ejpam-5687	128	8	ψi	ψi	ADJ
ejpam-5687	128	9	,	,	PUNCT
ejpam-5687	128	10	i	i	PRON
ejpam-5687	128	11	=	=	NOUN
ejpam-5687	128	12	1	1	NUM
ejpam-5687	128	13	,	,	PUNCT
ejpam-5687	128	14	2	2	NUM
ejpam-5687	128	15	,	,	PUNCT
ejpam-5687	128	16	.	.	PUNCT
ejpam-5687	128	17	.	.	PUNCT
ejpam-5687	129	1	.	.	PUNCT
ejpam-5687	130	1	,	,	PUNCT
ejpam-5687	130	2	7	7	X
ejpam-5687	130	3	,	,	PUNCT
ejpam-5687	130	4	this	this	PRON
ejpam-5687	130	5	implies	imply	VERB
ejpam-5687	130	6	that	that	SCONJ
ejpam-5687	130	7	there	there	PRON
ejpam-5687	130	8	exist	exist	VERB
ejpam-5687	130	9	an	an	DET
ejpam-5687	130	10	upper	upper	ADJ
ejpam-5687	130	11	bound	bound	NOUN
ejpam-5687	130	12	of	of	ADP
ejpam-5687	130	13	sh(u	sh(u	NOUN
ejpam-5687	130	14	)	)	PUNCT
ejpam-5687	130	15	,	,	PUNCT
ejpam-5687	130	16	eh(u	eh(u	NUM
ejpam-5687	130	17	)	)	PUNCT
ejpam-5687	130	18	,	,	PUNCT
ejpam-5687	130	19	ih(u	ih(u	NOUN
ejpam-5687	130	20	)	)	PUNCT
ejpam-5687	130	21	,	,	PUNCT
ejpam-5687	130	22	rh(u	rh(u	NOUN
ejpam-5687	130	23	)	)	PUNCT
ejpam-5687	130	24	,	,	PUNCT
ejpam-5687	130	25	sv(u	sv(u	PROPN
ejpam-5687	130	26	)	)	PUNCT
ejpam-5687	130	27	,	,	PUNCT
ejpam-5687	130	28	ev(u	ev(u	PUNCT
ejpam-5687	130	29	)	)	PUNCT
ejpam-5687	130	30	and	and	CCONJ
ejpam-5687	130	31	iv(u	iv(u	NUM
ejpam-5687	130	32	)	)	PUNCT
ejpam-5687	130	33	.	.	PUNCT
ejpam-5687	131	1	in	in	SCONJ
ejpam-5687	131	2	fact	fact	NOUN
ejpam-5687	131	3	,	,	PUNCT
ejpam-5687	131	4	if	if	SCONJ
ejpam-5687	131	5	we	we	PRON
ejpam-5687	131	6	consider	consider	VERB
ejpam-5687	131	7	two	two	NUM
ejpam-5687	131	8	functions	function	NOUN
ejpam-5687	131	9	,	,	PUNCT
ejpam-5687	131	10	sh	sh	PROPN
ejpam-5687	131	11	and	and	CCONJ
ejpam-5687	131	12	sh1	sh1	PROPN
ejpam-5687	131	13	,	,	PUNCT
ejpam-5687	131	14	such	such	ADJ
ejpam-5687	131	15	that	that	PRON
ejpam-5687	131	16	∥ψ1	∥ψ1	VERB
ejpam-5687	131	17	−	−	PROPN
ejpam-5687	131	18	ψ1∥	ψ1∥	NOUN
ejpam-5687	131	19	=	=	NOUN
ejpam-5687	131	20	∥∥∥∥(β1	∥∥∥∥(β1	PROPN
ejpam-5687	131	21	∥iv∥nv	∥iv∥nv	ADV
ejpam-5687	131	22	+	+	X
ejpam-5687	131	23	µh	µh	NOUN
ejpam-5687	131	24	)	)	PUNCT
ejpam-5687	131	25	(	(	PUNCT
ejpam-5687	131	26	sh	sh	INTJ
ejpam-5687	131	27	−	−	PROPN
ejpam-5687	131	28	sh1	sh1	PROPN
ejpam-5687	131	29	)	)	PUNCT
ejpam-5687	131	30	∥∥∥∥	∥∥∥∥	NUM
ejpam-5687	131	31	≤	≤	NUM
ejpam-5687	131	32	∥∥∥∥(β1	∥∥∥∥(β1	NOUN
ejpam-5687	131	33	∥iv∥nv	∥iv∥nv	ADV
ejpam-5687	131	34	+	+	X
ejpam-5687	131	35	µh	µh	NOUN
ejpam-5687	131	36	)	)	PUNCT
ejpam-5687	131	37	(	(	PUNCT
ejpam-5687	131	38	sh	sh	INTJ
ejpam-5687	131	39	−	−	PROPN
ejpam-5687	131	40	sh1	sh1	PROPN
ejpam-5687	131	41	)	)	PUNCT
ejpam-5687	131	42	∥∥∥∥	∥∥∥∥	NUM
ejpam-5687	131	43	,	,	PUNCT
ejpam-5687	131	44	(	(	PUNCT
ejpam-5687	131	45	8)	8)	NUM
ejpam-5687	131	46	η1	η1	NOUN
ejpam-5687	131	47	=	=	SYM
ejpam-5687	131	48	(	(	PUNCT
ejpam-5687	131	49	β1n1	β1n1	PUNCT
ejpam-5687	131	50	+	+	NUM
ejpam-5687	131	51	µh	µh	NOUN
ejpam-5687	131	52	)	)	PUNCT
ejpam-5687	131	53	,	,	PUNCT
ejpam-5687	131	54	n1	n1	NOUN
ejpam-5687	131	55	=	=	SYM
ejpam-5687	131	56	maxt∈q	maxt∈q	PROPN
ejpam-5687	131	57	||iv	||iv	NOUN
ejpam-5687	131	58	||	||	PROPN
ejpam-5687	131	59	nv	nv	PROPN
ejpam-5687	131	60	,	,	PUNCT
ejpam-5687	131	61	where	where	SCONJ
ejpam-5687	131	62	∥ψ1	∥ψ1	VERB
ejpam-5687	131	63	−	−	PROPN
ejpam-5687	131	64	ψ1∥	ψ1∥	NOUN
ejpam-5687	131	65	≤	≤	NUM
ejpam-5687	131	66	η1	η1	NOUN
ejpam-5687	131	67	∥sh	∥sh	PART
ejpam-5687	131	68	−	−	PROPN
ejpam-5687	131	69	sh1∥	sh1∥	PROPN
ejpam-5687	131	70	,	,	PUNCT
ejpam-5687	131	71	(	(	PUNCT
ejpam-5687	131	72	9	9	NUM
ejpam-5687	131	73	)	)	PUNCT
ejpam-5687	131	74	0	0	NUM
ejpam-5687	131	75	≤	≤	NUM
ejpam-5687	131	76	η1	η1	NOUN
ejpam-5687	131	77	<	<	X
ejpam-5687	131	78	1	1	NUM
ejpam-5687	131	79	and	and	CCONJ
ejpam-5687	131	80	ψ1	ψ1	ADJ
ejpam-5687	131	81	meet	meet	NOUN
ejpam-5687	131	82	lipschitz	lipschitz	NOUN
ejpam-5687	131	83	standards	standard	NOUN
ejpam-5687	131	84	.	.	PUNCT
ejpam-5687	132	1	by	by	ADP
ejpam-5687	132	2	using	use	VERB
ejpam-5687	132	3	the	the	DET
ejpam-5687	132	4	same	same	ADJ
ejpam-5687	132	5	procedure	procedure	NOUN
ejpam-5687	132	6	as	as	ADP
ejpam-5687	132	7	before	before	ADV
ejpam-5687	132	8	in	in	ADP
ejpam-5687	132	9	n.	n.	PROPN
ejpam-5687	132	10	ullah	ullah	PROPN
ejpam-5687	132	11	et	et	PROPN
ejpam-5687	132	12	al	al	PROPN
ejpam-5687	132	13	.	.	PUNCT
ejpam-5687	132	14	/	/	SYM
ejpam-5687	132	15	eur	eur	PROPN
ejpam-5687	132	16	.	.	PUNCT
ejpam-5687	133	1	j.	j.	PROPN
ejpam-5687	133	2	pure	pure	PROPN
ejpam-5687	133	3	appl	appl	PROPN
ejpam-5687	133	4	.	.	PROPN
ejpam-5687	133	5	math	math	PROPN
ejpam-5687	133	6	,	,	PUNCT
ejpam-5687	133	7	18	18	NUM
ejpam-5687	133	8	(	(	PUNCT
ejpam-5687	133	9	2	2	NUM
ejpam-5687	133	10	)	)	PUNCT
ejpam-5687	133	11	(	(	PUNCT
ejpam-5687	133	12	2025	2025	NUM
ejpam-5687	133	13	)	)	PUNCT
ejpam-5687	133	14	,	,	PUNCT
ejpam-5687	133	15	5687	5687	NUM
ejpam-5687	133	16	8	8	NUM
ejpam-5687	133	17	of	of	ADP
ejpam-5687	133	18	25	25	NUM
ejpam-5687	133	19	(	(	PUNCT
ejpam-5687	133	20	8)	8)	NUM
ejpam-5687	133	21	and	and	CCONJ
ejpam-5687	133	22	(	(	PUNCT
ejpam-5687	133	23	9	9	NUM
ejpam-5687	133	24	)	)	PUNCT
ejpam-5687	133	25	,	,	PUNCT
ejpam-5687	133	26	we	we	PRON
ejpam-5687	133	27	can	can	AUX
ejpam-5687	133	28	get	get	VERB
ejpam-5687	133	29	∥ψ2	∥ψ2	NOUN
ejpam-5687	134	1	−	−	PROPN
ejpam-5687	134	2	ψ2∥	ψ2∥	PROPN
ejpam-5687	134	3	≤	≤	X
ejpam-5687	134	4	η2	η2	PROPN
ejpam-5687	134	5	∥eh	∥eh	PROPN
ejpam-5687	134	6	−	−	PROPN
ejpam-5687	134	7	eh1∥	eh1∥	PROPN
ejpam-5687	134	8	,	,	PUNCT
ejpam-5687	134	9	∥ψ3	∥ψ3	NOUN
ejpam-5687	135	1	−	−	PROPN
ejpam-5687	135	2	ψ3∥	ψ3∥	ADJ
ejpam-5687	135	3	≤	≤	NUM
ejpam-5687	135	4	η3	η3	PROPN
ejpam-5687	135	5	∥ih	∥ih	VERB
ejpam-5687	135	6	−	−	PROPN
ejpam-5687	135	7	ih1∥	ih1∥	PROPN
ejpam-5687	135	8	,	,	PUNCT
ejpam-5687	135	9	∥ψ4	∥ψ4	VERB
ejpam-5687	135	10	−	−	PROPN
ejpam-5687	135	11	ψ4∥	ψ4∥	PROPN
ejpam-5687	135	12	≤	≤	PROPN
ejpam-5687	135	13	η4	η4	VERB
ejpam-5687	135	14	∥rh	∥rh	PROPN
ejpam-5687	135	15	−rh1∥	−rh1∥	PROPN
ejpam-5687	135	16	,	,	PUNCT
ejpam-5687	135	17	∥ψ5	∥ψ5	X
ejpam-5687	136	1	−	−	PROPN
ejpam-5687	136	2	ψ5∥	ψ5∥	PROPN
ejpam-5687	136	3	≤	≤	PROPN
ejpam-5687	136	4	η5	η5	PROPN
ejpam-5687	136	5	∥sv	∥sv	PROPN
ejpam-5687	136	6	−	−	PROPN
ejpam-5687	136	7	sv1∥	sv1∥	PROPN
ejpam-5687	136	8	,	,	PUNCT
ejpam-5687	136	9	∥ψ6	∥ψ6	VERB
ejpam-5687	136	10	−	−	PROPN
ejpam-5687	136	11	ψ6∥	ψ6∥	PROPN
ejpam-5687	136	12	≤	≤	PUNCT
ejpam-5687	136	13	η6	η6	PROPN
ejpam-5687	136	14	∥ev	∥ev	CCONJ
ejpam-5687	136	15	−	−	PROPN
ejpam-5687	136	16	ev1∥	ev1∥	PROPN
ejpam-5687	136	17	,	,	PUNCT
ejpam-5687	136	18	∥ψ7	∥ψ7	X
ejpam-5687	136	19	−	−	ADP
ejpam-5687	136	20	ψ7∥	ψ7∥	NOUN
ejpam-5687	136	21	≤	≤	NUM
ejpam-5687	136	22	η7	η7	NOUN
ejpam-5687	136	23	∥iv	∥iv	PROPN
ejpam-5687	136	24	−	−	PROPN
ejpam-5687	136	25	iv1∥	iv1∥	PROPN
ejpam-5687	136	26	.	.	PUNCT
ejpam-5687	137	1	(	(	PUNCT
ejpam-5687	137	2	10	10	NUM
ejpam-5687	137	3	)	)	PUNCT
ejpam-5687	137	4	in	in	ADP
ejpam-5687	137	5	the	the	DET
ejpam-5687	137	6	above	above	ADJ
ejpam-5687	137	7	(	(	PUNCT
ejpam-5687	137	8	10	10	NUM
ejpam-5687	137	9	)	)	PUNCT
ejpam-5687	137	10	,	,	PUNCT
ejpam-5687	137	11	we	we	PRON
ejpam-5687	137	12	have	have	VERB
ejpam-5687	137	13	η2	η2	ADJ
ejpam-5687	137	14	=	=	PUNCT
ejpam-5687	137	15	σh	σh	PROPN
ejpam-5687	137	16	+	+	PROPN
ejpam-5687	137	17	µh	µh	ADV
ejpam-5687	137	18	,	,	PUNCT
ejpam-5687	137	19	η3	η3	NOUN
ejpam-5687	137	20	=	=	PUNCT
ejpam-5687	137	21	γ	γ	X
ejpam-5687	137	22	+	+	X
ejpam-5687	137	23	µh	µh	PROPN
ejpam-5687	137	24	,	,	PUNCT
ejpam-5687	137	25	η4	η4	VERB
ejpam-5687	137	26	=	=	SYM
ejpam-5687	138	1	µh	µh	NOUN
ejpam-5687	138	2	,	,	PUNCT
ejpam-5687	138	3	η5	η5	PROPN
ejpam-5687	138	4	=	=	PUNCT
ejpam-5687	138	5	(	(	PUNCT
ejpam-5687	138	6	β2n5	β2n5	PUNCT
ejpam-5687	138	7	+	+	NUM
ejpam-5687	138	8	µh	µh	NOUN
ejpam-5687	138	9	)	)	PUNCT
ejpam-5687	138	10	,	,	PUNCT
ejpam-5687	138	11	n5	n5	PROPN
ejpam-5687	138	12	=	=	PUNCT
ejpam-5687	138	13	max	max	PROPN
ejpam-5687	138	14	u∈q	u∈q	PROPN
ejpam-5687	138	15	∥ih∥	∥ih∥	AUX
ejpam-5687	138	16	nh	nh	PROPN
ejpam-5687	138	17	,	,	PUNCT
ejpam-5687	138	18	η6	η6	PROPN
ejpam-5687	138	19	=	=	PUNCT
ejpam-5687	139	1	σv	σv	PROPN
ejpam-5687	139	2	+	+	CCONJ
ejpam-5687	139	3	µv	µv	NOUN
ejpam-5687	139	4	,	,	PUNCT
ejpam-5687	139	5	η7	η7	NOUN
ejpam-5687	139	6	=	=	SYM
ejpam-5687	139	7	µv	µv	NOUN
ejpam-5687	139	8	.	.	PUNCT
ejpam-5687	140	1	thus	thus	ADV
ejpam-5687	140	2	,	,	PUNCT
ejpam-5687	140	3	system	system	NOUN
ejpam-5687	140	4	(	(	PUNCT
ejpam-5687	140	5	6	6	NUM
ejpam-5687	140	6	)	)	PUNCT
ejpam-5687	140	7	reconstructed	reconstruct	VERB
ejpam-5687	140	8	the	the	PRON
ejpam-5687	140	9	as	as	SCONJ
ejpam-5687	140	10	follows	follow	VERB
ejpam-5687	140	11	as	as	ADP
ejpam-5687	140	12	system	system	NOUN
ejpam-5687	140	13	(	(	PUNCT
ejpam-5687	140	14	7	7	NUM
ejpam-5687	140	15	):	):	PUNCT
ejpam-5687	140	16	sh(u)−	sh(u)−	PROPN
ejpam-5687	140	17	sh(0	sh(0	NOUN
ejpam-5687	140	18	)	)	PUNCT
ejpam-5687	140	19	=	=	SYM
ejpam-5687	140	20	1	1	NUM
ejpam-5687	140	21	γ(p	γ(p	ADJ
ejpam-5687	140	22	)	)	PUNCT
ejpam-5687	140	23	∫	∫	PROPN
ejpam-5687	140	24	u	u	NOUN
ejpam-5687	140	25	0	0	NUM
ejpam-5687	141	1	(	(	PUNCT
ejpam-5687	141	2	u−	u−	PROPN
ejpam-5687	141	3	y)p−1ψ1(y	y)p−1ψ1(y	PROPN
ejpam-5687	141	4	,	,	PUNCT
ejpam-5687	141	5	sh(u))dy	sh(u))dy	PROPN
ejpam-5687	141	6	,	,	PUNCT
ejpam-5687	141	7	eh(u)−	eh(u)−	NOUN
ejpam-5687	141	8	eh(0	eh(0	NOUN
ejpam-5687	141	9	)	)	PUNCT
ejpam-5687	141	10	=	=	SYM
ejpam-5687	141	11	1	1	NUM
ejpam-5687	141	12	γ(p	γ(p	ADJ
ejpam-5687	141	13	)	)	PUNCT
ejpam-5687	141	14	∫	∫	PROPN
ejpam-5687	142	1	u	u	NOUN
ejpam-5687	142	2	0	0	NUM
ejpam-5687	142	3	(	(	PUNCT
ejpam-5687	142	4	u−	u−	PROPN
ejpam-5687	142	5	y)p−1ψ2(y	y)p−1ψ2(y	PROPN
ejpam-5687	142	6	,	,	PUNCT
ejpam-5687	142	7	eh(u))dy	eh(u))dy	PROPN
ejpam-5687	142	8	,	,	PUNCT
ejpam-5687	142	9	ih(u)−	ih(u)−	NOUN
ejpam-5687	142	10	ih(0	ih(0	NOUN
ejpam-5687	142	11	)	)	PUNCT
ejpam-5687	142	12	=	=	SYM
ejpam-5687	142	13	1	1	NUM
ejpam-5687	142	14	γ(p	γ(p	ADJ
ejpam-5687	142	15	)	)	PUNCT
ejpam-5687	142	16	∫	∫	PROPN
ejpam-5687	142	17	u	u	NOUN
ejpam-5687	142	18	0	0	NUM
ejpam-5687	142	19	(	(	PUNCT
ejpam-5687	142	20	u−	u−	PROPN
ejpam-5687	142	21	y)p−1ψ3(y	y)p−1ψ3(y	ADJ
ejpam-5687	142	22	,	,	PUNCT
ejpam-5687	142	23	ih(u))dy	ih(u))dy	NOUN
ejpam-5687	142	24	,	,	PUNCT
ejpam-5687	142	25	rh(u)−rh(0	rh(u)−rh(0	NOUN
ejpam-5687	142	26	)	)	PUNCT
ejpam-5687	142	27	=	=	SYM
ejpam-5687	142	28	1	1	NUM
ejpam-5687	142	29	γ(p	γ(p	ADJ
ejpam-5687	142	30	)	)	PUNCT
ejpam-5687	142	31	∫	∫	PROPN
ejpam-5687	142	32	u	u	NOUN
ejpam-5687	142	33	0	0	PROPN
ejpam-5687	143	1	(	(	PUNCT
ejpam-5687	143	2	u−	u−	PROPN
ejpam-5687	143	3	y)p−1ψ4(y	y)p−1ψ4(y	NOUN
ejpam-5687	143	4	,	,	PUNCT
ejpam-5687	143	5	rh(u))dy	rh(u))dy	PROPN
ejpam-5687	143	6	,	,	PUNCT
ejpam-5687	143	7	sv(u)−	sv(u)−	NOUN
ejpam-5687	143	8	sv(0	sv(0	NOUN
ejpam-5687	143	9	)	)	PUNCT
ejpam-5687	143	10	=	=	NOUN
ejpam-5687	143	11	1	1	NUM
ejpam-5687	143	12	γ(p	γ(p	ADJ
ejpam-5687	143	13	)	)	PUNCT
ejpam-5687	143	14	∫	∫	PROPN
ejpam-5687	144	1	u	u	NOUN
ejpam-5687	144	2	0	0	NUM
ejpam-5687	144	3	(	(	PUNCT
ejpam-5687	144	4	u−	u−	PROPN
ejpam-5687	144	5	y)p−1ψ5(y	y)p−1ψ5(y	ADJ
ejpam-5687	144	6	,	,	PUNCT
ejpam-5687	144	7	sv(u))dy	sv(u))dy	PROPN
ejpam-5687	144	8	,	,	PUNCT
ejpam-5687	144	9	ev(u)−	ev(u)−	PROPN
ejpam-5687	144	10	ev(0	ev(0	PROPN
ejpam-5687	144	11	)	)	PUNCT
ejpam-5687	144	12	=	=	SYM
ejpam-5687	144	13	1	1	NUM
ejpam-5687	144	14	γ(p	γ(p	ADJ
ejpam-5687	144	15	)	)	PUNCT
ejpam-5687	144	16	∫	∫	PROPN
ejpam-5687	144	17	u	u	NOUN
ejpam-5687	144	18	0	0	PROPN
ejpam-5687	144	19	(	(	PUNCT
ejpam-5687	144	20	u−	u−	PROPN
ejpam-5687	144	21	y)p−1ψ6(y	y)p−1ψ6(y	ADJ
ejpam-5687	144	22	,	,	PUNCT
ejpam-5687	144	23	ev(u))dy	ev(u))dy	ADJ
ejpam-5687	144	24	,	,	PUNCT
ejpam-5687	144	25	iv(u)−	iv(u)−	ADP
ejpam-5687	144	26	iv(0	iv(0	NOUN
ejpam-5687	144	27	)	)	PUNCT
ejpam-5687	144	28	=	=	SYM
ejpam-5687	144	29	1	1	NUM
ejpam-5687	144	30	γ(p	γ(p	ADJ
ejpam-5687	144	31	)	)	PUNCT
ejpam-5687	144	32	∫	∫	PROPN
ejpam-5687	144	33	u	u	NOUN
ejpam-5687	144	34	0	0	NUM
ejpam-5687	145	1	(	(	PUNCT
ejpam-5687	145	2	u−	u−	PROPN
ejpam-5687	145	3	y)p−1ψ7(y	y)p−1ψ7(y	NOUN
ejpam-5687	145	4	,	,	PUNCT
ejpam-5687	145	5	ih(u))dy	ih(u))dy	PROPN
ejpam-5687	145	6	.	.	PUNCT
ejpam-5687	146	1	(	(	PUNCT
ejpam-5687	146	2	11	11	NUM
ejpam-5687	146	3	)	)	PUNCT
ejpam-5687	146	4	n.	n.	PROPN
ejpam-5687	146	5	ullah	ullah	PROPN
ejpam-5687	146	6	et	et	PROPN
ejpam-5687	146	7	al	al	PROPN
ejpam-5687	146	8	.	.	PUNCT
ejpam-5687	146	9	/	/	SYM
ejpam-5687	146	10	eur	eur	PROPN
ejpam-5687	146	11	.	.	PUNCT
ejpam-5687	147	1	j.	j.	PROPN
ejpam-5687	147	2	pure	pure	PROPN
ejpam-5687	147	3	appl	appl	PROPN
ejpam-5687	147	4	.	.	PROPN
ejpam-5687	147	5	math	math	PROPN
ejpam-5687	147	6	,	,	PUNCT
ejpam-5687	147	7	18	18	NUM
ejpam-5687	147	8	(	(	PUNCT
ejpam-5687	147	9	2	2	NUM
ejpam-5687	147	10	)	)	PUNCT
ejpam-5687	147	11	(	(	PUNCT
ejpam-5687	147	12	2025	2025	NUM
ejpam-5687	147	13	)	)	PUNCT
ejpam-5687	147	14	,	,	PUNCT
ejpam-5687	147	15	5687	5687	NUM
ejpam-5687	147	16	9	9	NUM
ejpam-5687	147	17	of	of	ADP
ejpam-5687	147	18	25	25	NUM
ejpam-5687	147	19	the	the	DET
ejpam-5687	147	20	recursive	recursive	ADJ
ejpam-5687	147	21	form	form	NOUN
ejpam-5687	147	22	of	of	ADP
ejpam-5687	147	23	(	(	PUNCT
ejpam-5687	147	24	11	11	NUM
ejpam-5687	147	25	)	)	PUNCT
ejpam-5687	147	26	is	be	AUX
ejpam-5687	147	27	as	as	SCONJ
ejpam-5687	147	28	follows	follow	VERB
ejpam-5687	147	29	:	:	PUNCT
ejpam-5687	147	30	shn(u	shn(u	NOUN
ejpam-5687	147	31	)	)	PUNCT
ejpam-5687	147	32	=	=	NOUN
ejpam-5687	147	33	1	1	NUM
ejpam-5687	147	34	γ(p	γ(p	ADJ
ejpam-5687	147	35	)	)	PUNCT
ejpam-5687	148	1	∫	∫	PROPN
ejpam-5687	148	2	u	u	NOUN
ejpam-5687	148	3	0	0	NUM
ejpam-5687	148	4	(	(	PUNCT
ejpam-5687	148	5	u−	u−	NUM
ejpam-5687	148	6	y)p−1ψ1	y)p−1ψ1	NOUN
ejpam-5687	148	7	(	(	PUNCT
ejpam-5687	148	8	y	y	NOUN
ejpam-5687	148	9	,	,	PUNCT
ejpam-5687	148	10	sh(n−1)(u	sh(n−1)(u	NUM
ejpam-5687	148	11	)	)	PUNCT
ejpam-5687	148	12	)	)	PUNCT
ejpam-5687	149	1	dy	dy	NOUN
ejpam-5687	149	2	,	,	PUNCT
ejpam-5687	149	3	ehn(u	ehn(u	PROPN
ejpam-5687	149	4	)	)	PUNCT
ejpam-5687	149	5	=	=	NOUN
ejpam-5687	149	6	1	1	NUM
ejpam-5687	149	7	γ(p	γ(p	ADJ
ejpam-5687	149	8	)	)	PUNCT
ejpam-5687	149	9	∫	∫	PROPN
ejpam-5687	149	10	u	u	NOUN
ejpam-5687	149	11	0	0	PROPN
ejpam-5687	150	1	(	(	PUNCT
ejpam-5687	150	2	u−	u−	PROPN
ejpam-5687	150	3	y)p−1ψ2	y)p−1ψ2	NOUN
ejpam-5687	150	4	(	(	PUNCT
ejpam-5687	150	5	y	y	PROPN
ejpam-5687	150	6	,	,	PUNCT
ejpam-5687	150	7	eh(n−1)(u	eh(n−1)(u	NUM
ejpam-5687	150	8	)	)	PUNCT
ejpam-5687	150	9	)	)	PUNCT
ejpam-5687	151	1	dy	dy	NOUN
ejpam-5687	151	2	,	,	PUNCT
ejpam-5687	151	3	ihn(u	ihn(u	NOUN
ejpam-5687	151	4	)	)	PUNCT
ejpam-5687	151	5	=	=	SYM
ejpam-5687	151	6	1	1	NUM
ejpam-5687	151	7	γ(p	γ(p	ADJ
ejpam-5687	151	8	)	)	PUNCT
ejpam-5687	151	9	∫	∫	PROPN
ejpam-5687	151	10	u	u	NOUN
ejpam-5687	151	11	0	0	NUM
ejpam-5687	151	12	(	(	PUNCT
ejpam-5687	151	13	u−	u−	NUM
ejpam-5687	151	14	y)p−1ψ3	y)p−1ψ3	NOUN
ejpam-5687	151	15	(	(	PUNCT
ejpam-5687	151	16	y	y	PROPN
ejpam-5687	151	17	,	,	PUNCT
ejpam-5687	151	18	ih(n−1)(u	ih(n−1)(u	ADJ
ejpam-5687	151	19	)	)	PUNCT
ejpam-5687	151	20	)	)	PUNCT
ejpam-5687	152	1	dy	dy	NOUN
ejpam-5687	152	2	,	,	PUNCT
ejpam-5687	152	3	rhn(u	rhn(u	PROPN
ejpam-5687	152	4	)	)	PUNCT
ejpam-5687	152	5	=	=	SYM
ejpam-5687	152	6	1	1	NUM
ejpam-5687	152	7	γ(p	γ(p	ADJ
ejpam-5687	152	8	)	)	PUNCT
ejpam-5687	152	9	∫	∫	PROPN
ejpam-5687	152	10	u	u	NOUN
ejpam-5687	152	11	0	0	NUM
ejpam-5687	152	12	(	(	PUNCT
ejpam-5687	152	13	u−	u−	PROPN
ejpam-5687	152	14	y)p−1ψ4	y)p−1ψ4	NOUN
ejpam-5687	152	15	(	(	PUNCT
ejpam-5687	152	16	y	y	PROPN
ejpam-5687	152	17	,	,	PUNCT
ejpam-5687	152	18	rh(n−1)(u	rh(n−1)(u	ADJ
ejpam-5687	152	19	)	)	PUNCT
ejpam-5687	152	20	)	)	PUNCT
ejpam-5687	153	1	dy	dy	NOUN
ejpam-5687	153	2	,	,	PUNCT
ejpam-5687	153	3	svn(u	svn(u	PROPN
ejpam-5687	153	4	)	)	PUNCT
ejpam-5687	153	5	=	=	SYM
ejpam-5687	153	6	1	1	NUM
ejpam-5687	153	7	γ(p	γ(p	ADJ
ejpam-5687	153	8	)	)	PUNCT
ejpam-5687	153	9	∫	∫	PROPN
ejpam-5687	153	10	u	u	NOUN
ejpam-5687	153	11	0	0	PROPN
ejpam-5687	154	1	(	(	PUNCT
ejpam-5687	154	2	u−	u−	PROPN
ejpam-5687	154	3	y)p−1ψ5	y)p−1ψ5	NOUN
ejpam-5687	154	4	(	(	PUNCT
ejpam-5687	154	5	y	y	NOUN
ejpam-5687	154	6	,	,	PUNCT
ejpam-5687	154	7	sv(n−1)(u	sv(n−1)(u	NUM
ejpam-5687	154	8	)	)	PUNCT
ejpam-5687	154	9	)	)	PUNCT
ejpam-5687	155	1	dy	dy	X
ejpam-5687	155	2	,	,	PUNCT
ejpam-5687	155	3	evn(u	evn(u	NOUN
ejpam-5687	155	4	)	)	PUNCT
ejpam-5687	155	5	=	=	SYM
ejpam-5687	155	6	1	1	NUM
ejpam-5687	155	7	γ(p	γ(p	ADJ
ejpam-5687	155	8	)	)	PUNCT
ejpam-5687	155	9	∫	∫	PROPN
ejpam-5687	155	10	u	u	NOUN
ejpam-5687	155	11	0	0	NUM
ejpam-5687	156	1	(	(	PUNCT
ejpam-5687	156	2	u−	u−	PROPN
ejpam-5687	156	3	y)p−1ψ6	y)p−1ψ6	NOUN
ejpam-5687	156	4	(	(	PUNCT
ejpam-5687	156	5	y	y	NOUN
ejpam-5687	156	6	,	,	PUNCT
ejpam-5687	156	7	ev(n−1)(u	ev(n−1)(u	NUM
ejpam-5687	156	8	)	)	PUNCT
ejpam-5687	156	9	)	)	PUNCT
ejpam-5687	157	1	dy	dy	NOUN
ejpam-5687	157	2	,	,	PUNCT
ejpam-5687	157	3	ivn(u	ivn(u	NOUN
ejpam-5687	157	4	)	)	PUNCT
ejpam-5687	157	5	=	=	SYM
ejpam-5687	157	6	1	1	NUM
ejpam-5687	157	7	γ(p	γ(p	ADJ
ejpam-5687	157	8	)	)	PUNCT
ejpam-5687	157	9	∫	∫	PROPN
ejpam-5687	157	10	u	u	NOUN
ejpam-5687	157	11	0	0	PROPN
ejpam-5687	158	1	(	(	PUNCT
ejpam-5687	158	2	u−	u−	PROPN
ejpam-5687	158	3	y)p−1ψ7	y)p−1ψ7	NOUN
ejpam-5687	158	4	(	(	PUNCT
ejpam-5687	158	5	y	y	NOUN
ejpam-5687	158	6	,	,	PUNCT
ejpam-5687	158	7	iv(n−1)(u	iv(n−1)(u	ADJ
ejpam-5687	158	8	)	)	PUNCT
ejpam-5687	158	9	)	)	PUNCT
ejpam-5687	159	1	dy	dy	NOUN
ejpam-5687	159	2	,	,	PUNCT
ejpam-5687	159	3	(	(	PUNCT
ejpam-5687	159	4	12	12	NUM
ejpam-5687	159	5	)	)	PUNCT
ejpam-5687	159	6	related	relate	VERB
ejpam-5687	159	7	to	to	ADP
ejpam-5687	159	8	sh0	sh0	NOUN
ejpam-5687	159	9	=	=	PUNCT
ejpam-5687	159	10	sh(0	sh(0	NOUN
ejpam-5687	159	11	)	)	PUNCT
ejpam-5687	159	12	,	,	PUNCT
ejpam-5687	159	13	eh0	eh0	VERB
ejpam-5687	159	14	=	=	SYM
ejpam-5687	159	15	eh(0	eh(0	NOUN
ejpam-5687	159	16	)	)	PUNCT
ejpam-5687	159	17	,	,	PUNCT
ejpam-5687	159	18	ih0	ih0	NOUN
ejpam-5687	159	19	=	=	PUNCT
ejpam-5687	159	20	ih(0	ih(0	NOUN
ejpam-5687	159	21	)	)	PUNCT
ejpam-5687	159	22	,	,	PUNCT
ejpam-5687	159	23	rh0	rh0	PROPN
ejpam-5687	159	24	=	=	PUNCT
ejpam-5687	159	25	rh(0	rh(0	NOUN
ejpam-5687	159	26	)	)	PUNCT
ejpam-5687	159	27	,	,	PUNCT
ejpam-5687	159	28	sh0	sh0	NOUN
ejpam-5687	159	29	=	=	SYM
ejpam-5687	159	30	sv(0	sv(0	PROPN
ejpam-5687	159	31	)	)	PUNCT
ejpam-5687	159	32	,	,	PUNCT
ejpam-5687	159	33	eh0	eh0	NOUN
ejpam-5687	159	34	and	and	CCONJ
ejpam-5687	159	35	iv0	iv0	NOUN
ejpam-5687	159	36	=	=	PROPN
ejpam-5687	159	37	iv(0	iv(0	PROPN
ejpam-5687	159	38	)	)	PUNCT
ejpam-5687	159	39	.	.	PUNCT
ejpam-5687	160	1	as	as	ADP
ejpam-5687	160	2	a	a	DET
ejpam-5687	160	3	result	result	NOUN
ejpam-5687	160	4	,	,	PUNCT
ejpam-5687	160	5	the	the	DET
ejpam-5687	160	6	difference	difference	NOUN
ejpam-5687	160	7	between	between	ADP
ejpam-5687	160	8	concepts	concept	NOUN
ejpam-5687	160	9	that	that	PRON
ejpam-5687	160	10	follow	follow	VERB
ejpam-5687	160	11	produces	produce	VERB
ejpam-5687	160	12	ξsh	ξsh	PRON
ejpam-5687	160	13	,	,	PUNCT
ejpam-5687	160	14	n(u	n(u	PROPN
ejpam-5687	160	15	)	)	PUNCT
ejpam-5687	160	16	=	=	PRON
ejpam-5687	160	17	shn(u)−	shn(u)−	VERB
ejpam-5687	160	18	sh(n−1)(u	sh(n−1)(u	NOUN
ejpam-5687	160	19	)	)	PUNCT
ejpam-5687	160	20	=	=	SYM
ejpam-5687	160	21	1	1	NUM
ejpam-5687	160	22	γ(p	γ(p	ADJ
ejpam-5687	160	23	)	)	PUNCT
ejpam-5687	160	24	∫	∫	PROPN
ejpam-5687	161	1	u	u	NOUN
ejpam-5687	161	2	0	0	PROPN
ejpam-5687	161	3	(	(	PUNCT
ejpam-5687	161	4	u−	u−	PROPN
ejpam-5687	161	5	y)p−1	y)p−1	NOUN
ejpam-5687	161	6	(	(	PUNCT
ejpam-5687	161	7	ψ1(x	ψ1(x	PROPN
ejpam-5687	161	8	,	,	PUNCT
ejpam-5687	161	9	sh(n−1)(y))−	sh(n−1)(y))−	PROPN
ejpam-5687	161	10	ψ1(y	ψ1(y	PROPN
ejpam-5687	161	11	,	,	PUNCT
ejpam-5687	161	12	sh(n−2)(y	sh(n−2)(y	NUM
ejpam-5687	161	13	)	)	PUNCT
ejpam-5687	161	14	)	)	PUNCT
ejpam-5687	161	15	)	)	PUNCT
ejpam-5687	162	1	dy	dy	NOUN
ejpam-5687	162	2	,	,	PUNCT
ejpam-5687	162	3	ξeh	ξeh	PROPN
ejpam-5687	162	4	,	,	PUNCT
ejpam-5687	162	5	n(u	n(u	PROPN
ejpam-5687	162	6	)	)	PUNCT
ejpam-5687	162	7	=	=	PRON
ejpam-5687	163	1	ehn(u)−	ehn(u)−	NOUN
ejpam-5687	163	2	eh(n−1)(u	eh(n−1)(u	NOUN
ejpam-5687	163	3	)	)	PUNCT
ejpam-5687	163	4	=	=	SYM
ejpam-5687	163	5	1	1	NUM
ejpam-5687	163	6	γ(p	γ(p	ADJ
ejpam-5687	163	7	)	)	PUNCT
ejpam-5687	163	8	∫	∫	PROPN
ejpam-5687	164	1	u	u	NOUN
ejpam-5687	164	2	0	0	PROPN
ejpam-5687	164	3	(	(	PUNCT
ejpam-5687	164	4	u−	u−	PROPN
ejpam-5687	164	5	y)p−1	y)p−1	NOUN
ejpam-5687	164	6	(	(	PUNCT
ejpam-5687	164	7	ψ2(x	ψ2(x	PROPN
ejpam-5687	164	8	,	,	PUNCT
ejpam-5687	164	9	eh(n−1)(y))−	eh(n−1)(y))−	NOUN
ejpam-5687	164	10	ψ2(y	ψ2(y	SYM
ejpam-5687	164	11	,	,	PUNCT
ejpam-5687	164	12	eh(n−2)(y	eh(n−2)(y	NUM
ejpam-5687	164	13	)	)	PUNCT
ejpam-5687	164	14	)	)	PUNCT
ejpam-5687	164	15	)	)	PUNCT
ejpam-5687	165	1	dy	dy	NOUN
ejpam-5687	165	2	,	,	PUNCT
ejpam-5687	165	3	ξih	ξih	NOUN
ejpam-5687	165	4	,	,	PUNCT
ejpam-5687	165	5	n(u	n(u	PROPN
ejpam-5687	165	6	)	)	PUNCT
ejpam-5687	165	7	=	=	NOUN
ejpam-5687	166	1	ihn(u)−	ihn(u)−	PROPN
ejpam-5687	166	2	ih(n−1)(u	ih(n−1)(u	VERB
ejpam-5687	166	3	)	)	PUNCT
ejpam-5687	166	4	=	=	SYM
ejpam-5687	166	5	1	1	NUM
ejpam-5687	166	6	γ(p	γ(p	ADJ
ejpam-5687	166	7	)	)	PUNCT
ejpam-5687	166	8	∫	∫	PROPN
ejpam-5687	167	1	u	u	NOUN
ejpam-5687	167	2	0	0	PROPN
ejpam-5687	167	3	(	(	PUNCT
ejpam-5687	167	4	u−	u−	PROPN
ejpam-5687	167	5	y)p−1	y)p−1	NOUN
ejpam-5687	167	6	(	(	PUNCT
ejpam-5687	167	7	ψ3(x	ψ3(x	PROPN
ejpam-5687	167	8	,	,	PUNCT
ejpam-5687	167	9	ih(n−1)(y))−	ih(n−1)(y))−	ADJ
ejpam-5687	167	10	ψ3(y	ψ3(y	NOUN
ejpam-5687	167	11	,	,	PUNCT
ejpam-5687	167	12	ih(n−2)(y	ih(n−2)(y	NOUN
ejpam-5687	167	13	)	)	PUNCT
ejpam-5687	167	14	)	)	PUNCT
ejpam-5687	167	15	)	)	PUNCT
ejpam-5687	168	1	dy	dy	NOUN
ejpam-5687	168	2	,	,	PUNCT
ejpam-5687	168	3	ξrh	ξrh	ADV
ejpam-5687	168	4	,	,	PUNCT
ejpam-5687	168	5	n(u	n(u	PROPN
ejpam-5687	168	6	)	)	PUNCT
ejpam-5687	168	7	=	=	PUNCT
ejpam-5687	168	8	rhn(u)−rh(n−1)(u	rhn(u)−rh(n−1)(u	NOUN
ejpam-5687	168	9	)	)	PUNCT
ejpam-5687	168	10	=	=	SYM
ejpam-5687	168	11	1	1	NUM
ejpam-5687	168	12	γ(p	γ(p	ADJ
ejpam-5687	168	13	)	)	PUNCT
ejpam-5687	168	14	∫	∫	PROPN
ejpam-5687	169	1	u	u	NOUN
ejpam-5687	169	2	0	0	PROPN
ejpam-5687	169	3	(	(	PUNCT
ejpam-5687	169	4	u−	u−	INTJ
ejpam-5687	169	5	y)p−1	y)p−1	NOUN
ejpam-5687	169	6	(	(	PUNCT
ejpam-5687	169	7	ψ4(x	ψ4(x	ADV
ejpam-5687	169	8	,	,	PUNCT
ejpam-5687	169	9	rh(n−1)(y))−	rh(n−1)(y))−	VERB
ejpam-5687	169	10	ψ4(y	ψ4(y	PROPN
ejpam-5687	169	11	,	,	PUNCT
ejpam-5687	169	12	rh(n−2)(y	rh(n−2)(y	PROPN
ejpam-5687	169	13	)	)	PUNCT
ejpam-5687	169	14	)	)	PUNCT
ejpam-5687	169	15	)	)	PUNCT
ejpam-5687	170	1	dy	dy	NOUN
ejpam-5687	170	2	,	,	PUNCT
ejpam-5687	170	3	ξsv	ξsv	PROPN
ejpam-5687	170	4	,	,	PUNCT
ejpam-5687	170	5	n(u	n(u	PROPN
ejpam-5687	170	6	)	)	PUNCT
ejpam-5687	170	7	=	=	PUNCT
ejpam-5687	171	1	svn(u)−	svn(u)−	NOUN
ejpam-5687	171	2	sv(n−1)(u	sv(n−1)(u	VERB
ejpam-5687	171	3	)	)	PUNCT
ejpam-5687	171	4	=	=	SYM
ejpam-5687	171	5	1	1	NUM
ejpam-5687	171	6	γ(p	γ(p	ADJ
ejpam-5687	171	7	)	)	PUNCT
ejpam-5687	171	8	∫	∫	PROPN
ejpam-5687	171	9	u	u	NOUN
ejpam-5687	171	10	0	0	PROPN
ejpam-5687	171	11	(	(	PUNCT
ejpam-5687	171	12	u−	u−	INTJ
ejpam-5687	171	13	y)p−1	y)p−1	NOUN
ejpam-5687	171	14	(	(	PUNCT
ejpam-5687	171	15	ψ5(x	ψ5(x	NOUN
ejpam-5687	171	16	,	,	PUNCT
ejpam-5687	171	17	sv(n−1)(y))−	sv(n−1)(y))−	AUX
ejpam-5687	171	18	ψ5(y	ψ5(y	NOUN
ejpam-5687	171	19	,	,	PUNCT
ejpam-5687	171	20	sv(n−2)(y	sv(n−2)(y	NOUN
ejpam-5687	171	21	)	)	PUNCT
ejpam-5687	171	22	)	)	PUNCT
ejpam-5687	171	23	)	)	PUNCT
ejpam-5687	172	1	dy	dy	NOUN
ejpam-5687	172	2	,	,	PUNCT
ejpam-5687	172	3	ξev	ξev	PROPN
ejpam-5687	172	4	,	,	PUNCT
ejpam-5687	172	5	n(u	n(u	PROPN
ejpam-5687	172	6	)	)	PUNCT
ejpam-5687	172	7	=	=	PRON
ejpam-5687	173	1	evn(u)−	evn(u)−	NOUN
ejpam-5687	173	2	ev(n−1)(u	ev(n−1)(u	NOUN
ejpam-5687	173	3	)	)	PUNCT
ejpam-5687	173	4	=	=	SYM
ejpam-5687	173	5	1	1	NUM
ejpam-5687	173	6	γ(p	γ(p	ADJ
ejpam-5687	173	7	)	)	PUNCT
ejpam-5687	173	8	∫	∫	PROPN
ejpam-5687	173	9	u	u	NOUN
ejpam-5687	173	10	0	0	PROPN
ejpam-5687	174	1	(	(	PUNCT
ejpam-5687	174	2	u−	u−	PROPN
ejpam-5687	174	3	y)p−1	y)p−1	NOUN
ejpam-5687	174	4	(	(	PUNCT
ejpam-5687	174	5	ψ6(x	ψ6(x	PROPN
ejpam-5687	174	6	,	,	PUNCT
ejpam-5687	174	7	ev(n−1)(y))−	ev(n−1)(y))−	NOUN
ejpam-5687	174	8	ψ6(y	ψ6(y	PROPN
ejpam-5687	174	9	,	,	PUNCT
ejpam-5687	174	10	ev(n−2)(y	ev(n−2)(y	NUM
ejpam-5687	174	11	)	)	PUNCT
ejpam-5687	174	12	)	)	PUNCT
ejpam-5687	174	13	)	)	PUNCT
ejpam-5687	175	1	dy	dy	NOUN
ejpam-5687	175	2	,	,	PUNCT
ejpam-5687	175	3	ξiv	ξiv	NOUN
ejpam-5687	175	4	,	,	PUNCT
ejpam-5687	175	5	n(u	n(u	PROPN
ejpam-5687	175	6	)	)	PUNCT
ejpam-5687	175	7	=	=	PUNCT
ejpam-5687	176	1	ivn(u)−	ivn(u)−	NOUN
ejpam-5687	176	2	iv(n−1)(u	iv(n−1)(u	ADJ
ejpam-5687	176	3	)	)	PUNCT
ejpam-5687	176	4	=	=	SYM
ejpam-5687	176	5	1	1	NUM
ejpam-5687	176	6	γ(p	γ(p	ADJ
ejpam-5687	176	7	)	)	PUNCT
ejpam-5687	176	8	∫	∫	PROPN
ejpam-5687	177	1	u	u	NOUN
ejpam-5687	177	2	0	0	PROPN
ejpam-5687	177	3	(	(	PUNCT
ejpam-5687	177	4	u−	u−	PROPN
ejpam-5687	177	5	y)p−1	y)p−1	NOUN
ejpam-5687	177	6	(	(	PUNCT
ejpam-5687	177	7	ψ7(x	ψ7(x	PROPN
ejpam-5687	177	8	,	,	PUNCT
ejpam-5687	177	9	iv(n−1)(y))−	iv(n−1)(y))−	NUM
ejpam-5687	177	10	ψ7(y	ψ7(y	PROPN
ejpam-5687	177	11	,	,	PUNCT
ejpam-5687	177	12	iv(n−2)(y	iv(n−2)(y	NOUN
ejpam-5687	177	13	)	)	PUNCT
ejpam-5687	177	14	)	)	PUNCT
ejpam-5687	177	15	)	)	PUNCT
ejpam-5687	178	1	dy	dy	NOUN
ejpam-5687	178	2	.	.	PUNCT
ejpam-5687	179	1	(	(	PUNCT
ejpam-5687	179	2	13	13	NUM
ejpam-5687	179	3	)	)	PUNCT
ejpam-5687	179	4	n.	n.	PROPN
ejpam-5687	179	5	ullah	ullah	PROPN
ejpam-5687	179	6	et	et	PROPN
ejpam-5687	179	7	al	al	PROPN
ejpam-5687	179	8	.	.	PUNCT
ejpam-5687	179	9	/	/	SYM
ejpam-5687	179	10	eur	eur	PROPN
ejpam-5687	179	11	.	.	PUNCT
ejpam-5687	180	1	j.	j.	PROPN
ejpam-5687	180	2	pure	pure	PROPN
ejpam-5687	180	3	appl	appl	PROPN
ejpam-5687	180	4	.	.	PROPN
ejpam-5687	180	5	math	math	PROPN
ejpam-5687	180	6	,	,	PUNCT
ejpam-5687	180	7	18	18	NUM
ejpam-5687	180	8	(	(	PUNCT
ejpam-5687	180	9	2	2	NUM
ejpam-5687	180	10	)	)	PUNCT
ejpam-5687	180	11	(	(	PUNCT
ejpam-5687	180	12	2025	2025	NUM
ejpam-5687	180	13	)	)	PUNCT
ejpam-5687	180	14	,	,	PUNCT
ejpam-5687	180	15	5687	5687	NUM
ejpam-5687	180	16	10	10	NUM
ejpam-5687	180	17	of	of	ADP
ejpam-5687	180	18	25	25	NUM
ejpam-5687	180	19	assuming	assume	VERB
ejpam-5687	180	20	that	that	SCONJ
ejpam-5687	180	21	shn(u	shn(u	NOUN
ejpam-5687	180	22	)	)	PUNCT
ejpam-5687	180	23	=	=	SYM
ejpam-5687	180	24	n∑	n∑	PROPN
ejpam-5687	180	25	j=0	j=0	PROPN
ejpam-5687	180	26	ξshn	ξshn	PROPN
ejpam-5687	180	27	,	,	PUNCT
ejpam-5687	180	28	j(u	j(u	PROPN
ejpam-5687	180	29	)	)	PUNCT
ejpam-5687	180	30	,	,	PUNCT
ejpam-5687	180	31	ehn(u	ehn(u	PROPN
ejpam-5687	180	32	)	)	PUNCT
ejpam-5687	180	33	=	=	SYM
ejpam-5687	180	34	n∑	n∑	ADJ
ejpam-5687	180	35	j=0	j=0	PROPN
ejpam-5687	180	36	ξehn	ξehn	PROPN
ejpam-5687	180	37	,	,	PUNCT
ejpam-5687	180	38	j(u	j(u	PROPN
ejpam-5687	180	39	)	)	PUNCT
ejpam-5687	180	40	,	,	PUNCT
ejpam-5687	180	41	ihn(u	ihn(u	NOUN
ejpam-5687	180	42	)	)	PUNCT
ejpam-5687	180	43	=	=	SYM
ejpam-5687	180	44	n∑	n∑	PROPN
ejpam-5687	180	45	j=0	j=0	PROPN
ejpam-5687	180	46	ξihn	ξihn	NOUN
ejpam-5687	180	47	,	,	PUNCT
ejpam-5687	180	48	j(u	j(u	PROPN
ejpam-5687	180	49	)	)	PUNCT
ejpam-5687	180	50	,	,	PUNCT
ejpam-5687	180	51	rhn(u	rhn(u	PROPN
ejpam-5687	180	52	)	)	PUNCT
ejpam-5687	180	53	=	=	SYM
ejpam-5687	180	54	n∑	n∑	PROPN
ejpam-5687	180	55	j=0	j=0	PROPN
ejpam-5687	180	56	ξrhn	ξrhn	PROPN
ejpam-5687	180	57	,	,	PUNCT
ejpam-5687	180	58	j(u	j(u	PROPN
ejpam-5687	180	59	)	)	PUNCT
ejpam-5687	180	60	,	,	PUNCT
ejpam-5687	180	61	svn(u	svn(u	PROPN
ejpam-5687	180	62	)	)	PUNCT
ejpam-5687	180	63	=	=	SYM
ejpam-5687	180	64	n∑	n∑	NOUN
ejpam-5687	180	65	j=0	j=0	PROPN
ejpam-5687	180	66	ξsvn	ξsvn	NOUN
ejpam-5687	180	67	,	,	PUNCT
ejpam-5687	180	68	j(u	j(u	PROPN
ejpam-5687	180	69	)	)	PUNCT
ejpam-5687	180	70	,	,	PUNCT
ejpam-5687	180	71	evn(u	evn(u	NOUN
ejpam-5687	180	72	)	)	PUNCT
ejpam-5687	180	73	=	=	SYM
ejpam-5687	180	74	n∑	n∑	PROPN
ejpam-5687	180	75	j=0	j=0	PROPN
ejpam-5687	180	76	ξevn	ξevn	NOUN
ejpam-5687	180	77	,	,	PUNCT
ejpam-5687	180	78	j(u	j(u	PROPN
ejpam-5687	180	79	)	)	PUNCT
ejpam-5687	180	80	,	,	PUNCT
ejpam-5687	180	81	ivn(u	ivn(u	NOUN
ejpam-5687	180	82	)	)	PUNCT
ejpam-5687	180	83	=	=	SYM
ejpam-5687	181	1	n∑	n∑	PROPN
ejpam-5687	181	2	j=0	j=0	PROPN
ejpam-5687	181	3	ξivn	ξivn	PROPN
ejpam-5687	181	4	,	,	PUNCT
ejpam-5687	181	5	j(u	j(u	PROPN
ejpam-5687	181	6	)	)	PUNCT
ejpam-5687	181	7	.	.	PUNCT
ejpam-5687	182	1	(	(	PUNCT
ejpam-5687	182	2	14	14	NUM
ejpam-5687	182	3	)	)	PUNCT
ejpam-5687	182	4	thus	thus	ADV
ejpam-5687	182	5	,	,	PUNCT
ejpam-5687	182	6	based	base	VERB
ejpam-5687	182	7	on	on	ADP
ejpam-5687	182	8	equations	equation	NOUN
ejpam-5687	182	9	(	(	PUNCT
ejpam-5687	182	10	9	9	NUM
ejpam-5687	182	11	)	)	PUNCT
ejpam-5687	182	12	and	and	CCONJ
ejpam-5687	182	13	(	(	PUNCT
ejpam-5687	182	14	10	10	NUM
ejpam-5687	182	15	)	)	PUNCT
ejpam-5687	182	16	as	as	ADV
ejpam-5687	182	17	well	well	ADV
ejpam-5687	182	18	as	as	ADP
ejpam-5687	182	19	the	the	DET
ejpam-5687	182	20	relationships	relationship	NOUN
ejpam-5687	182	21			NUM
ejpam-5687	182	22	ξsh	ξsh	NUM
ejpam-5687	182	23	,	,	PUNCT
ejpam-5687	182	24	n−1(u	n−1(u	NOUN
ejpam-5687	182	25	)	)	PUNCT
ejpam-5687	182	26	=	=	SYM
ejpam-5687	182	27	sh(n−1)(u)−	sh(n−1)(u)−	NOUN
ejpam-5687	182	28	sh(n−2)(u	sh(n−2)(u	NUM
ejpam-5687	182	29	)	)	PUNCT
ejpam-5687	182	30	,	,	PUNCT
ejpam-5687	182	31	ξeh	ξeh	NOUN
ejpam-5687	182	32	,	,	PUNCT
ejpam-5687	182	33	n−1(u	n−1(u	NOUN
ejpam-5687	182	34	)	)	PUNCT
ejpam-5687	182	35	=	=	PRON
ejpam-5687	182	36	eh(n−1)(u)−	eh(n−1)(u)−	NOUN
ejpam-5687	182	37	eh(n−2)(u	eh(n−2)(u	NUM
ejpam-5687	182	38	)	)	PUNCT
ejpam-5687	182	39	,	,	PUNCT
ejpam-5687	182	40	ξih	ξih	NOUN
ejpam-5687	182	41	,	,	PUNCT
ejpam-5687	182	42	n−1(u	n−1(u	NOUN
ejpam-5687	182	43	)	)	PUNCT
ejpam-5687	182	44	=	=	SYM
ejpam-5687	183	1	ih(n−1)(u)−	ih(n−1)(u)−	NOUN
ejpam-5687	183	2	ih(n−2)(u	ih(n−2)(u	NUM
ejpam-5687	183	3	)	)	PUNCT
ejpam-5687	183	4	,	,	PUNCT
ejpam-5687	183	5	ξrh	ξrh	ADV
ejpam-5687	183	6	,	,	PUNCT
ejpam-5687	183	7	n−1(u	n−1(u	NOUN
ejpam-5687	183	8	)	)	PUNCT
ejpam-5687	183	9	=	=	PUNCT
ejpam-5687	183	10	rh(n−1)(u)−rh(n−2)(u	rh(n−1)(u)−rh(n−2)(u	PROPN
ejpam-5687	183	11	)	)	PUNCT
ejpam-5687	183	12	,	,	PUNCT
ejpam-5687	183	13	ξsv	ξsv	INTJ
ejpam-5687	183	14	,	,	PUNCT
ejpam-5687	183	15	n−1(u	n−1(u	NOUN
ejpam-5687	183	16	)	)	PUNCT
ejpam-5687	183	17	=	=	NOUN
ejpam-5687	183	18	sv(n−1)(u)−	sv(n−1)(u)−	NOUN
ejpam-5687	183	19	sv(n−2)(u	sv(n−2)(u	ADJ
ejpam-5687	183	20	)	)	PUNCT
ejpam-5687	183	21	,	,	PUNCT
ejpam-5687	183	22	ξev	ξev	PROPN
ejpam-5687	183	23	,	,	PUNCT
ejpam-5687	183	24	n−1(u	n−1(u	NOUN
ejpam-5687	183	25	)	)	PUNCT
ejpam-5687	183	26	=	=	NOUN
ejpam-5687	183	27	ev(n−1)(u)−	ev(n−1)(u)−	NOUN
ejpam-5687	183	28	ev(n−2)(u	ev(n−2)(u	VERB
ejpam-5687	183	29	)	)	PUNCT
ejpam-5687	183	30	,	,	PUNCT
ejpam-5687	183	31	ξiv	ξiv	VERB
ejpam-5687	183	32	,	,	PUNCT
ejpam-5687	183	33	n−1(u	n−1(u	NOUN
ejpam-5687	183	34	)	)	PUNCT
ejpam-5687	184	1	=	=	PRON
ejpam-5687	184	2	iv(n−1)(u)−	iv(n−1)(u)−	NOUN
ejpam-5687	184	3	iv(n−2)(u	iv(n−2)(u	ADJ
ejpam-5687	184	4	)	)	PUNCT
ejpam-5687	184	5	.	.	PUNCT
ejpam-5687	185	1	(	(	PUNCT
ejpam-5687	185	2	15	15	X
ejpam-5687	185	3	)	)	PUNCT
ejpam-5687	185	4	n.	n.	PROPN
ejpam-5687	185	5	ullah	ullah	PROPN
ejpam-5687	185	6	et	et	PROPN
ejpam-5687	185	7	al	al	PROPN
ejpam-5687	185	8	.	.	PUNCT
ejpam-5687	185	9	/	/	SYM
ejpam-5687	185	10	eur	eur	PROPN
ejpam-5687	185	11	.	.	PUNCT
ejpam-5687	186	1	j.	j.	PROPN
ejpam-5687	186	2	pure	pure	PROPN
ejpam-5687	186	3	appl	appl	PROPN
ejpam-5687	186	4	.	.	PROPN
ejpam-5687	186	5	math	math	PROPN
ejpam-5687	186	6	,	,	PUNCT
ejpam-5687	186	7	18	18	NUM
ejpam-5687	186	8	(	(	PUNCT
ejpam-5687	186	9	2	2	NUM
ejpam-5687	186	10	)	)	PUNCT
ejpam-5687	186	11	(	(	PUNCT
ejpam-5687	186	12	2025	2025	NUM
ejpam-5687	186	13	)	)	PUNCT
ejpam-5687	186	14	,	,	PUNCT
ejpam-5687	186	15	5687	5687	NUM
ejpam-5687	186	16	11	11	NUM
ejpam-5687	186	17	of	of	ADP
ejpam-5687	186	18	25	25	NUM
ejpam-5687	186	19	provides	provide	VERB
ejpam-5687	186	20	∥ξsh	∥ξsh	NOUN
ejpam-5687	186	21	,	,	PUNCT
ejpam-5687	186	22	n∥	n∥	NOUN
ejpam-5687	186	23	=	=	NOUN
ejpam-5687	186	24	η1	η1	NOUN
ejpam-5687	186	25	γ(p	γ(p	PROPN
ejpam-5687	186	26	)	)	PUNCT
ejpam-5687	186	27	∫	∫	PROPN
ejpam-5687	186	28	u	u	NOUN
ejpam-5687	186	29	0	0	NUM
ejpam-5687	186	30	∥ξsh	∥ξsh	X
ejpam-5687	186	31	,	,	PUNCT
ejpam-5687	186	32	n−1∥	n−1∥	NOUN
ejpam-5687	186	33	(	(	PUNCT
ejpam-5687	186	34	u−	u−	PROPN
ejpam-5687	186	35	y)p−1dy	y)p−1dy	PROPN
ejpam-5687	186	36	,	,	PUNCT
ejpam-5687	186	37	∥ξeh	∥ξeh	PROPN
ejpam-5687	186	38	,	,	PUNCT
ejpam-5687	187	1	n∥	n∥	NOUN
ejpam-5687	187	2	=	=	SYM
ejpam-5687	187	3	η2	η2	VERB
ejpam-5687	187	4	γ(p	γ(p	PROPN
ejpam-5687	187	5	)	)	PUNCT
ejpam-5687	187	6	∫	∫	PROPN
ejpam-5687	187	7	u	u	NOUN
ejpam-5687	187	8	0	0	PROPN
ejpam-5687	187	9	∥ξeh	∥ξeh	PROPN
ejpam-5687	187	10	,	,	PUNCT
ejpam-5687	187	11	n−1∥	n−1∥	NOUN
ejpam-5687	187	12	(	(	PUNCT
ejpam-5687	187	13	u−	u−	PROPN
ejpam-5687	187	14	y)p−1dy	y)p−1dy	PROPN
ejpam-5687	187	15	,	,	PUNCT
ejpam-5687	187	16	∥ξih	∥ξih	ADV
ejpam-5687	187	17	,	,	PUNCT
ejpam-5687	187	18	n∥	n∥	NOUN
ejpam-5687	187	19	=	=	SYM
ejpam-5687	187	20	η3	η3	PROPN
ejpam-5687	187	21	γ(p	γ(p	PROPN
ejpam-5687	187	22	)	)	PUNCT
ejpam-5687	187	23	∫	∫	PROPN
ejpam-5687	187	24	u	u	NOUN
ejpam-5687	187	25	0	0	PROPN
ejpam-5687	187	26	∥ξih	∥ξih	NOUN
ejpam-5687	187	27	,	,	PUNCT
ejpam-5687	187	28	n−1∥	n−1∥	NOUN
ejpam-5687	187	29	(	(	PUNCT
ejpam-5687	187	30	u−	u−	PROPN
ejpam-5687	187	31	y)p−1dy	y)p−1dy	PROPN
ejpam-5687	187	32	,	,	PUNCT
ejpam-5687	187	33	∥ξrh	∥ξrh	PROPN
ejpam-5687	187	34	,	,	PUNCT
ejpam-5687	187	35	n∥	n∥	NOUN
ejpam-5687	187	36	=	=	VERB
ejpam-5687	187	37	η4	η4	VERB
ejpam-5687	187	38	γ(p	γ(p	PROPN
ejpam-5687	187	39	)	)	PUNCT
ejpam-5687	187	40	∫	∫	PROPN
ejpam-5687	187	41	u	u	NOUN
ejpam-5687	187	42	0	0	PROPN
ejpam-5687	187	43	∥ξrh	∥ξrh	PROPN
ejpam-5687	187	44	,	,	PUNCT
ejpam-5687	187	45	n−1∥	n−1∥	NOUN
ejpam-5687	187	46	(	(	PUNCT
ejpam-5687	187	47	u−	u−	PROPN
ejpam-5687	187	48	y)p−1dy	y)p−1dy	PROPN
ejpam-5687	187	49	,	,	PUNCT
ejpam-5687	187	50	∥ξsh	∥ξsh	ADV
ejpam-5687	187	51	,	,	PUNCT
ejpam-5687	187	52	n∥	n∥	NOUN
ejpam-5687	187	53	=	=	SYM
ejpam-5687	187	54	η5	η5	PROPN
ejpam-5687	187	55	γ(p	γ(p	PROPN
ejpam-5687	187	56	)	)	PUNCT
ejpam-5687	187	57	∫	∫	PROPN
ejpam-5687	187	58	u	u	NOUN
ejpam-5687	187	59	0	0	NUM
ejpam-5687	187	60	∥ξsv	∥ξsv	NOUN
ejpam-5687	187	61	,	,	PUNCT
ejpam-5687	187	62	n−1∥	n−1∥	NOUN
ejpam-5687	187	63	(	(	PUNCT
ejpam-5687	187	64	u−	u−	PROPN
ejpam-5687	187	65	y)p−1dy	y)p−1dy	PROPN
ejpam-5687	187	66	,	,	PUNCT
ejpam-5687	187	67	∥ξev	∥ξev	INTJ
ejpam-5687	187	68	,	,	PUNCT
ejpam-5687	187	69	n∥	n∥	NOUN
ejpam-5687	187	70	=	=	PUNCT
ejpam-5687	187	71	η6	η6	PROPN
ejpam-5687	187	72	γ(p	γ(p	PROPN
ejpam-5687	187	73	)	)	PUNCT
ejpam-5687	187	74	∫	∫	PROPN
ejpam-5687	187	75	u	u	NOUN
ejpam-5687	187	76	0	0	PROPN
ejpam-5687	187	77	∥ξev	∥ξev	PROPN
ejpam-5687	187	78	,	,	PUNCT
ejpam-5687	187	79	n−1∥	n−1∥	NOUN
ejpam-5687	187	80	(	(	PUNCT
ejpam-5687	187	81	u−	u−	PROPN
ejpam-5687	187	82	y)p−1dy	y)p−1dy	NOUN
ejpam-5687	187	83	,	,	PUNCT
ejpam-5687	187	84	∥ξiv	∥ξiv	NOUN
ejpam-5687	187	85	,	,	PUNCT
ejpam-5687	187	86	n∥	n∥	NOUN
ejpam-5687	187	87	=	=	SYM
ejpam-5687	187	88	η7	η7	NOUN
ejpam-5687	187	89	γ(p	γ(p	NOUN
ejpam-5687	187	90	)	)	PUNCT
ejpam-5687	187	91	∫	∫	PROPN
ejpam-5687	187	92	u	u	NOUN
ejpam-5687	187	93	0	0	PROPN
ejpam-5687	187	94	∥ξiv	∥ξiv	NOUN
ejpam-5687	187	95	,	,	PUNCT
ejpam-5687	187	96	n−1∥	n−1∥	NOUN
ejpam-5687	187	97	(	(	PUNCT
ejpam-5687	187	98	u−	u−	PROPN
ejpam-5687	187	99	y)p−1dy	y)p−1dy	PROPN
ejpam-5687	187	100	.	.	PUNCT
ejpam-5687	188	1	(	(	PUNCT
ejpam-5687	188	2	16	16	NUM
ejpam-5687	188	3	)	)	PUNCT
ejpam-5687	188	4	we	we	PRON
ejpam-5687	188	5	construct	construct	VERB
ejpam-5687	188	6	and	and	CCONJ
ejpam-5687	188	7	prove	prove	VERB
ejpam-5687	188	8	the	the	DET
ejpam-5687	188	9	subsequent	subsequent	ADJ
ejpam-5687	188	10	theorem	theorem	NOUN
ejpam-5687	188	11	based	base	VERB
ejpam-5687	188	12	on	on	ADP
ejpam-5687	188	13	the	the	DET
ejpam-5687	188	14	analysis	analysis	NOUN
ejpam-5687	188	15	above	above	ADV
ejpam-5687	188	16	:	:	PUNCT
ejpam-5687	188	17	theorem	theorem	NOUN
ejpam-5687	188	18	1	1	NUM
ejpam-5687	188	19	.	.	PUNCT
ejpam-5687	188	20	suppose	suppose	VERB
ejpam-5687	188	21	that	that	SCONJ
ejpam-5687	188	22	the	the	DET
ejpam-5687	188	23	function	function	NOUN
ejpam-5687	188	24	ψi	ψi	ADP
ejpam-5687	188	25	:	:	PUNCT
ejpam-5687	189	1	[	[	X
ejpam-5687	189	2	0	0	NUM
ejpam-5687	189	3	,	,	PUNCT
ejpam-5687	189	4	t	t	PROPN
ejpam-5687	189	5	]	]	PUNCT
ejpam-5687	189	6	×	×	PROPN
ejpam-5687	189	7	r7	r7	PROPN
ejpam-5687	189	8	→	→	SYM
ejpam-5687	189	9	r	r	NOUN
ejpam-5687	189	10	,	,	PUNCT
ejpam-5687	189	11	such	such	ADJ
ejpam-5687	189	12	that	that	SCONJ
ejpam-5687	189	13	ψi	ψi	SCONJ
ejpam-5687	189	14	∈	∈	PROPN
ejpam-5687	189	15	d([0	d([0	NOUN
ejpam-5687	189	16	,	,	PUNCT
ejpam-5687	189	17	u	u	NOUN
ejpam-5687	189	18	]	]	X
ejpam-5687	189	19	,	,	PUNCT
ejpam-5687	189	20	r	r	NOUN
ejpam-5687	189	21	)	)	PUNCT
ejpam-5687	189	22	for	for	ADP
ejpam-5687	189	23	any	any	DET
ejpam-5687	189	24	sh(u	sh(u	NOUN
ejpam-5687	189	25	)	)	PUNCT
ejpam-5687	189	26	,	,	PUNCT
ejpam-5687	189	27	eh(u	eh(u	NUM
ejpam-5687	189	28	)	)	PUNCT
ejpam-5687	189	29	,	,	PUNCT
ejpam-5687	189	30	ih(u	ih(u	NOUN
ejpam-5687	189	31	)	)	PUNCT
ejpam-5687	189	32	,	,	PUNCT
ejpam-5687	189	33	rh(u	rh(u	NOUN
ejpam-5687	189	34	)	)	PUNCT
ejpam-5687	189	35	,	,	PUNCT
ejpam-5687	189	36	sv(u	sv(u	PROPN
ejpam-5687	189	37	)	)	PUNCT
ejpam-5687	189	38	,	,	PUNCT
ejpam-5687	189	39	ev(u	ev(u	PUNCT
ejpam-5687	189	40	)	)	PUNCT
ejpam-5687	189	41	,	,	PUNCT
ejpam-5687	189	42	iv(u	iv(u	NUM
ejpam-5687	189	43	)	)	PUNCT
ejpam-5687	189	44	∈	∈	PROPN
ejpam-5687	189	45	d([0	d([0	PROPN
ejpam-5687	189	46	,	,	PUNCT
ejpam-5687	189	47	t	t	X
ejpam-5687	189	48	]	]	PUNCT
ejpam-5687	189	49	,	,	PUNCT
ejpam-5687	189	50	r	r	NOUN
ejpam-5687	189	51	)	)	PUNCT
ejpam-5687	189	52	satisfies	satisfy	VERB
ejpam-5687	189	53	the	the	DET
ejpam-5687	189	54	lipschitz	lipschitz	NOUN
ejpam-5687	189	55	and	and	CCONJ
ejpam-5687	189	56	contraction	contraction	NOUN
ejpam-5687	189	57	condition	condition	NOUN
ejpam-5687	189	58	0	0	PUNCT
ejpam-5687	189	59	<	<	X
ejpam-5687	189	60	ηi	ηi	X
ejpam-5687	189	61	<	<	X
ejpam-5687	189	62	1	1	NUM
ejpam-5687	189	63	,	,	PUNCT
ejpam-5687	189	64	i	i	PRON
ejpam-5687	189	65	=	=	NOUN
ejpam-5687	189	66	1	1	NUM
ejpam-5687	189	67	,	,	PUNCT
ejpam-5687	189	68	.	.	PUNCT
ejpam-5687	189	69	.	.	PUNCT
ejpam-5687	190	1	.	.	PUNCT
ejpam-5687	191	1	,	,	PUNCT
ejpam-5687	191	2	7	7	X
ejpam-5687	191	3	.	.	PUNCT
ejpam-5687	191	4	then	then	ADV
ejpam-5687	191	5	,	,	PUNCT
ejpam-5687	191	6	the	the	DET
ejpam-5687	191	7	vector	vector	NOUN
ejpam-5687	191	8	-	-	PUNCT
ejpam-5687	191	9	borne	bear	VERB
ejpam-5687	191	10	caputo	caputo	PROPN
ejpam-5687	191	11	-	-	PUNCT
ejpam-5687	191	12	fabrizio	fabrizio	PROPN
ejpam-5687	191	13	fractional	fractional	ADJ
ejpam-5687	191	14	-	-	PUNCT
ejpam-5687	191	15	order	order	NOUN
ejpam-5687	191	16	(	(	PUNCT
ejpam-5687	191	17	4	4	X
ejpam-5687	191	18	)	)	PUNCT
ejpam-5687	191	19	possess	possess	VERB
ejpam-5687	191	20	a	a	DET
ejpam-5687	191	21	unique	unique	ADJ
ejpam-5687	191	22	solution	solution	NOUN
ejpam-5687	191	23	if	if	SCONJ
ejpam-5687	191	24	up	up	ADV
ejpam-5687	191	25	γ(p+	γ(p+	PROPN
ejpam-5687	191	26	1	1	NUM
ejpam-5687	191	27	)	)	PUNCT
ejpam-5687	191	28	ηi	ηi	NOUN
ejpam-5687	191	29	<	<	X
ejpam-5687	191	30	1	1	NUM
ejpam-5687	191	31	,	,	PUNCT
ejpam-5687	191	32	i	i	PRON
ejpam-5687	191	33	=	=	NOUN
ejpam-5687	191	34	1	1	NUM
ejpam-5687	191	35	,	,	PUNCT
ejpam-5687	191	36	.	.	PUNCT
ejpam-5687	191	37	.	.	PUNCT
ejpam-5687	192	1	.	.	PUNCT
ejpam-5687	193	1	,	,	PUNCT
ejpam-5687	193	2	7	7	X
ejpam-5687	193	3	.	.	PUNCT
ejpam-5687	193	4	(	(	PUNCT
ejpam-5687	193	5	17	17	NUM
ejpam-5687	193	6	)	)	PUNCT
ejpam-5687	193	7	is	be	AUX
ejpam-5687	193	8	true	true	ADJ
ejpam-5687	193	9	for	for	ADP
ejpam-5687	193	10	t	t	PROPN
ejpam-5687	193	11	∈	∈	PROPN
ejpam-5687	194	1	[	[	X
ejpam-5687	194	2	0	0	NUM
ejpam-5687	194	3	,	,	PUNCT
ejpam-5687	194	4	u	u	NOUN
ejpam-5687	194	5	]	]	PUNCT
ejpam-5687	194	6	.	.	PUNCT
ejpam-5687	195	1	remark	remark	PROPN
ejpam-5687	195	2	1	1	NUM
ejpam-5687	195	3	.	.	PUNCT
ejpam-5687	196	1	existence	existence	NOUN
ejpam-5687	196	2	and	and	CCONJ
ejpam-5687	196	3	uniqueness	uniqueness	NOUN
ejpam-5687	196	4	results	result	NOUN
ejpam-5687	196	5	are	be	AUX
ejpam-5687	196	6	important	important	ADJ
ejpam-5687	196	7	in	in	ADP
ejpam-5687	196	8	epidemiology	epidemiology	NOUN
ejpam-5687	196	9	,	,	PUNCT
ejpam-5687	196	10	as	as	SCONJ
ejpam-5687	196	11	they	they	PRON
ejpam-5687	196	12	need	need	VERB
ejpam-5687	196	13	to	to	PART
ejpam-5687	196	14	build	build	VERB
ejpam-5687	196	15	mathematical	mathematical	ADJ
ejpam-5687	196	16	models	model	NOUN
ejpam-5687	196	17	to	to	PART
ejpam-5687	196	18	predict	predict	VERB
ejpam-5687	196	19	the	the	DET
ejpam-5687	196	20	spread	spread	NOUN
ejpam-5687	196	21	of	of	ADP
ejpam-5687	196	22	diseases	disease	NOUN
ejpam-5687	196	23	and	and	CCONJ
ejpam-5687	196	24	help	help	VERB
ejpam-5687	196	25	develop	develop	VERB
ejpam-5687	196	26	public	public	ADJ
ejpam-5687	196	27	health	health	NOUN
ejpam-5687	196	28	policies	policy	NOUN
ejpam-5687	196	29	and	and	CCONJ
ejpam-5687	196	30	vaccination	vaccination	NOUN
ejpam-5687	196	31	strategies	strategy	NOUN
ejpam-5687	196	32	,	,	PUNCT
ejpam-5687	196	33	all	all	PRON
ejpam-5687	196	34	of	of	ADP
ejpam-5687	196	35	which	which	PRON
ejpam-5687	196	36	are	be	AUX
ejpam-5687	196	37	necessary	necessary	ADJ
ejpam-5687	196	38	to	to	ADP
ejpam-5687	196	39	better	well	ADJ
ejpam-5687	196	40	decision	decision	NOUN
ejpam-5687	196	41	-	-	PUNCT
ejpam-5687	196	42	making	making	NOUN
ejpam-5687	196	43	.	.	PUNCT
ejpam-5687	197	1	for	for	ADP
ejpam-5687	197	2	example	example	NOUN
ejpam-5687	197	3	,	,	PUNCT
ejpam-5687	197	4	in	in	ADP
ejpam-5687	197	5	practical	practical	ADJ
ejpam-5687	197	6	fields	field	NOUN
ejpam-5687	197	7	such	such	ADJ
ejpam-5687	197	8	as	as	ADP
ejpam-5687	197	9	engineering	engineering	NOUN
ejpam-5687	197	10	,	,	PUNCT
ejpam-5687	197	11	physics	physics	NOUN
ejpam-5687	197	12	and	and	CCONJ
ejpam-5687	197	13	biology	biology	NOUN
ejpam-5687	197	14	,	,	PUNCT
ejpam-5687	197	15	the	the	DET
ejpam-5687	197	16	transmission	transmission	NOUN
ejpam-5687	197	17	dynamics	dynamic	NOUN
ejpam-5687	197	18	of	of	ADP
ejpam-5687	197	19	covid-19	covid-19	PROPN
ejpam-5687	197	20	,	,	PUNCT
ejpam-5687	197	21	hiv	hiv	PROPN
ejpam-5687	197	22	/	/	SYM
ejpam-5687	197	23	aids	aid	NOUN
ejpam-5687	197	24	and	and	CCONJ
ejpam-5687	197	25	disease	disease	NOUN
ejpam-5687	197	26	are	be	AUX
ejpam-5687	197	27	just	just	ADV
ejpam-5687	197	28	a	a	DET
ejpam-5687	197	29	few	few	ADJ
ejpam-5687	197	30	examples	example	NOUN
ejpam-5687	197	31	.	.	PUNCT
ejpam-5687	198	1	proof	proof	NOUN
ejpam-5687	198	2	.	.	PUNCT
ejpam-5687	199	1	the	the	DET
ejpam-5687	199	2	equation	equation	NOUN
ejpam-5687	199	3	(	(	PUNCT
ejpam-5687	199	4	16	16	NUM
ejpam-5687	199	5	)	)	PUNCT
ejpam-5687	199	6	provides	provide	VERB
ejpam-5687	199	7	,	,	PUNCT
ejpam-5687	199	8	if	if	SCONJ
ejpam-5687	199	9	ψi	ψi	ADP
ejpam-5687	199	10	,	,	PUNCT
ejpam-5687	199	11	i	i	PRON
ejpam-5687	199	12	=	=	NOUN
ejpam-5687	199	13	1	1	NUM
ejpam-5687	199	14	,	,	PUNCT
ejpam-5687	199	15	.	.	PUNCT
ejpam-5687	199	16	.	.	PUNCT
ejpam-5687	200	1	.	.	PUNCT
ejpam-5687	201	1	,	,	PUNCT
ejpam-5687	201	2	7	7	NUM
ejpam-5687	201	3	,	,	PUNCT
ejpam-5687	201	4	meets	meet	VERB
ejpam-5687	201	5	the	the	DET
ejpam-5687	201	6	lipchitz	lipchitz	NOUN
ejpam-5687	201	7	condition	condition	NOUN
ejpam-5687	201	8	,	,	PUNCT
ejpam-5687	202	1	n.	n.	PROPN
ejpam-5687	202	2	ullah	ullah	PROPN
ejpam-5687	202	3	et	et	PROPN
ejpam-5687	202	4	al	al	PROPN
ejpam-5687	202	5	.	.	PUNCT
ejpam-5687	202	6	/	/	SYM
ejpam-5687	202	7	eur	eur	PROPN
ejpam-5687	202	8	.	.	PUNCT
ejpam-5687	203	1	j.	j.	PROPN
ejpam-5687	203	2	pure	pure	PROPN
ejpam-5687	203	3	appl	appl	PROPN
ejpam-5687	203	4	.	.	PROPN
ejpam-5687	203	5	math	math	PROPN
ejpam-5687	203	6	,	,	PUNCT
ejpam-5687	203	7	18	18	NUM
ejpam-5687	203	8	(	(	PUNCT
ejpam-5687	203	9	2	2	NUM
ejpam-5687	203	10	)	)	PUNCT
ejpam-5687	203	11	(	(	PUNCT
ejpam-5687	203	12	2025	2025	NUM
ejpam-5687	203	13	)	)	PUNCT
ejpam-5687	203	14	,	,	PUNCT
ejpam-5687	203	15	5687	5687	NUM
ejpam-5687	203	16	12	12	NUM
ejpam-5687	203	17	of	of	ADP
ejpam-5687	203	18	25	25	NUM
ejpam-5687	203	19	while	while	NOUN
ejpam-5687	203	20	sh(u	sh(u	NUM
ejpam-5687	203	21	)	)	PUNCT
ejpam-5687	203	22	,	,	PUNCT
ejpam-5687	203	23	eh(u	eh(u	NUM
ejpam-5687	203	24	)	)	PUNCT
ejpam-5687	203	25	,	,	PUNCT
ejpam-5687	203	26	ih(u	ih(u	NOUN
ejpam-5687	203	27	)	)	PUNCT
ejpam-5687	203	28	,	,	PUNCT
ejpam-5687	203	29	rh(u	rh(u	NOUN
ejpam-5687	203	30	)	)	PUNCT
ejpam-5687	203	31	,	,	PUNCT
ejpam-5687	203	32	sv(u	sv(u	PROPN
ejpam-5687	203	33	)	)	PUNCT
ejpam-5687	203	34	,	,	PUNCT
ejpam-5687	203	35	ev(u	ev(u	PUNCT
ejpam-5687	203	36	)	)	PUNCT
ejpam-5687	203	37	and	and	CCONJ
ejpam-5687	203	38	iv(u	iv(u	NUM
ejpam-5687	203	39	)	)	PUNCT
ejpam-5687	203	40	are	be	AUX
ejpam-5687	203	41	confined	confine	VERB
ejpam-5687	203	42	.	.	PUNCT
ejpam-5687	204	1	∥ξsh	∥ξsh	NOUN
ejpam-5687	204	2	,	,	PUNCT
ejpam-5687	204	3	n(u)∥	n(u)∥	X
ejpam-5687	204	4	≤	≤	X
ejpam-5687	204	5	∥sh0(u)∥	∥sh0(u)∥	PROPN
ejpam-5687	204	6	(	(	PUNCT
ejpam-5687	204	7	up	up	ADV
ejpam-5687	204	8	γ(p+	γ(p+	PROPN
ejpam-5687	204	9	1	1	NUM
ejpam-5687	204	10	)	)	PUNCT
ejpam-5687	204	11	η1	η1	NOUN
ejpam-5687	204	12	)	)	PUNCT
ejpam-5687	204	13	n	n	NOUN
ejpam-5687	204	14	,	,	PUNCT
ejpam-5687	204	15	∥ξeh	∥ξeh	PROPN
ejpam-5687	204	16	,	,	PUNCT
ejpam-5687	204	17	n(t)∥	n(t)∥	NOUN
ejpam-5687	204	18	≤	≤	NUM
ejpam-5687	204	19	∥eh0(u)∥	∥eh0(u)∥	PUNCT
ejpam-5687	204	20	(	(	PUNCT
ejpam-5687	204	21	up	up	ADV
ejpam-5687	204	22	γ(p+	γ(p+	PROPN
ejpam-5687	204	23	1	1	NUM
ejpam-5687	204	24	)	)	PUNCT
ejpam-5687	204	25	η2	η2	PROPN
ejpam-5687	204	26	)	)	PUNCT
ejpam-5687	204	27	n	n	X
ejpam-5687	204	28	,	,	PUNCT
ejpam-5687	204	29	∥ξih	∥ξih	ADV
ejpam-5687	204	30	,	,	PUNCT
ejpam-5687	204	31	n(tu∥	n(tu∥	PROPN
ejpam-5687	204	32	≤	≤	X
ejpam-5687	204	33	∥ih0(u)∥	∥ih0(u)∥	PUNCT
ejpam-5687	204	34	(	(	PUNCT
ejpam-5687	204	35	up	up	ADV
ejpam-5687	204	36	γ(p+	γ(p+	PROPN
ejpam-5687	204	37	1	1	NUM
ejpam-5687	204	38	)	)	PUNCT
ejpam-5687	204	39	η3	η3	NOUN
ejpam-5687	204	40	)	)	PUNCT
ejpam-5687	204	41	n	n	X
ejpam-5687	204	42	,	,	PUNCT
ejpam-5687	204	43	∥ξrh	∥ξrh	PROPN
ejpam-5687	204	44	,	,	PUNCT
ejpam-5687	204	45	n(u)∥	n(u)∥	ADJ
ejpam-5687	204	46	≤	≤	NOUN
ejpam-5687	204	47	∥rh0(u)∥	∥rh0(u)∥	X
ejpam-5687	204	48	(	(	PUNCT
ejpam-5687	204	49	up	up	ADV
ejpam-5687	204	50	γ(p+	γ(p+	PROPN
ejpam-5687	204	51	1	1	NUM
ejpam-5687	204	52	)	)	PUNCT
ejpam-5687	204	53	η4	η4	VERB
ejpam-5687	204	54	)	)	PUNCT
ejpam-5687	204	55	n	n	CCONJ
ejpam-5687	204	56	,	,	PUNCT
ejpam-5687	204	57	∥ξsv	∥ξsv	PROPN
ejpam-5687	204	58	,	,	PUNCT
ejpam-5687	204	59	n(u)∥	n(u)∥	ADJ
ejpam-5687	204	60	≤	≤	NUM
ejpam-5687	204	61	∥sv0(u)∥	∥sv0(u)∥	NUM
ejpam-5687	204	62	(	(	PUNCT
ejpam-5687	204	63	up	up	ADV
ejpam-5687	204	64	γ(p+	γ(p+	PROPN
ejpam-5687	204	65	1	1	NUM
ejpam-5687	204	66	)	)	PUNCT
ejpam-5687	204	67	η5	η5	NOUN
ejpam-5687	204	68	)	)	PUNCT
ejpam-5687	204	69	n	n	CCONJ
ejpam-5687	204	70	,	,	PUNCT
ejpam-5687	204	71	∥ξev	∥ξev	PROPN
ejpam-5687	204	72	,	,	PUNCT
ejpam-5687	204	73	n(u)∥	n(u)∥	ADJ
ejpam-5687	204	74	≤	≤	X
ejpam-5687	204	75	∥ev0(u)∥	∥ev0(u)∥	NUM
ejpam-5687	204	76	(	(	PUNCT
ejpam-5687	204	77	up	up	ADP
ejpam-5687	204	78	γ(p+	γ(p+	PROPN
ejpam-5687	204	79	1	1	NUM
ejpam-5687	204	80	)	)	PUNCT
ejpam-5687	204	81	η6	η6	NOUN
ejpam-5687	204	82	)	)	PUNCT
ejpam-5687	204	83	n	n	CCONJ
ejpam-5687	204	84	,	,	PUNCT
ejpam-5687	204	85	∥ξiv	∥ξiv	NOUN
ejpam-5687	204	86	,	,	PUNCT
ejpam-5687	204	87	n(u)∥	n(u)∥	ADJ
ejpam-5687	204	88	≤	≤	X
ejpam-5687	204	89	∥ev0(u)∥	∥ev0(u)∥	NUM
ejpam-5687	204	90	(	(	PUNCT
ejpam-5687	204	91	up	up	ADP
ejpam-5687	204	92	γ(p+	γ(p+	PROPN
ejpam-5687	204	93	1	1	NUM
ejpam-5687	204	94	)	)	PUNCT
ejpam-5687	204	95	η7	η7	NOUN
ejpam-5687	204	96	)	)	PUNCT
ejpam-5687	204	97	n	n	CCONJ
ejpam-5687	204	98	.	.	PUNCT
ejpam-5687	205	1	(	(	PUNCT
ejpam-5687	205	2	18	18	NUM
ejpam-5687	205	3	)	)	PUNCT
ejpam-5687	205	4	=	=	NOUN
ejpam-5687	205	5	⇒	⇒	NOUN
ejpam-5687	205	6	∥ξsh	∥ξsh	ADV
ejpam-5687	205	7	,	,	PUNCT
ejpam-5687	205	8	n∥	n∥	NOUN
ejpam-5687	205	9	≤	≤	NOUN
ejpam-5687	205	10	1	1	NUM
ejpam-5687	205	11	γ(p	γ(p	NUM
ejpam-5687	205	12	)	)	PUNCT
ejpam-5687	205	13	∫	∫	PROPN
ejpam-5687	205	14	u	u	NOUN
ejpam-5687	205	15	0	0	PROPN
ejpam-5687	205	16	(	(	PUNCT
ejpam-5687	205	17	u−	u−	PROPN
ejpam-5687	205	18	y)p−1	y)p−1	NOUN
ejpam-5687	205	19	(	(	PUNCT
ejpam-5687	205	20	ψ1	ψ1	PROPN
ejpam-5687	205	21	(	(	PUNCT
ejpam-5687	205	22	y	y	NOUN
ejpam-5687	205	23	,	,	PUNCT
ejpam-5687	205	24	shn(y))−	shn(y))−	ADJ
ejpam-5687	205	25	ψ1	ψ1	NOUN
ejpam-5687	205	26	(	(	PUNCT
ejpam-5687	205	27	y	y	NOUN
ejpam-5687	205	28	,	,	PUNCT
ejpam-5687	205	29	sh(n−1)(y	sh(n−1)(y	NUM
ejpam-5687	205	30	)	)	PUNCT
ejpam-5687	205	31	)	)	PUNCT
ejpam-5687	205	32	)	)	PUNCT
ejpam-5687	206	1	dy	dy	NOUN
ejpam-5687	206	2	,	,	PUNCT
ejpam-5687	206	3	∥ξeh	∥ξeh	PROPN
ejpam-5687	206	4	,	,	PUNCT
ejpam-5687	206	5	n∥	n∥	NOUN
ejpam-5687	206	6	≤	≤	NOUN
ejpam-5687	206	7	1	1	NUM
ejpam-5687	206	8	γ(p	γ(p	NUM
ejpam-5687	206	9	)	)	PUNCT
ejpam-5687	206	10	∫	∫	PROPN
ejpam-5687	206	11	u	u	NOUN
ejpam-5687	206	12	0	0	PROPN
ejpam-5687	207	1	(	(	PUNCT
ejpam-5687	207	2	u−	u−	PROPN
ejpam-5687	207	3	y)p−1	y)p−1	NOUN
ejpam-5687	207	4	(	(	PUNCT
ejpam-5687	207	5	ψ2	ψ2	NOUN
ejpam-5687	207	6	(	(	PUNCT
ejpam-5687	207	7	y	y	NOUN
ejpam-5687	207	8	,	,	PUNCT
ejpam-5687	207	9	ehn(y))−	ehn(y))−	NUM
ejpam-5687	207	10	ψ2	ψ2	NOUN
ejpam-5687	207	11	(	(	PUNCT
ejpam-5687	207	12	y	y	NOUN
ejpam-5687	207	13	,	,	PUNCT
ejpam-5687	207	14	eh(n−1)(y	eh(n−1)(y	NOUN
ejpam-5687	207	15	)	)	PUNCT
ejpam-5687	207	16	)	)	PUNCT
ejpam-5687	207	17	)	)	PUNCT
ejpam-5687	208	1	dy	dy	NOUN
ejpam-5687	208	2	,	,	PUNCT
ejpam-5687	208	3	∥ξih	∥ξih	ADV
ejpam-5687	208	4	,	,	PUNCT
ejpam-5687	208	5	n∥	n∥	NOUN
ejpam-5687	208	6	≤	≤	NOUN
ejpam-5687	208	7	1	1	NUM
ejpam-5687	208	8	γ(p	γ(p	NUM
ejpam-5687	208	9	)	)	PUNCT
ejpam-5687	208	10	∫	∫	PROPN
ejpam-5687	208	11	u	u	NOUN
ejpam-5687	208	12	0	0	PROPN
ejpam-5687	209	1	(	(	PUNCT
ejpam-5687	209	2	u−	u−	PROPN
ejpam-5687	209	3	y)p−1	y)p−1	NOUN
ejpam-5687	209	4	(	(	PUNCT
ejpam-5687	209	5	ψ3	ψ3	PROPN
ejpam-5687	209	6	(	(	PUNCT
ejpam-5687	209	7	y	y	PROPN
ejpam-5687	209	8	,	,	PUNCT
ejpam-5687	209	9	ihn(y))−	ihn(y))−	ADJ
ejpam-5687	209	10	ψ3	ψ3	NOUN
ejpam-5687	209	11	(	(	PUNCT
ejpam-5687	209	12	y	y	PROPN
ejpam-5687	209	13	,	,	PUNCT
ejpam-5687	209	14	ih(n−1)(y	ih(n−1)(y	NUM
ejpam-5687	209	15	)	)	PUNCT
ejpam-5687	209	16	)	)	PUNCT
ejpam-5687	209	17	)	)	PUNCT
ejpam-5687	210	1	dy	dy	NOUN
ejpam-5687	210	2	,	,	PUNCT
ejpam-5687	210	3	∥ξrh	∥ξrh	PROPN
ejpam-5687	210	4	,	,	PUNCT
ejpam-5687	210	5	n∥	n∥	NOUN
ejpam-5687	210	6	≤	≤	NOUN
ejpam-5687	210	7	1	1	NUM
ejpam-5687	210	8	γ(p	γ(p	NUM
ejpam-5687	210	9	)	)	PUNCT
ejpam-5687	210	10	∫	∫	PROPN
ejpam-5687	210	11	u	u	NOUN
ejpam-5687	210	12	0	0	PROPN
ejpam-5687	211	1	(	(	PUNCT
ejpam-5687	211	2	u−	u−	PROPN
ejpam-5687	211	3	y)p−1	y)p−1	NOUN
ejpam-5687	211	4	(	(	PUNCT
ejpam-5687	211	5	ψ4	ψ4	PROPN
ejpam-5687	211	6	(	(	PUNCT
ejpam-5687	211	7	y	y	PROPN
ejpam-5687	211	8	,	,	PUNCT
ejpam-5687	211	9	rhn(y))−	rhn(y))−	PROPN
ejpam-5687	211	10	ψ4	ψ4	PROPN
ejpam-5687	211	11	(	(	PUNCT
ejpam-5687	211	12	y	y	NOUN
ejpam-5687	211	13	,	,	PUNCT
ejpam-5687	211	14	rh(n−1)(y	rh(n−1)(y	NUM
ejpam-5687	211	15	)	)	PUNCT
ejpam-5687	211	16	)	)	PUNCT
ejpam-5687	211	17	)	)	PUNCT
ejpam-5687	212	1	dy	dy	NOUN
ejpam-5687	212	2	,	,	PUNCT
ejpam-5687	212	3	∥ξsv	∥ξsv	NOUN
ejpam-5687	212	4	,	,	PUNCT
ejpam-5687	212	5	n∥	n∥	NOUN
ejpam-5687	212	6	≤	≤	NOUN
ejpam-5687	212	7	1	1	NUM
ejpam-5687	212	8	γ(p	γ(p	NUM
ejpam-5687	212	9	)	)	PUNCT
ejpam-5687	212	10	∫	∫	PROPN
ejpam-5687	213	1	u	u	NOUN
ejpam-5687	213	2	0	0	PROPN
ejpam-5687	213	3	(	(	PUNCT
ejpam-5687	213	4	u−	u−	PROPN
ejpam-5687	213	5	y)p−1	y)p−1	NOUN
ejpam-5687	213	6	(	(	PUNCT
ejpam-5687	213	7	ψ5	ψ5	PROPN
ejpam-5687	213	8	(	(	PUNCT
ejpam-5687	213	9	y	y	PROPN
ejpam-5687	213	10	,	,	PUNCT
ejpam-5687	213	11	svn(y))−	svn(y))−	ADJ
ejpam-5687	213	12	ψ5	ψ5	NOUN
ejpam-5687	213	13	(	(	PUNCT
ejpam-5687	213	14	y	y	NOUN
ejpam-5687	213	15	,	,	PUNCT
ejpam-5687	213	16	sv(n−1)(y	sv(n−1)(y	NOUN
ejpam-5687	213	17	)	)	PUNCT
ejpam-5687	213	18	)	)	PUNCT
ejpam-5687	213	19	)	)	PUNCT
ejpam-5687	214	1	dy	dy	NOUN
ejpam-5687	214	2	,	,	PUNCT
ejpam-5687	214	3	∥ξev	∥ξev	PROPN
ejpam-5687	214	4	,	,	PUNCT
ejpam-5687	214	5	n∥	n∥	NOUN
ejpam-5687	214	6	≤	≤	NOUN
ejpam-5687	214	7	1	1	NUM
ejpam-5687	214	8	γ(p	γ(p	NUM
ejpam-5687	214	9	)	)	PUNCT
ejpam-5687	214	10	∫	∫	PROPN
ejpam-5687	214	11	u	u	NOUN
ejpam-5687	214	12	0	0	PROPN
ejpam-5687	215	1	(	(	PUNCT
ejpam-5687	215	2	u−	u−	PROPN
ejpam-5687	215	3	y)p−1	y)p−1	NOUN
ejpam-5687	215	4	(	(	PUNCT
ejpam-5687	215	5	ψ6	ψ6	PROPN
ejpam-5687	215	6	(	(	PUNCT
ejpam-5687	215	7	y	y	PROPN
ejpam-5687	215	8	,	,	PUNCT
ejpam-5687	215	9	evn(y))−	evn(y))−	ADJ
ejpam-5687	215	10	ψ6	ψ6	NOUN
ejpam-5687	215	11	(	(	PUNCT
ejpam-5687	215	12	y	y	NOUN
ejpam-5687	215	13	,	,	PUNCT
ejpam-5687	215	14	ev(n−1)(y	ev(n−1)(y	NUM
ejpam-5687	215	15	)	)	PUNCT
ejpam-5687	215	16	)	)	PUNCT
ejpam-5687	215	17	)	)	PUNCT
ejpam-5687	216	1	dy	dy	NOUN
ejpam-5687	216	2	,	,	PUNCT
ejpam-5687	216	3	∥ξiv	∥ξiv	NOUN
ejpam-5687	216	4	,	,	PUNCT
ejpam-5687	216	5	n∥	n∥	NOUN
ejpam-5687	216	6	≤	≤	ADJ
ejpam-5687	216	7	1	1	NUM
ejpam-5687	216	8	γ(p	γ(p	NUM
ejpam-5687	216	9	)	)	PUNCT
ejpam-5687	216	10	∫	∫	PROPN
ejpam-5687	216	11	u	u	NOUN
ejpam-5687	216	12	0	0	PROPN
ejpam-5687	217	1	(	(	PUNCT
ejpam-5687	217	2	u−	u−	PROPN
ejpam-5687	217	3	y)p−1	y)p−1	NOUN
ejpam-5687	217	4	(	(	PUNCT
ejpam-5687	217	5	ψ7	ψ7	PROPN
ejpam-5687	217	6	(	(	PUNCT
ejpam-5687	217	7	y	y	PROPN
ejpam-5687	217	8	,	,	PUNCT
ejpam-5687	217	9	ivn(y))−	ivn(y))−	ADJ
ejpam-5687	217	10	ψ7	ψ7	PROPN
ejpam-5687	217	11	(	(	PUNCT
ejpam-5687	217	12	y	y	PROPN
ejpam-5687	217	13	,	,	PUNCT
ejpam-5687	217	14	iv(n−1)(y	iv(n−1)(y	NOUN
ejpam-5687	217	15	)	)	PUNCT
ejpam-5687	217	16	)	)	PUNCT
ejpam-5687	217	17	)	)	PUNCT
ejpam-5687	218	1	dy	dy	NOUN
ejpam-5687	218	2	.	.	PUNCT
ejpam-5687	219	1	(	(	PUNCT
ejpam-5687	219	2	19	19	NUM
ejpam-5687	219	3	)	)	PUNCT
ejpam-5687	219	4	n.	n.	PROPN
ejpam-5687	219	5	ullah	ullah	PROPN
ejpam-5687	219	6	et	et	PROPN
ejpam-5687	219	7	al	al	PROPN
ejpam-5687	219	8	.	.	PUNCT
ejpam-5687	219	9	/	/	SYM
ejpam-5687	219	10	eur	eur	PROPN
ejpam-5687	219	11	.	.	PUNCT
ejpam-5687	220	1	j.	j.	PROPN
ejpam-5687	220	2	pure	pure	PROPN
ejpam-5687	220	3	appl	appl	PROPN
ejpam-5687	220	4	.	.	PROPN
ejpam-5687	220	5	math	math	PROPN
ejpam-5687	220	6	,	,	PUNCT
ejpam-5687	220	7	18	18	NUM
ejpam-5687	220	8	(	(	PUNCT
ejpam-5687	220	9	2	2	NUM
ejpam-5687	220	10	)	)	PUNCT
ejpam-5687	220	11	(	(	PUNCT
ejpam-5687	220	12	2025	2025	NUM
ejpam-5687	220	13	)	)	PUNCT
ejpam-5687	220	14	,	,	PUNCT
ejpam-5687	220	15	5687	5687	NUM
ejpam-5687	220	16	13	13	NUM
ejpam-5687	220	17	of	of	ADP
ejpam-5687	220	18	25	25	NUM
ejpam-5687	220	19	recursively	recursively	ADV
ejpam-5687	220	20	,	,	PUNCT
ejpam-5687	220	21	using	use	VERB
ejpam-5687	220	22	the	the	DET
ejpam-5687	220	23	same	same	ADJ
ejpam-5687	220	24	procedure	procedure	NOUN
ejpam-5687	220	25	,	,	PUNCT
ejpam-5687	220	26	we	we	PRON
ejpam-5687	220	27	obtain	obtain	VERB
ejpam-5687	220	28	:	:	PUNCT
ejpam-5687	220	29	∥ξsh	∥ξsh	ADV
ejpam-5687	220	30	,	,	PUNCT
ejpam-5687	220	31	n(u)∥	n(u)∥	ADJ
ejpam-5687	220	32	≤	≤	X
ejpam-5687	220	33	∥sh0(u)∥	∥sh0(u)∥	PROPN
ejpam-5687	220	34	(	(	PUNCT
ejpam-5687	220	35	up	up	ADV
ejpam-5687	220	36	γ(p+	γ(p+	PROPN
ejpam-5687	220	37	1	1	NUM
ejpam-5687	220	38	)	)	PUNCT
ejpam-5687	220	39	η1	η1	NOUN
ejpam-5687	220	40	)	)	PUNCT
ejpam-5687	220	41	n+1	n+1	PROPN
ejpam-5687	220	42	,	,	PUNCT
ejpam-5687	220	43	∥ξeh	∥ξeh	PROPN
ejpam-5687	220	44	,	,	PUNCT
ejpam-5687	220	45	n(u)∥	n(u)∥	ADJ
ejpam-5687	220	46	≤	≤	X
ejpam-5687	220	47	∥eh0(u)∥	∥eh0(u)∥	PUNCT
ejpam-5687	220	48	(	(	PUNCT
ejpam-5687	220	49	up	up	ADV
ejpam-5687	220	50	γ(p+	γ(p+	PROPN
ejpam-5687	220	51	1	1	NUM
ejpam-5687	220	52	)	)	PUNCT
ejpam-5687	220	53	η2	η2	PROPN
ejpam-5687	220	54	)	)	PUNCT
ejpam-5687	220	55	n+1	n+1	PROPN
ejpam-5687	220	56	,	,	PUNCT
ejpam-5687	220	57	∥ξih	∥ξih	ADV
ejpam-5687	220	58	,	,	PUNCT
ejpam-5687	220	59	n(u)∥	n(u)∥	ADJ
ejpam-5687	220	60	≤	≤	X
ejpam-5687	220	61	∥ih0(u)∥	∥ih0(u)∥	PUNCT
ejpam-5687	220	62	(	(	PUNCT
ejpam-5687	220	63	up	up	ADV
ejpam-5687	220	64	γ(p+	γ(p+	PROPN
ejpam-5687	220	65	1	1	NUM
ejpam-5687	220	66	)	)	PUNCT
ejpam-5687	220	67	η3	η3	NOUN
ejpam-5687	220	68	)	)	PUNCT
ejpam-5687	220	69	n+1	n+1	PROPN
ejpam-5687	220	70	,	,	PUNCT
ejpam-5687	220	71	∥ξrh	∥ξrh	PROPN
ejpam-5687	220	72	,	,	PUNCT
ejpam-5687	220	73	n(u)∥	n(u)∥	ADJ
ejpam-5687	220	74	≤	≤	NOUN
ejpam-5687	220	75	∥rh0(u)∥	∥rh0(u)∥	X
ejpam-5687	220	76	(	(	PUNCT
ejpam-5687	220	77	up	up	ADV
ejpam-5687	220	78	γ(p+	γ(p+	PROPN
ejpam-5687	220	79	1	1	NUM
ejpam-5687	220	80	)	)	PUNCT
ejpam-5687	220	81	η4	η4	VERB
ejpam-5687	220	82	)	)	PUNCT
ejpam-5687	220	83	n+1	n+1	PROPN
ejpam-5687	220	84	,	,	PUNCT
ejpam-5687	220	85	∥ξsv	∥ξsv	PROPN
ejpam-5687	220	86	,	,	PUNCT
ejpam-5687	220	87	n(u)∥	n(u)∥	ADJ
ejpam-5687	220	88	≤	≤	NUM
ejpam-5687	220	89	∥sv0(u)∥	∥sv0(u)∥	NUM
ejpam-5687	220	90	(	(	PUNCT
ejpam-5687	220	91	up	up	ADV
ejpam-5687	220	92	γ(p+	γ(p+	PROPN
ejpam-5687	220	93	1	1	NUM
ejpam-5687	220	94	)	)	PUNCT
ejpam-5687	220	95	η5	η5	NOUN
ejpam-5687	220	96	)	)	PUNCT
ejpam-5687	220	97	n+1	n+1	PROPN
ejpam-5687	220	98	,	,	PUNCT
ejpam-5687	220	99	∥ξev	∥ξev	PROPN
ejpam-5687	220	100	,	,	PUNCT
ejpam-5687	220	101	n(u)∥	n(u)∥	ADJ
ejpam-5687	220	102	≤	≤	X
ejpam-5687	220	103	∥ev0(u)∥	∥ev0(u)∥	NUM
ejpam-5687	220	104	(	(	PUNCT
ejpam-5687	220	105	up	up	ADP
ejpam-5687	220	106	γ(p+	γ(p+	PROPN
ejpam-5687	220	107	1	1	NUM
ejpam-5687	220	108	)	)	PUNCT
ejpam-5687	220	109	η6	η6	NOUN
ejpam-5687	220	110	)	)	PUNCT
ejpam-5687	220	111	n+1	n+1	PROPN
ejpam-5687	220	112	,	,	PUNCT
ejpam-5687	220	113	∥ξiv	∥ξiv	NOUN
ejpam-5687	220	114	,	,	PUNCT
ejpam-5687	220	115	n(u)∥	n(u)∥	ADJ
ejpam-5687	220	116	≤	≤	X
ejpam-5687	220	117	∥iv0(u)∥	∥iv0(u)∥	ADV
ejpam-5687	220	118	(	(	PUNCT
ejpam-5687	220	119	up	up	ADV
ejpam-5687	220	120	γ(p+	γ(p+	PROPN
ejpam-5687	220	121	1	1	NUM
ejpam-5687	220	122	)	)	PUNCT
ejpam-5687	220	123	η1	η1	NOUN
ejpam-5687	220	124	)	)	PUNCT
ejpam-5687	220	125	n+1	n+1	PROPN
ejpam-5687	220	126	,	,	PUNCT
ejpam-5687	220	127	(	(	PUNCT
ejpam-5687	220	128	20	20	NUM
ejpam-5687	220	129	)	)	PUNCT
ejpam-5687	220	130	to	to	PART
ejpam-5687	220	131	be	be	AUX
ejpam-5687	220	132	limn→∞	limn→∞	ADJ
ejpam-5687	220	133	∥ξsh	∥ξsh	X
ejpam-5687	220	134	,	,	PUNCT
ejpam-5687	220	135	n(u)∥	n(u)∥	X
ejpam-5687	220	136	=	=	SYM
ejpam-5687	220	137	0	0	NUM
ejpam-5687	220	138	,	,	PUNCT
ejpam-5687	220	139	limn→∞	limn→∞	PROPN
ejpam-5687	220	140	∥ξeh	∥ξeh	PROPN
ejpam-5687	220	141	,	,	PUNCT
ejpam-5687	220	142	n(u)∥	n(u)∥	X
ejpam-5687	220	143	=	=	SYM
ejpam-5687	220	144	0	0	NUM
ejpam-5687	220	145	,	,	PUNCT
ejpam-5687	220	146	limn→∞	limn→∞	PROPN
ejpam-5687	220	147	∥ξih	∥ξih	NOUN
ejpam-5687	220	148	,	,	PUNCT
ejpam-5687	220	149	n(u)∥	n(u)∥	X
ejpam-5687	220	150	=	=	SYM
ejpam-5687	220	151	0	0	NUM
ejpam-5687	220	152	,	,	PUNCT
ejpam-5687	220	153	limn→∞	limn→∞	PROPN
ejpam-5687	220	154	∥ξrh	∥ξrh	PROPN
ejpam-5687	220	155	,	,	PUNCT
ejpam-5687	220	156	n(u)∥	n(u)∥	X
ejpam-5687	220	157	=	=	SYM
ejpam-5687	220	158	0	0	NUM
ejpam-5687	220	159	,	,	PUNCT
ejpam-5687	220	160	limn→∞	limn→∞	PROPN
ejpam-5687	220	161	∥ξsv	∥ξsv	NOUN
ejpam-5687	220	162	,	,	PUNCT
ejpam-5687	220	163	n(u)∥	n(u)∥	X
ejpam-5687	220	164	=	=	SYM
ejpam-5687	220	165	0	0	NUM
ejpam-5687	220	166	,	,	PUNCT
ejpam-5687	220	167	limn→∞	limn→∞	X
ejpam-5687	220	168	∥ξev	∥ξev	PROPN
ejpam-5687	220	169	,	,	PUNCT
ejpam-5687	220	170	n(u)∥	n(u)∥	X
ejpam-5687	220	171	=	=	SYM
ejpam-5687	220	172	0	0	NUM
ejpam-5687	220	173	,	,	PUNCT
ejpam-5687	220	174	limn→∞	limn→∞	PROPN
ejpam-5687	220	175	∥ξiv	∥ξiv	NOUN
ejpam-5687	220	176	,	,	PUNCT
ejpam-5687	220	177	n(u)∥	n(u)∥	X
ejpam-5687	221	1	=	=	SYM
ejpam-5687	222	1	0	0	X
ejpam-5687	222	2	.	.	PUNCT
ejpam-5687	223	1	this	this	PRON
ejpam-5687	223	2	ensures	ensure	VERB
ejpam-5687	223	3	that	that	SCONJ
ejpam-5687	223	4	the	the	DET
ejpam-5687	223	5	proposed	propose	VERB
ejpam-5687	223	6	(	(	PUNCT
ejpam-5687	223	7	4	4	X
ejpam-5687	223	8	)	)	PUNCT
ejpam-5687	223	9	will	will	AUX
ejpam-5687	223	10	have	have	VERB
ejpam-5687	223	11	a	a	DET
ejpam-5687	223	12	solution	solution	NOUN
ejpam-5687	223	13	.	.	PUNCT
ejpam-5687	224	1	we	we	PRON
ejpam-5687	224	2	follow	follow	VERB
ejpam-5687	224	3	these	these	DET
ejpam-5687	224	4	steps	step	NOUN
ejpam-5687	224	5	to	to	PART
ejpam-5687	224	6	prove	prove	VERB
ejpam-5687	224	7	the	the	DET
ejpam-5687	224	8	uniqueness	uniqueness	NOUN
ejpam-5687	224	9	of	of	ADP
ejpam-5687	224	10	the	the	DET
ejpam-5687	224	11	answer	answer	NOUN
ejpam-5687	224	12	.	.	PUNCT
ejpam-5687	225	1	please	please	INTJ
ejpam-5687	225	2	allow	allow	VERB
ejpam-5687	225	3	sh1(u	sh1(u	NOUN
ejpam-5687	225	4	)	)	PUNCT
ejpam-5687	225	5	,	,	PUNCT
ejpam-5687	225	6	eh1(u	eh1(u	PROPN
ejpam-5687	225	7	)	)	PUNCT
ejpam-5687	225	8	,	,	PUNCT
ejpam-5687	225	9	ih1(u	ih1(u	PROPN
ejpam-5687	225	10	)	)	PUNCT
ejpam-5687	225	11	,	,	PUNCT
ejpam-5687	225	12	rh1(u	rh1(u	NOUN
ejpam-5687	225	13	)	)	PUNCT
ejpam-5687	225	14	,	,	PUNCT
ejpam-5687	225	15	sv1(u	sv1(u	PROPN
ejpam-5687	225	16	)	)	PUNCT
ejpam-5687	225	17	,	,	PUNCT
ejpam-5687	225	18	ev1(u	ev1(u	NOUN
ejpam-5687	225	19	)	)	PUNCT
ejpam-5687	225	20	,	,	PUNCT
ejpam-5687	225	21	iv1(u	iv1(u	PROPN
ejpam-5687	225	22	)	)	PUNCT
ejpam-5687	225	23	to	to	PART
ejpam-5687	225	24	be	be	AUX
ejpam-5687	225	25	the	the	DET
ejpam-5687	225	26	solution	solution	NOUN
ejpam-5687	225	27	system	system	NOUN
ejpam-5687	225	28	for	for	ADP
ejpam-5687	225	29	(	(	PUNCT
ejpam-5687	225	30	4	4	NUM
ejpam-5687	225	31	)	)	PUNCT
ejpam-5687	225	32	.	.	PUNCT
ejpam-5687	226	1	∥sh	∥sh	PROPN
ejpam-5687	226	2	−	−	NOUN
ejpam-5687	226	3	sh1∥	sh1∥	PROPN
ejpam-5687	226	4	=	=	SYM
ejpam-5687	226	5	∥∥∥∥	∥∥∥∥	PROPN
ejpam-5687	226	6	1	1	NUM
ejpam-5687	226	7	γ(p	γ(p	ADJ
ejpam-5687	226	8	)	)	PUNCT
ejpam-5687	226	9	∫	∫	PROPN
ejpam-5687	226	10	u	u	NOUN
ejpam-5687	226	11	0	0	NUM
ejpam-5687	227	1	(	(	PUNCT
ejpam-5687	227	2	u−	u−	PROPN
ejpam-5687	227	3	y)p−1ψ1(y	y)p−1ψ1(y	PROPN
ejpam-5687	227	4	,	,	PUNCT
ejpam-5687	227	5	sh(u))−	sh(u))−	VERB
ejpam-5687	227	6	ψ1(y	ψ1(y	ADP
ejpam-5687	227	7	,	,	PUNCT
ejpam-5687	227	8	sh1(u	sh1(u	NOUN
ejpam-5687	227	9	)	)	PUNCT
ejpam-5687	227	10	)	)	PUNCT
ejpam-5687	228	1	dy	dy	NOUN
ejpam-5687	228	2	∥∥∥∥	∥∥∥∥	NUM
ejpam-5687	228	3	,	,	PUNCT
ejpam-5687	228	4	≤	≤	NUM
ejpam-5687	228	5	(	(	PUNCT
ejpam-5687	228	6	up	up	ADV
ejpam-5687	228	7	γ(p+	γ(p+	PROPN
ejpam-5687	228	8	1	1	NUM
ejpam-5687	228	9	)	)	PUNCT
ejpam-5687	228	10	η1	η1	NOUN
ejpam-5687	228	11	)	)	PUNCT
ejpam-5687	228	12	∥sh	∥sh	PROPN
ejpam-5687	228	13	−	−	PROPN
ejpam-5687	228	14	sh1∥	sh1∥	PROPN
ejpam-5687	228	15	.	.	PUNCT
ejpam-5687	229	1	(	(	PUNCT
ejpam-5687	229	2	21	21	NUM
ejpam-5687	229	3	)	)	PUNCT
ejpam-5687	229	4	provided	provide	VERB
ejpam-5687	229	5	that	that	PRON
ejpam-5687	229	6	∥sh	∥sh	ADP
ejpam-5687	229	7	−	−	PROPN
ejpam-5687	229	8	sh1∥	sh1∥	PROPN
ejpam-5687	229	9	(	(	PUNCT
ejpam-5687	229	10	1−	1−	NUM
ejpam-5687	229	11	up	up	ADP
ejpam-5687	229	12	γ(p+	γ(p+	PROPN
ejpam-5687	229	13	1	1	NUM
ejpam-5687	229	14	)	)	PUNCT
ejpam-5687	229	15	η1	η1	NOUN
ejpam-5687	229	16	)	)	PUNCT
ejpam-5687	229	17	≤	≤	NOUN
ejpam-5687	229	18	0	0	NUM
ejpam-5687	229	19	.	.	PUNCT
ejpam-5687	230	1	(	(	PUNCT
ejpam-5687	230	2	22	22	NUM
ejpam-5687	230	3	)	)	PUNCT
ejpam-5687	230	4	so	so	ADV
ejpam-5687	230	5	,	,	PUNCT
ejpam-5687	230	6	∥sh	∥sh	PROPN
ejpam-5687	230	7	−	−	PROPN
ejpam-5687	230	8	sh1∥	sh1∥	PROPN
ejpam-5687	230	9	=	=	SYM
ejpam-5687	230	10	0	0	PUNCT
ejpam-5687	231	1	it	it	PRON
ejpam-5687	231	2	’s	’	VERB
ejpam-5687	231	3	implied.sh(u	implied.sh(u	X
ejpam-5687	231	4	)	)	PUNCT
ejpam-5687	232	1	→	→	SYM
ejpam-5687	232	2	sh1(u	sh1(u	NUM
ejpam-5687	232	3	)	)	PUNCT
ejpam-5687	232	4	.	.	PUNCT
ejpam-5687	233	1	we	we	PRON
ejpam-5687	233	2	can	can	AUX
ejpam-5687	233	3	get	get	VERB
ejpam-5687	233	4	eh(u	eh(u	NUM
ejpam-5687	233	5	)	)	PUNCT
ejpam-5687	233	6	,	,	PUNCT
ejpam-5687	233	7	ih(u	ih(u	NOUN
ejpam-5687	233	8	)	)	PUNCT
ejpam-5687	233	9	,	,	PUNCT
ejpam-5687	233	10	rh(u	rh(u	NOUN
ejpam-5687	233	11	)	)	PUNCT
ejpam-5687	233	12	,	,	PUNCT
ejpam-5687	233	13	sv(u	sv(u	PROPN
ejpam-5687	233	14	)	)	PUNCT
ejpam-5687	233	15	,	,	PUNCT
ejpam-5687	233	16	ev(u	ev(u	PUNCT
ejpam-5687	233	17	)	)	PUNCT
ejpam-5687	233	18	,	,	PUNCT
ejpam-5687	233	19	and	and	CCONJ
ejpam-5687	233	20	iv(u	iv(u	NUM
ejpam-5687	233	21	)	)	PUNCT
ejpam-5687	233	22	by	by	ADP
ejpam-5687	233	23	using	use	VERB
ejpam-5687	233	24	the	the	DET
ejpam-5687	233	25	same	same	ADJ
ejpam-5687	233	26	procedure	procedure	NOUN
ejpam-5687	233	27	.	.	PUNCT
ejpam-5687	234	1	this	this	PRON
ejpam-5687	234	2	complete	complete	VERB
ejpam-5687	234	3	the	the	DET
ejpam-5687	234	4	proof	proof	NOUN
ejpam-5687	234	5	of	of	ADP
ejpam-5687	234	6	the	the	DET
ejpam-5687	234	7	(	(	PUNCT
ejpam-5687	234	8	1	1	NUM
ejpam-5687	234	9	)	)	PUNCT
ejpam-5687	234	10	.	.	PUNCT
ejpam-5687	235	1	the	the	DET
ejpam-5687	235	2	positivity	positivity	NOUN
ejpam-5687	235	3	and	and	CCONJ
ejpam-5687	235	4	limit	limit	NOUN
ejpam-5687	235	5	of	of	ADP
ejpam-5687	235	6	solutions	solution	NOUN
ejpam-5687	235	7	is	be	AUX
ejpam-5687	235	8	an	an	DET
ejpam-5687	235	9	important	important	ADJ
ejpam-5687	235	10	part	part	NOUN
ejpam-5687	235	11	of	of	ADP
ejpam-5687	235	12	an	an	DET
ejpam-5687	235	13	epidemiological	epidemiological	ADJ
ejpam-5687	235	14	model	model	NOUN
ejpam-5687	235	15	because	because	SCONJ
ejpam-5687	235	16	of	of	ADP
ejpam-5687	235	17	several	several	ADJ
ejpam-5687	235	18	other	other	ADJ
ejpam-5687	235	19	features	feature	NOUN
ejpam-5687	235	20	.	.	PUNCT
ejpam-5687	236	1	for	for	ADP
ejpam-5687	236	2	this	this	DET
ejpam-5687	236	3	paper	paper	NOUN
ejpam-5687	236	4	,	,	PUNCT
ejpam-5687	236	5	we	we	PRON
ejpam-5687	236	6	prove	prove	VERB
ejpam-5687	236	7	that	that	SCONJ
ejpam-5687	236	8	for	for	ADP
ejpam-5687	236	9	every	every	DET
ejpam-5687	236	10	u	u	NOUN
ejpam-5687	236	11	>	>	X
ejpam-5687	236	12	0	0	PUNCT
ejpam-5687	237	1	all	all	DET
ejpam-5687	237	2	state	state	NOUN
ejpam-5687	237	3	n.	n.	PROPN
ejpam-5687	237	4	ullah	ullah	PROPN
ejpam-5687	237	5	et	et	PROPN
ejpam-5687	237	6	al	al	PROPN
ejpam-5687	237	7	.	.	PUNCT
ejpam-5687	237	8	/	/	SYM
ejpam-5687	237	9	eur	eur	PROPN
ejpam-5687	237	10	.	.	PUNCT
ejpam-5687	238	1	j.	j.	PROPN
ejpam-5687	238	2	pure	pure	PROPN
ejpam-5687	238	3	appl	appl	PROPN
ejpam-5687	238	4	.	.	PROPN
ejpam-5687	238	5	math	math	PROPN
ejpam-5687	238	6	,	,	PUNCT
ejpam-5687	238	7	18	18	NUM
ejpam-5687	238	8	(	(	PUNCT
ejpam-5687	238	9	2	2	NUM
ejpam-5687	238	10	)	)	PUNCT
ejpam-5687	238	11	(	(	PUNCT
ejpam-5687	238	12	2025	2025	NUM
ejpam-5687	238	13	)	)	PUNCT
ejpam-5687	238	14	,	,	PUNCT
ejpam-5687	238	15	5687	5687	NUM
ejpam-5687	238	16	14	14	NUM
ejpam-5687	238	17	of	of	ADP
ejpam-5687	238	18	25	25	NUM
ejpam-5687	238	19	variables	variable	NOUN
ejpam-5687	238	20	are	be	AUX
ejpam-5687	238	21	non	non	ADJ
ejpam-5687	238	22	-	-	ADJ
ejpam-5687	238	23	negative	negative	ADJ
ejpam-5687	238	24	.	.	PUNCT
ejpam-5687	239	1	so	so	ADV
ejpam-5687	239	2	from	from	ADP
ejpam-5687	239	3	system(4	system(4	NOUN
ejpam-5687	239	4	)	)	PUNCT
ejpam-5687	239	5	we	we	PRON
ejpam-5687	239	6	get	get	VERB
ejpam-5687	239	7	:	:	PUNCT
ejpam-5687	239	8	cdp	cdp	NOUN
ejpam-5687	239	9	0,ush(u	0,ush(u	NUM
ejpam-5687	239	10	)	)	PUNCT
ejpam-5687	239	11	∣∣∣	∣∣∣	NOUN
ejpam-5687	240	1	sh=0	sh=0	PROPN
ejpam-5687	240	2	=	=	PUNCT
ejpam-5687	240	3	λh	λh	ADP
ejpam-5687	240	4	≥	≥	NOUN
ejpam-5687	240	5	0	0	NUM
ejpam-5687	240	6	,	,	PUNCT
ejpam-5687	240	7	cdp	cdp	X
ejpam-5687	240	8	0,ueh(u	0,ueh(u	NUM
ejpam-5687	240	9	)	)	PUNCT
ejpam-5687	240	10	∣∣∣	∣∣∣	NOUN
ejpam-5687	240	11	eh=0	eh=0	NUM
ejpam-5687	240	12	=	=	SYM
ejpam-5687	240	13	β1sh	β1sh	PUNCT
ejpam-5687	240	14	iv	iv	NUM
ejpam-5687	240	15	nv	nv	PROPN
ejpam-5687	240	16	≥	≥	NUM
ejpam-5687	240	17	0	0	NUM
ejpam-5687	240	18	,	,	PUNCT
ejpam-5687	240	19	cdp	cdp	X
ejpam-5687	240	20	0,uih(u	0,uih(u	NUM
ejpam-5687	240	21	)	)	PUNCT
ejpam-5687	240	22	∣∣∣	∣∣∣	NOUN
ejpam-5687	240	23	ih=0	ih=0	NOUN
ejpam-5687	240	24	=	=	SYM
ejpam-5687	240	25	σheh	σheh	ADJ
ejpam-5687	240	26	≥	≥	NOUN
ejpam-5687	240	27	0	0	NUM
ejpam-5687	240	28	,	,	PUNCT
ejpam-5687	240	29	cdp	cdp	X
ejpam-5687	240	30	0,urh(u	0,urh(u	NUM
ejpam-5687	240	31	)	)	PUNCT
ejpam-5687	240	32	∣∣∣	∣∣∣	NOUN
ejpam-5687	240	33	rh=0	rh=0	NOUN
ejpam-5687	240	34	=	=	SYM
ejpam-5687	240	35	γih	γih	NOUN
ejpam-5687	240	36	≥	≥	NOUN
ejpam-5687	240	37	0	0	NUM
ejpam-5687	240	38	,	,	PUNCT
ejpam-5687	240	39	cdp	cdp	X
ejpam-5687	240	40	0,usv(u	0,usv(u	NUM
ejpam-5687	240	41	)	)	PUNCT
ejpam-5687	240	42	∣∣∣p	∣∣∣p	NOUN
ejpam-5687	240	43	sv=0	sv=0	NOUN
ejpam-5687	240	44	=	=	SYM
ejpam-5687	240	45	λv	λv	X
ejpam-5687	240	46	≥	≥	NOUN
ejpam-5687	240	47	0	0	NUM
ejpam-5687	240	48	,	,	PUNCT
ejpam-5687	240	49	cdp	cdp	X
ejpam-5687	240	50	0,uev(u	0,uev(u	NUM
ejpam-5687	240	51	)	)	PUNCT
ejpam-5687	240	52	∣∣∣p	∣∣∣p	NOUN
ejpam-5687	240	53	ev=0	ev=0	NOUN
ejpam-5687	240	54	=	=	SYM
ejpam-5687	240	55	β2sv	β2sv	PUNCT
ejpam-5687	240	56	ih	ih	PROPN
ejpam-5687	240	57	nh	nh	PROPN
ejpam-5687	240	58	≥	≥	PROPN
ejpam-5687	240	59	0	0	NUM
ejpam-5687	240	60	,	,	PUNCT
ejpam-5687	240	61	cdp	cdp	VERB
ejpam-5687	240	62	0,uiv(u	0,uiv(u	NUM
ejpam-5687	240	63	)	)	PUNCT
ejpam-5687	240	64	∣∣∣p	∣∣∣p	NOUN
ejpam-5687	240	65	iv=0	iv=0	NUM
ejpam-5687	240	66	=	=	PUNCT
ejpam-5687	240	67	σvev	σvev	NOUN
ejpam-5687	240	68	≥	≥	NOUN
ejpam-5687	240	69	0	0	NUM
ejpam-5687	240	70	.	.	PUNCT
ejpam-5687	241	1	(	(	PUNCT
ejpam-5687	241	2	23	23	NUM
ejpam-5687	241	3	)	)	PUNCT
ejpam-5687	241	4	theorem	theorem	NOUN
ejpam-5687	241	5	2	2	NUM
ejpam-5687	241	6	.	.	PUNCT
ejpam-5687	242	1	the	the	DET
ejpam-5687	242	2	region	region	NOUN
ejpam-5687	242	3	υh	υh	X
ejpam-5687	242	4	=	=	X
ejpam-5687	242	5	{	{	PUNCT
ejpam-5687	242	6	(	(	PUNCT
ejpam-5687	242	7	sh	sh	INTJ
ejpam-5687	242	8	,	,	PUNCT
ejpam-5687	242	9	eh	eh	INTJ
ejpam-5687	242	10	,	,	PUNCT
ejpam-5687	242	11	ih	ih	X
ejpam-5687	242	12	,	,	PUNCT
ejpam-5687	242	13	rh	rh	PROPN
ejpam-5687	242	14	)	)	PUNCT
ejpam-5687	242	15	∈	∈	PROPN
ejpam-5687	242	16	υh+	υh+	VERB
ejpam-5687	242	17	:	:	PUNCT
ejpam-5687	242	18	0	0	NUM
ejpam-5687	242	19	<	<	X
ejpam-5687	242	20	nh(u	nh(u	X
ejpam-5687	242	21	)	)	PUNCT
ejpam-5687	242	22	=	=	SYM
ejpam-5687	242	23	(	(	PUNCT
ejpam-5687	242	24	sh(u	sh(u	X
ejpam-5687	242	25	)	)	PUNCT
ejpam-5687	242	26	+	+	CCONJ
ejpam-5687	242	27	eh(u	eh(u	NUM
ejpam-5687	242	28	)	)	PUNCT
ejpam-5687	243	1	+	+	NOUN
ejpam-5687	243	2	ih(u	ih(u	PUNCT
ejpam-5687	243	3	)	)	PUNCT
ejpam-5687	244	1	+	+	NOUN
ejpam-5687	244	2	rh(u	rh(u	X
ejpam-5687	244	3	)	)	PUNCT
ejpam-5687	244	4	)	)	PUNCT
ejpam-5687	244	5	≤	≤	NOUN
ejpam-5687	244	6	λh	λh	ADP
ejpam-5687	244	7	µh	µh	NOUN
ejpam-5687	244	8	}	}	PUNCT
ejpam-5687	244	9	,	,	PUNCT
ejpam-5687	244	10	and	and	CCONJ
ejpam-5687	244	11	υv	υv	X
ejpam-5687	244	12	=	=	PUNCT
ejpam-5687	244	13	{	{	PUNCT
ejpam-5687	244	14	(	(	PUNCT
ejpam-5687	244	15	sv	sv	INTJ
ejpam-5687	244	16	,	,	PUNCT
ejpam-5687	244	17	ev	ev	PROPN
ejpam-5687	244	18	,	,	PUNCT
ejpam-5687	244	19	iv	iv	X
ejpam-5687	244	20	)	)	PUNCT
ejpam-5687	244	21	∈	∈	PROPN
ejpam-5687	244	22	υv+	υv+	NOUN
ejpam-5687	244	23	:	:	PUNCT
ejpam-5687	244	24	0	0	NUM
ejpam-5687	244	25	<	<	X
ejpam-5687	244	26	nv(u	nv(u	NUM
ejpam-5687	244	27	)	)	PUNCT
ejpam-5687	244	28	=	=	SYM
ejpam-5687	244	29	(	(	PUNCT
ejpam-5687	244	30	sv(u	sv(u	PROPN
ejpam-5687	244	31	)	)	PUNCT
ejpam-5687	244	32	+	+	CCONJ
ejpam-5687	244	33	ev(u	ev(u	PUNCT
ejpam-5687	244	34	)	)	PUNCT
ejpam-5687	244	35	+	+	CCONJ
ejpam-5687	244	36	iv(u	iv(u	NUM
ejpam-5687	244	37	)	)	PUNCT
ejpam-5687	244	38	)	)	PUNCT
ejpam-5687	245	1	≤	≤	NOUN
ejpam-5687	246	1	λv	λv	ADP
ejpam-5687	246	2	µv	µv	PROPN
ejpam-5687	246	3	}	}	PUNCT
ejpam-5687	246	4	,	,	PUNCT
ejpam-5687	246	5	are	be	AUX
ejpam-5687	246	6	positively	positively	ADV
ejpam-5687	246	7	invariant	invariant	ADJ
ejpam-5687	246	8	for	for	ADP
ejpam-5687	246	9	all	all	DET
ejpam-5687	246	10	u	u	PROPN
ejpam-5687	246	11	≥	≥	NOUN
ejpam-5687	246	12	0	0	NUM
ejpam-5687	246	13	.	.	PUNCT
ejpam-5687	247	1	proof	proof	NOUN
ejpam-5687	247	2	.	.	PUNCT
ejpam-5687	248	1	to	to	PART
ejpam-5687	248	2	add	add	VERB
ejpam-5687	248	3	the	the	DET
ejpam-5687	248	4	equations	equation	NOUN
ejpam-5687	248	5	of	of	ADP
ejpam-5687	248	6	(	(	PUNCT
ejpam-5687	248	7	4	4	NUM
ejpam-5687	248	8	)	)	PUNCT
ejpam-5687	248	9	of	of	ADP
ejpam-5687	248	10	human	human	ADJ
ejpam-5687	248	11	and	and	CCONJ
ejpam-5687	248	12	vector	vector	NOUN
ejpam-5687	248	13	compartment	compartment	NOUN
ejpam-5687	248	14	,	,	PUNCT
ejpam-5687	248	15	we	we	PRON
ejpam-5687	248	16	get	get	VERB
ejpam-5687	248	17	cdpnh(u	cdpnh(u	NOUN
ejpam-5687	248	18	)	)	PUNCT
ejpam-5687	248	19	=	=	NOUN
ejpam-5687	248	20	λh	λh	ADP
ejpam-5687	248	21	−	−	PROPN
ejpam-5687	248	22	µhnh	µhnh	ADJ
ejpam-5687	248	23	,	,	PUNCT
ejpam-5687	248	24	cdpnv(u	cdpnv(u	NOUN
ejpam-5687	248	25	)	)	PUNCT
ejpam-5687	248	26	=	=	SYM
ejpam-5687	249	1	λv	λv	ADP
ejpam-5687	249	2	−	−	PROPN
ejpam-5687	249	3	µvnv	µvnv	NOUN
ejpam-5687	249	4	,	,	PUNCT
ejpam-5687	249	5	(	(	PUNCT
ejpam-5687	249	6	24	24	NUM
ejpam-5687	249	7	)	)	PUNCT
ejpam-5687	249	8	use	use	NOUN
ejpam-5687	249	9	of	of	ADP
ejpam-5687	249	10	standard	standard	ADJ
ejpam-5687	249	11	comparison	comparison	NOUN
ejpam-5687	249	12	theorem	theorem	VERB
ejpam-5687	249	13	[	[	X
ejpam-5687	249	14	36	36	NUM
ejpam-5687	249	15	]	]	PUNCT
ejpam-5687	249	16	,	,	PUNCT
ejpam-5687	249	17	provides	provide	VERB
ejpam-5687	249	18	nh(u	nh(u	NOUN
ejpam-5687	249	19	)	)	PUNCT
ejpam-5687	249	20	≤	≤	NOUN
ejpam-5687	249	21	(	(	PUNCT
ejpam-5687	249	22	nh(0)−	nh(0)−	NOUN
ejpam-5687	249	23	λh	λh	ADP
ejpam-5687	249	24	µh	µh	NOUN
ejpam-5687	249	25	)	)	PUNCT
ejpam-5687	249	26	fp	fp	PROPN
ejpam-5687	249	27	(	(	PUNCT
ejpam-5687	249	28	−µhtp	−µhtp	NOUN
ejpam-5687	249	29	)	)	PUNCT
ejpam-5687	249	30	+	+	CCONJ
ejpam-5687	249	31	λh	λh	ADP
ejpam-5687	249	32	µh	µh	ADV
ejpam-5687	249	33	,	,	PUNCT
ejpam-5687	249	34	∀u	∀u	NOUN
ejpam-5687	249	35	∈	∈	NOUN
ejpam-5687	250	1	[	[	X
ejpam-5687	250	2	0,∞	0,∞	NOUN
ejpam-5687	250	3	)	)	PUNCT
ejpam-5687	250	4	,	,	PUNCT
ejpam-5687	250	5	nv(u	nv(u	CCONJ
ejpam-5687	250	6	)	)	PUNCT
ejpam-5687	250	7	≤	≤	NOUN
ejpam-5687	250	8	(	(	PUNCT
ejpam-5687	250	9	nv(0)−	nv(0)−	NOUN
ejpam-5687	250	10	λv	λv	X
ejpam-5687	250	11	µv	µv	PROPN
ejpam-5687	250	12	)	)	PUNCT
ejpam-5687	251	1	fp	fp	PROPN
ejpam-5687	251	2	(	(	PUNCT
ejpam-5687	251	3	−µvtp	−µvtp	PROPN
ejpam-5687	251	4	)	)	PUNCT
ejpam-5687	252	1	+	+	CCONJ
ejpam-5687	252	2	λv	λv	ADP
ejpam-5687	252	3	µv	µv	NOUN
ejpam-5687	252	4	,	,	PUNCT
ejpam-5687	253	1	∀u	∀u	NOUN
ejpam-5687	253	2	∈	∈	NOUN
ejpam-5687	254	1	[	[	X
ejpam-5687	254	2	0,∞	0,∞	NOUN
ejpam-5687	254	3	)	)	PUNCT
ejpam-5687	254	4	,	,	PUNCT
ejpam-5687	254	5	(	(	PUNCT
ejpam-5687	254	6	25	25	NUM
ejpam-5687	254	7	)	)	PUNCT
ejpam-5687	254	8	this	this	PRON
ejpam-5687	254	9	implies	imply	VERB
ejpam-5687	254	10	that	that	PRON
ejpam-5687	254	11	nh(u	nh(u	NOUN
ejpam-5687	254	12	)	)	PUNCT
ejpam-5687	254	13	→	→	PUNCT
ejpam-5687	254	14	λh	λh	ADP
ejpam-5687	254	15	µh	µh	ADP
ejpam-5687	254	16	t→	t→	X
ejpam-5687	254	17	∞	∞	PROPN
ejpam-5687	254	18	and	and	CCONJ
ejpam-5687	254	19	nv(u	nv(u	NUM
ejpam-5687	254	20	)	)	PUNCT
ejpam-5687	254	21	→	→	SYM
ejpam-5687	254	22	λv	λv	ADP
ejpam-5687	254	23	µv	µv	PROPN
ejpam-5687	254	24	t→	t→	PROPN
ejpam-5687	254	25	∞.	∞.	PROPN
ejpam-5687	254	26	next	next	ADV
ejpam-5687	254	27	,	,	PUNCT
ejpam-5687	254	28	let	let	VERB
ejpam-5687	254	29	s	s	PRON
ejpam-5687	254	30	=	=	X
ejpam-5687	254	31	(	(	PUNCT
ejpam-5687	254	32	sh(u	sh(u	NOUN
ejpam-5687	254	33	)	)	PUNCT
ejpam-5687	254	34	,	,	PUNCT
ejpam-5687	254	35	eh(u	eh(u	NUM
ejpam-5687	254	36	)	)	PUNCT
ejpam-5687	254	37	,	,	PUNCT
ejpam-5687	254	38	ih(u	ih(u	NOUN
ejpam-5687	254	39	)	)	PUNCT
ejpam-5687	254	40	,	,	PUNCT
ejpam-5687	254	41	rh(u	rh(u	NOUN
ejpam-5687	254	42	)	)	PUNCT
ejpam-5687	254	43	,	,	PUNCT
ejpam-5687	254	44	sv(u	sv(u	PROPN
ejpam-5687	254	45	)	)	PUNCT
ejpam-5687	254	46	,	,	PUNCT
ejpam-5687	254	47	ev(u	ev(u	PUNCT
ejpam-5687	254	48	)	)	PUNCT
ejpam-5687	254	49	,	,	PUNCT
ejpam-5687	254	50	iv(u	iv(u	NUM
ejpam-5687	254	51	)	)	PUNCT
ejpam-5687	254	52	)	)	PUNCT
ejpam-5687	255	1	,	,	PUNCT
ejpam-5687	255	2	then	then	ADV
ejpam-5687	255	3	υ	υ	PROPN
ejpam-5687	255	4	=	=	PUNCT
ejpam-5687	255	5	{	{	PUNCT
ejpam-5687	255	6	s	s	NOUN
ejpam-5687	255	7	∈	∈	PROPN
ejpam-5687	255	8	r7	r7	NOUN
ejpam-5687	255	9	+	+	CCONJ
ejpam-5687	255	10	:	:	SYM
ejpam-5687	255	11	0	0	NUM
ejpam-5687	255	12	<	<	X
ejpam-5687	255	13	nh(u	nh(u	X
ejpam-5687	255	14	)	)	PUNCT
ejpam-5687	255	15	≤	≤	NOUN
ejpam-5687	255	16	λh	λh	ADP
ejpam-5687	255	17	µh	µh	PROPN
ejpam-5687	255	18	,	,	PUNCT
ejpam-5687	255	19	0	0	NUM
ejpam-5687	255	20	<	<	X
ejpam-5687	255	21	nv(u	nv(u	NUM
ejpam-5687	255	22	)	)	PUNCT
ejpam-5687	255	23	≤	≤	NOUN
ejpam-5687	256	1	λv	λv	ADP
ejpam-5687	256	2	µv	µv	PROPN
ejpam-5687	256	3	}	}	PUNCT
ejpam-5687	256	4	,	,	PUNCT
ejpam-5687	256	5	(	(	PUNCT
ejpam-5687	256	6	26	26	NUM
ejpam-5687	256	7	)	)	PUNCT
ejpam-5687	256	8	is	be	AUX
ejpam-5687	256	9	the	the	DET
ejpam-5687	256	10	biologically	biologically	ADV
ejpam-5687	256	11	applicable	applicable	ADJ
ejpam-5687	256	12	region	region	NOUN
ejpam-5687	256	13	of	of	ADP
ejpam-5687	256	14	the	the	DET
ejpam-5687	256	15	model	model	NOUN
ejpam-5687	256	16	(	(	PUNCT
ejpam-5687	256	17	4	4	NUM
ejpam-5687	256	18	)	)	PUNCT
ejpam-5687	256	19	of	of	ADP
ejpam-5687	256	20	the	the	DET
ejpam-5687	256	21	infection	infection	NOUN
ejpam-5687	256	22	.	.	PUNCT
ejpam-5687	257	1	n.	n.	PROPN
ejpam-5687	257	2	ullah	ullah	PROPN
ejpam-5687	257	3	et	et	PROPN
ejpam-5687	257	4	al	al	PROPN
ejpam-5687	257	5	.	.	PUNCT
ejpam-5687	257	6	/	/	SYM
ejpam-5687	257	7	eur	eur	PROPN
ejpam-5687	257	8	.	.	PUNCT
ejpam-5687	258	1	j.	j.	PROPN
ejpam-5687	258	2	pure	pure	PROPN
ejpam-5687	258	3	appl	appl	PROPN
ejpam-5687	258	4	.	.	PROPN
ejpam-5687	258	5	math	math	PROPN
ejpam-5687	258	6	,	,	PUNCT
ejpam-5687	258	7	18	18	NUM
ejpam-5687	258	8	(	(	PUNCT
ejpam-5687	258	9	2	2	NUM
ejpam-5687	258	10	)	)	PUNCT
ejpam-5687	258	11	(	(	PUNCT
ejpam-5687	258	12	2025	2025	NUM
ejpam-5687	258	13	)	)	PUNCT
ejpam-5687	258	14	,	,	PUNCT
ejpam-5687	258	15	5687	5687	NUM
ejpam-5687	258	16	15	15	NUM
ejpam-5687	258	17	of	of	ADP
ejpam-5687	258	18	25	25	NUM
ejpam-5687	258	19	3.2	3.2	NUM
ejpam-5687	258	20	.	.	PUNCT
ejpam-5687	259	1	disease	disease	NOUN
ejpam-5687	259	2	-	-	PUNCT
ejpam-5687	259	3	free	free	ADJ
ejpam-5687	259	4	steady	steady	ADJ
ejpam-5687	259	5	state	state	NOUN
ejpam-5687	259	6	here	here	ADV
ejpam-5687	259	7	,	,	PUNCT
ejpam-5687	259	8	we	we	PRON
ejpam-5687	259	9	denote	denote	VERB
ejpam-5687	259	10	the	the	DET
ejpam-5687	259	11	disease	disease	NOUN
ejpam-5687	259	12	-	-	PUNCT
ejpam-5687	259	13	free	free	ADJ
ejpam-5687	259	14	steady	steady	ADJ
ejpam-5687	259	15	state	state	NOUN
ejpam-5687	259	16	of	of	ADP
ejpam-5687	259	17	our	our	PRON
ejpam-5687	259	18	system	system	NOUN
ejpam-5687	259	19	by	by	ADP
ejpam-5687	259	20	e0	e0	PROPN
ejpam-5687	259	21	and	and	CCONJ
ejpam-5687	259	22	is	be	AUX
ejpam-5687	259	23	determined	determine	VERB
ejpam-5687	259	24	from	from	ADP
ejpam-5687	259	25	the	the	DET
ejpam-5687	259	26	following	follow	VERB
ejpam-5687	259	27	system	system	NOUN
ejpam-5687	259	28	in	in	ADP
ejpam-5687	259	29	the	the	DET
ejpam-5687	259	30	absence	absence	NOUN
ejpam-5687	259	31	of	of	ADP
ejpam-5687	259	32	infection:	infection:	NOUN
ejpam-5687	259	33	λh	λh	ADP
ejpam-5687	259	34	−	−	PROPN
ejpam-5687	259	35	β1sh	β1sh	PUNCT
ejpam-5687	259	36	iv	iv	NUM
ejpam-5687	259	37	nv	nv	PROPN
ejpam-5687	259	38	−	−	PROPN
ejpam-5687	259	39	µhsh	µhsh	NOUN
ejpam-5687	259	40	=	=	SYM
ejpam-5687	259	41	0	0	NUM
ejpam-5687	259	42	,	,	PUNCT
ejpam-5687	259	43	β1sh	β1sh	PUNCT
ejpam-5687	260	1	iv	iv	X
ejpam-5687	260	2	nv	nv	PROPN
ejpam-5687	260	3	−	−	PROPN
ejpam-5687	260	4	(	(	PUNCT
ejpam-5687	260	5	σh	σh	PROPN
ejpam-5687	260	6	+	+	X
ejpam-5687	260	7	µh)eh	µh)eh	X
ejpam-5687	260	8	=	=	SYM
ejpam-5687	260	9	0	0	NUM
ejpam-5687	260	10	,	,	PUNCT
ejpam-5687	260	11	σheh	σheh	ADJ
ejpam-5687	260	12	−	−	PROPN
ejpam-5687	260	13	(	(	PUNCT
ejpam-5687	260	14	γ	γ	X
ejpam-5687	260	15	+	+	X
ejpam-5687	260	16	µh)ih	µh)ih	SYM
ejpam-5687	260	17	=	=	SYM
ejpam-5687	260	18	0	0	NUM
ejpam-5687	260	19	,	,	PUNCT
ejpam-5687	260	20	γih	γih	NOUN
ejpam-5687	260	21	−	−	PROPN
ejpam-5687	261	1	µhrh	µhrh	NOUN
ejpam-5687	262	1	=	=	NOUN
ejpam-5687	262	2	0	0	PROPN
ejpam-5687	262	3	,	,	PUNCT
ejpam-5687	262	4	λv	λv	ADP
ejpam-5687	262	5	−	−	PROPN
ejpam-5687	262	6	β2sv	β2sv	PUNCT
ejpam-5687	262	7	ih	ih	PROPN
ejpam-5687	262	8	nh	nh	PROPN
ejpam-5687	263	1	−	−	PROPN
ejpam-5687	263	2	µvsv	µvsv	ADJ
ejpam-5687	263	3	=	=	SYM
ejpam-5687	263	4	0	0	NUM
ejpam-5687	263	5	,	,	PUNCT
ejpam-5687	263	6	β2sv	β2sv	PUNCT
ejpam-5687	263	7	ih	ih	NOUN
ejpam-5687	263	8	nh	nh	PROPN
ejpam-5687	263	9	−	−	PROPN
ejpam-5687	264	1	(	(	PUNCT
ejpam-5687	264	2	σv	σv	VERB
ejpam-5687	264	3	+	+	PUNCT
ejpam-5687	264	4	µv)ev	µv)ev	PUNCT
ejpam-5687	264	5	=	=	SYM
ejpam-5687	264	6	0	0	NUM
ejpam-5687	264	7	,	,	PUNCT
ejpam-5687	264	8	σvev	σvev	NOUN
ejpam-5687	264	9	−	−	PROPN
ejpam-5687	264	10	µviv	µviv	NOUN
ejpam-5687	264	11	=	=	NOUN
ejpam-5687	264	12	0	0	X
ejpam-5687	264	13	.	.	PUNCT
ejpam-5687	265	1	(	(	PUNCT
ejpam-5687	265	2	27	27	NUM
ejpam-5687	265	3	)	)	PUNCT
ejpam-5687	265	4	from	from	ADP
ejpam-5687	265	5	the	the	DET
ejpam-5687	265	6	first	first	ADJ
ejpam-5687	265	7	equation	equation	NOUN
ejpam-5687	265	8	of	of	ADP
ejpam-5687	265	9	(	(	PUNCT
ejpam-5687	265	10	27	27	NUM
ejpam-5687	265	11	)	)	PUNCT
ejpam-5687	265	12	,	,	PUNCT
ejpam-5687	265	13	we	we	PRON
ejpam-5687	265	14	have	have	VERB
ejpam-5687	265	15	λh	λh	VERB
ejpam-5687	265	16	−	−	PRON
ejpam-5687	265	17	µhsh	µhsh	NOUN
ejpam-5687	265	18	=	=	SYM
ejpam-5687	265	19	0	0	PUNCT
ejpam-5687	266	1	=	=	NOUN
ejpam-5687	266	2	⇒	⇒	NOUN
ejpam-5687	266	3	s0	s0	NOUN
ejpam-5687	266	4	h	h	NOUN
ejpam-5687	267	1	=	=	PUNCT
ejpam-5687	267	2	λh	λh	ADP
ejpam-5687	267	3	µh	µh	INTJ
ejpam-5687	267	4	,	,	PUNCT
ejpam-5687	267	5	(	(	PUNCT
ejpam-5687	267	6	28	28	NUM
ejpam-5687	267	7	)	)	PUNCT
ejpam-5687	267	8	and	and	CCONJ
ejpam-5687	267	9	from	from	ADP
ejpam-5687	267	10	the	the	DET
ejpam-5687	267	11	fifth	fifth	ADJ
ejpam-5687	267	12	equation	equation	NOUN
ejpam-5687	267	13	of	of	ADP
ejpam-5687	267	14	(	(	PUNCT
ejpam-5687	267	15	27	27	NUM
ejpam-5687	267	16	)	)	PUNCT
ejpam-5687	267	17	,	,	PUNCT
ejpam-5687	267	18	we	we	PRON
ejpam-5687	267	19	have	have	VERB
ejpam-5687	267	20	λv	λv	INTJ
ejpam-5687	267	21	−	−	PROPN
ejpam-5687	267	22	µvsv	µvsv	ADJ
ejpam-5687	267	23	=	=	SYM
ejpam-5687	267	24	0	0	PUNCT
ejpam-5687	268	1	=	=	NOUN
ejpam-5687	268	2	⇒	⇒	NOUN
ejpam-5687	268	3	s0	s0	PROPN
ejpam-5687	268	4	v	v	NOUN
ejpam-5687	269	1	=	=	X
ejpam-5687	269	2	λv	λv	X
ejpam-5687	269	3	µv	µv	NOUN
ejpam-5687	269	4	.	.	PUNCT
ejpam-5687	270	1	(	(	PUNCT
ejpam-5687	270	2	29	29	NUM
ejpam-5687	270	3	)	)	PUNCT
ejpam-5687	270	4	thus	thus	ADV
ejpam-5687	270	5	,	,	PUNCT
ejpam-5687	270	6	the	the	DET
ejpam-5687	270	7	dfe	dfe	PROPN
ejpam-5687	270	8	of	of	ADP
ejpam-5687	270	9	our	our	PRON
ejpam-5687	270	10	system	system	NOUN
ejpam-5687	270	11	is	be	AUX
ejpam-5687	270	12	e0(s0	e0(s0	NOUN
ejpam-5687	270	13	h	h	NOUN
ejpam-5687	270	14	,	,	PUNCT
ejpam-5687	270	15	e	e	PROPN
ejpam-5687	270	16	0	0	NUM
ejpam-5687	270	17	h	h	NOUN
ejpam-5687	270	18	,	,	PUNCT
ejpam-5687	271	1	i	i	PRON
ejpam-5687	271	2	0	0	NUM
ejpam-5687	271	3	h	h	NOUN
ejpam-5687	271	4	,	,	PUNCT
ejpam-5687	271	5	r	r	NOUN
ejpam-5687	271	6	0	0	NUM
ejpam-5687	271	7	h	h	NOUN
ejpam-5687	271	8	,	,	PUNCT
ejpam-5687	271	9	s	s	PART
ejpam-5687	271	10	0	0	NUM
ejpam-5687	271	11	v	v	NOUN
ejpam-5687	271	12	,	,	PUNCT
ejpam-5687	271	13	e	e	PROPN
ejpam-5687	271	14	0	0	NUM
ejpam-5687	271	15	v	v	NOUN
ejpam-5687	271	16	,	,	PUNCT
ejpam-5687	271	17	i	i	PRON
ejpam-5687	271	18	0	0	NUM
ejpam-5687	271	19	v	v	NOUN
ejpam-5687	271	20	)	)	PUNCT
ejpam-5687	271	21	=	=	SYM
ejpam-5687	272	1	(	(	PUNCT
ejpam-5687	272	2	λh	λh	ADP
ejpam-5687	272	3	µh	µh	INTJ
ejpam-5687	272	4	,	,	PUNCT
ejpam-5687	272	5	0	0	NUM
ejpam-5687	272	6	,	,	PUNCT
ejpam-5687	272	7	0	0	NUM
ejpam-5687	272	8	,	,	PUNCT
ejpam-5687	272	9	0	0	NUM
ejpam-5687	272	10	,	,	PUNCT
ejpam-5687	272	11	λv	λv	ADP
ejpam-5687	272	12	µv	µv	PROPN
ejpam-5687	272	13	,	,	PUNCT
ejpam-5687	272	14	0	0	NUM
ejpam-5687	272	15	,	,	PUNCT
ejpam-5687	272	16	0	0	NUM
ejpam-5687	272	17	)	)	PUNCT
ejpam-5687	272	18	.	.	PUNCT
ejpam-5687	273	1	(	(	PUNCT
ejpam-5687	273	2	30	30	NUM
ejpam-5687	273	3	)	)	PUNCT
ejpam-5687	273	4	3.3	3.3	NUM
ejpam-5687	273	5	.	.	PUNCT
ejpam-5687	274	1	basic	basic	ADJ
ejpam-5687	274	2	reproduction	reproduction	NOUN
ejpam-5687	274	3	number	number	NOUN
ejpam-5687	274	4	the	the	DET
ejpam-5687	274	5	basic	basic	ADJ
ejpam-5687	274	6	reproduction	reproduction	NOUN
ejpam-5687	274	7	number	number	NOUN
ejpam-5687	274	8	,	,	PUNCT
ejpam-5687	274	9	r0	r0	NOUN
ejpam-5687	274	10	,	,	PUNCT
ejpam-5687	274	11	is	be	AUX
ejpam-5687	274	12	a	a	DET
ejpam-5687	274	13	key	key	ADJ
ejpam-5687	274	14	metric	metric	NOUN
ejpam-5687	274	15	in	in	ADP
ejpam-5687	274	16	epidemiology	epidemiology	NOUN
ejpam-5687	274	17	,	,	PUNCT
ejpam-5687	274	18	representing	represent	VERB
ejpam-5687	274	19	the	the	DET
ejpam-5687	274	20	average	average	ADJ
ejpam-5687	274	21	number	number	NOUN
ejpam-5687	274	22	of	of	ADP
ejpam-5687	274	23	secondary	secondary	ADJ
ejpam-5687	274	24	infections	infection	NOUN
ejpam-5687	274	25	caused	cause	VERB
ejpam-5687	274	26	by	by	ADP
ejpam-5687	274	27	one	one	NUM
ejpam-5687	274	28	infected	infect	VERB
ejpam-5687	274	29	individual	individual	NOUN
ejpam-5687	274	30	in	in	ADP
ejpam-5687	274	31	a	a	DET
ejpam-5687	274	32	fully	fully	ADV
ejpam-5687	274	33	susceptible	susceptible	ADJ
ejpam-5687	274	34	population	population	NOUN
ejpam-5687	274	35	.	.	PUNCT
ejpam-5687	275	1	it	it	PRON
ejpam-5687	275	2	is	be	AUX
ejpam-5687	275	3	an	an	DET
ejpam-5687	275	4	important	important	ADJ
ejpam-5687	275	5	parameter	parameter	NOUN
ejpam-5687	275	6	which	which	PRON
ejpam-5687	275	7	helps	help	VERB
ejpam-5687	275	8	in	in	ADP
ejpam-5687	275	9	designing	design	VERB
ejpam-5687	275	10	effective	effective	ADJ
ejpam-5687	275	11	control	control	NOUN
ejpam-5687	275	12	measures	measure	NOUN
ejpam-5687	275	13	,	,	PUNCT
ejpam-5687	275	14	such	such	ADJ
ejpam-5687	275	15	as	as	ADP
ejpam-5687	275	16	vaccination	vaccination	NOUN
ejpam-5687	275	17	or	or	CCONJ
ejpam-5687	275	18	social	social	ADJ
ejpam-5687	275	19	distancing	distancing	NOUN
ejpam-5687	275	20	,	,	PUNCT
ejpam-5687	275	21	to	to	PART
ejpam-5687	275	22	reduce	reduce	VERB
ejpam-5687	275	23	disease	disease	NOUN
ejpam-5687	275	24	spread	spread	VERB
ejpam-5687	275	25	.	.	PUNCT
ejpam-5687	276	1	to	to	PART
ejpam-5687	276	2	calculate	calculate	VERB
ejpam-5687	276	3	r0	r0	NOUN
ejpam-5687	276	4	,	,	PUNCT
ejpam-5687	276	5	we	we	PRON
ejpam-5687	276	6	apply	apply	VERB
ejpam-5687	276	7	the	the	DET
ejpam-5687	276	8	next	next	ADJ
ejpam-5687	276	9	-	-	PUNCT
ejpam-5687	276	10	generation	generation	NOUN
ejpam-5687	276	11	matrix	matrix	NOUN
ejpam-5687	276	12	method	method	NOUN
ejpam-5687	276	13	,	,	PUNCT
ejpam-5687	276	14	which	which	PRON
ejpam-5687	276	15	includes	include	VERB
ejpam-5687	276	16	the	the	DET
ejpam-5687	276	17	matrices	matrix	NOUN
ejpam-5687	276	18	f	f	PROPN
ejpam-5687	276	19	and	and	CCONJ
ejpam-5687	276	20	v	v	ADP
ejpam-5687	276	21	[	[	X
ejpam-5687	276	22	17	17	NUM
ejpam-5687	276	23	,	,	PUNCT
ejpam-5687	276	24	18	18	NUM
ejpam-5687	276	25	]	]	PUNCT
ejpam-5687	276	26	as	as	ADP
ejpam-5687	276	27	f	f	PROPN
ejpam-5687	276	28	=	=	PROPN
ejpam-5687	276	29			NOUN
ejpam-5687	276	30	0	0	NUM
ejpam-5687	276	31	0	0	SYM
ejpam-5687	276	32	0	0	NUM
ejpam-5687	276	33	β1	β1	PROPN
ejpam-5687	276	34	s0	s0	PROPN
ejpam-5687	276	35	h	h	PROPN
ejpam-5687	276	36	s0	s0	PROPN
ejpam-5687	276	37	v	v	ADP
ejpam-5687	276	38	0	0	NUM
ejpam-5687	276	39	0	0	NUM
ejpam-5687	276	40	0	0	NUM
ejpam-5687	276	41	0	0	SYM
ejpam-5687	276	42	0	0	NUM
ejpam-5687	276	43	β2	β2	NOUN
ejpam-5687	276	44	s0	s0	PROPN
ejpam-5687	276	45	v	v	ADP
ejpam-5687	276	46	s0	s0	PROPN
ejpam-5687	276	47	h	h	NOUN
ejpam-5687	276	48	0	0	NUM
ejpam-5687	276	49	0	0	NUM
ejpam-5687	276	50	0	0	NUM
ejpam-5687	276	51	0	0	NUM
ejpam-5687	276	52	0	0	NUM
ejpam-5687	276	53	0	0	NUM
ejpam-5687	276	54			NOUN
ejpam-5687	276	55	and	and	CCONJ
ejpam-5687	276	56	v	v	NOUN
ejpam-5687	276	57	=	=	SYM
ejpam-5687	276	58			X
ejpam-5687	276	59	σh	σh	ADP
ejpam-5687	276	60	+	+	NOUN
ejpam-5687	276	61	µh	µh	NOUN
ejpam-5687	276	62	0	0	NUM
ejpam-5687	276	63	0	0	NUM
ejpam-5687	276	64	0	0	NUM
ejpam-5687	276	65	−σh	−σh	NUM
ejpam-5687	276	66	γ	γ	NOUN
ejpam-5687	276	67	+	+	NOUN
ejpam-5687	276	68	µh	µh	NOUN
ejpam-5687	276	69	0	0	NUM
ejpam-5687	276	70	0	0	NUM
ejpam-5687	276	71	0	0	NUM
ejpam-5687	276	72	0	0	NUM
ejpam-5687	277	1	σv	σv	PROPN
ejpam-5687	278	1	+	+	CCONJ
ejpam-5687	278	2	µv	µv	PROPN
ejpam-5687	278	3	0	0	NUM
ejpam-5687	278	4	0	0	NUM
ejpam-5687	278	5	0	0	NUM
ejpam-5687	278	6	−σv	−σv	ADP
ejpam-5687	278	7	µv	µv	PROPN
ejpam-5687	278	8			PROPN
ejpam-5687	279	1	n.	n.	PROPN
ejpam-5687	279	2	ullah	ullah	PROPN
ejpam-5687	279	3	et	et	PROPN
ejpam-5687	279	4	al	al	PROPN
ejpam-5687	279	5	.	.	PUNCT
ejpam-5687	279	6	/	/	SYM
ejpam-5687	279	7	eur	eur	PROPN
ejpam-5687	279	8	.	.	PUNCT
ejpam-5687	280	1	j.	j.	PROPN
ejpam-5687	280	2	pure	pure	PROPN
ejpam-5687	280	3	appl	appl	PROPN
ejpam-5687	280	4	.	.	PROPN
ejpam-5687	280	5	math	math	PROPN
ejpam-5687	280	6	,	,	PUNCT
ejpam-5687	280	7	18	18	NUM
ejpam-5687	280	8	(	(	PUNCT
ejpam-5687	280	9	2	2	NUM
ejpam-5687	280	10	)	)	PUNCT
ejpam-5687	280	11	(	(	PUNCT
ejpam-5687	280	12	2025	2025	NUM
ejpam-5687	280	13	)	)	PUNCT
ejpam-5687	280	14	,	,	PUNCT
ejpam-5687	280	15	5687	5687	NUM
ejpam-5687	280	16	16	16	NUM
ejpam-5687	280	17	of	of	ADP
ejpam-5687	280	18	25	25	NUM
ejpam-5687	280	19	this	this	PRON
ejpam-5687	280	20	implies	imply	VERB
ejpam-5687	280	21	that	that	SCONJ
ejpam-5687	280	22	fv	fv	PROPN
ejpam-5687	280	23	−1	−1	NOUN
ejpam-5687	280	24	=	=	PUNCT
ejpam-5687	280	25			NOUN
ejpam-5687	280	26	0	0	NUM
ejpam-5687	280	27	0	0	NUM
ejpam-5687	280	28	β1σvs0	β1σvs0	NOUN
ejpam-5687	280	29	h	h	NOUN
ejpam-5687	280	30	µv(µv+σv)s0	µv(µv+σv)s0	NOUN
ejpam-5687	280	31	v	v	X
ejpam-5687	280	32	β1s0	β1s0	PUNCT
ejpam-5687	280	33	h	h	NOUN
ejpam-5687	280	34	µvs0	µvs0	NOUN
ejpam-5687	280	35	v	v	ADP
ejpam-5687	280	36	0	0	NUM
ejpam-5687	280	37	0	0	NUM
ejpam-5687	280	38	0	0	NUM
ejpam-5687	280	39	0	0	NUM
ejpam-5687	281	1	β2σhs	β2σhs	PROPN
ejpam-5687	281	2	0	0	NUM
ejpam-5687	281	3	v	v	NOUN
ejpam-5687	281	4	(	(	PUNCT
ejpam-5687	281	5	σh+µh)(γ+µh)s	σh+µh)(γ+µh)s	PROPN
ejpam-5687	281	6	0	0	NUM
ejpam-5687	281	7	h	h	NOUN
ejpam-5687	282	1	β2s0	β2s0	X
ejpam-5687	282	2	v	v	X
ejpam-5687	282	3	(	(	PUNCT
ejpam-5687	282	4	γ+µh)s	γ+µh)s	NOUN
ejpam-5687	282	5	0	0	NUM
ejpam-5687	282	6	h	h	NOUN
ejpam-5687	282	7	0	0	NUM
ejpam-5687	282	8	0	0	NUM
ejpam-5687	282	9	0	0	NUM
ejpam-5687	282	10	0	0	NUM
ejpam-5687	282	11	0	0	NUM
ejpam-5687	282	12	0	0	NUM
ejpam-5687	282	13			NOUN
ejpam-5687	282	14	(	(	PUNCT
ejpam-5687	282	15	31	31	NUM
ejpam-5687	282	16	)	)	PUNCT
ejpam-5687	282	17	after	after	ADP
ejpam-5687	282	18	simplification	simplification	NOUN
ejpam-5687	282	19	,	,	PUNCT
ejpam-5687	282	20	r0	r0	NOUN
ejpam-5687	282	21	is	be	AUX
ejpam-5687	282	22	obtained	obtain	VERB
ejpam-5687	282	23	by	by	ADP
ejpam-5687	282	24	ρ	ρ	PROPN
ejpam-5687	282	25	(	(	PUNCT
ejpam-5687	282	26	fv−1	fv−1	PROPN
ejpam-5687	282	27	)	)	PUNCT
ejpam-5687	282	28	,	,	PUNCT
ejpam-5687	282	29	as	as	ADP
ejpam-5687	282	30	r0	r0	NOUN
ejpam-5687	282	31	=	=	NOUN
ejpam-5687	282	32	√	√	PROPN
ejpam-5687	282	33	β1β2	β1β2	PRON
ejpam-5687	282	34	σhσv	σhσv	X
ejpam-5687	282	35	(	(	PUNCT
ejpam-5687	282	36	σh	σh	PROPN
ejpam-5687	282	37	+	+	ADJ
ejpam-5687	282	38	µh)(γ	µh)(γ	PROPN
ejpam-5687	283	1	+	+	PUNCT
ejpam-5687	283	2	µh)µv(σv	µh)µv(σv	PUNCT
ejpam-5687	283	3	+	+	X
ejpam-5687	283	4	µv	µv	PROPN
ejpam-5687	283	5	)	)	PUNCT
ejpam-5687	283	6	(	(	PUNCT
ejpam-5687	283	7	32	32	NUM
ejpam-5687	283	8	)	)	PUNCT
ejpam-5687	283	9	theorem	theorem	NOUN
ejpam-5687	283	10	3	3	NUM
ejpam-5687	283	11	.	.	PUNCT
ejpam-5687	284	1	the	the	DET
ejpam-5687	284	2	dfe	dfe	PROPN
ejpam-5687	284	3	of	of	ADP
ejpam-5687	284	4	the	the	DET
ejpam-5687	284	5	model	model	NOUN
ejpam-5687	284	6	(	(	PUNCT
ejpam-5687	284	7	4	4	NUM
ejpam-5687	284	8	)	)	PUNCT
ejpam-5687	284	9	is	be	AUX
ejpam-5687	284	10	locally	locally	ADV
ejpam-5687	284	11	asymptotically	asymptotically	ADV
ejpam-5687	284	12	stable	stable	ADJ
ejpam-5687	284	13	if	if	SCONJ
ejpam-5687	284	14	r0	r0	NOUN
ejpam-5687	284	15	<	<	X
ejpam-5687	284	16	1	1	NUM
ejpam-5687	284	17	,	,	PUNCT
ejpam-5687	284	18	in	in	ADP
ejpam-5687	284	19	any	any	DET
ejpam-5687	284	20	other	other	ADJ
ejpam-5687	284	21	case	case	NOUN
ejpam-5687	284	22	it	it	PRON
ejpam-5687	284	23	is	be	AUX
ejpam-5687	284	24	unstable	unstable	ADJ
ejpam-5687	284	25	.	.	PUNCT
ejpam-5687	285	1	the	the	DET
ejpam-5687	285	2	endemic	endemic	ADJ
ejpam-5687	285	3	equilibrium	equilibrium	NOUN
ejpam-5687	285	4	points	point	NOUN
ejpam-5687	285	5	of	of	ADP
ejpam-5687	285	6	our	our	PRON
ejpam-5687	285	7	system	system	NOUN
ejpam-5687	285	8	is	be	AUX
ejpam-5687	285	9	denoted	denote	VERB
ejpam-5687	285	10	by	by	ADP
ejpam-5687	285	11	e∗	e∗	NOUN
ejpam-5687	285	12	and	and	CCONJ
ejpam-5687	285	13	is	be	AUX
ejpam-5687	285	14	given	give	VERB
ejpam-5687	285	15	by	by	ADP
ejpam-5687	285	16	the	the	DET
ejpam-5687	285	17	following	follow	VERB
ejpam-5687	285	18	e∗	e∗	PROPN
ejpam-5687	286	1	=	=	SYM
ejpam-5687	286	2	(	(	PUNCT
ejpam-5687	286	3	s∗	s∗	PROPN
ejpam-5687	286	4	h	h	NOUN
ejpam-5687	286	5	,	,	PUNCT
ejpam-5687	286	6	e	e	PROPN
ejpam-5687	286	7	∗	∗	NOUN
ejpam-5687	286	8	h	h	NOUN
ejpam-5687	286	9	,	,	PUNCT
ejpam-5687	286	10	i	i	PRON
ejpam-5687	286	11	∗	∗	VERB
ejpam-5687	286	12	h	h	NOUN
ejpam-5687	286	13	,	,	PUNCT
ejpam-5687	286	14	r	r	NOUN
ejpam-5687	286	15	∗	∗	NOUN
ejpam-5687	286	16	h	h	NOUN
ejpam-5687	286	17	,	,	PUNCT
ejpam-5687	286	18	s	s	PART
ejpam-5687	286	19	∗	∗	NOUN
ejpam-5687	286	20	v	v	NOUN
ejpam-5687	286	21	,	,	PUNCT
ejpam-5687	286	22	e	e	NOUN
ejpam-5687	286	23	∗	∗	NOUN
ejpam-5687	286	24	v	v	NUM
ejpam-5687	286	25	,	,	PUNCT
ejpam-5687	286	26	i	i	PRON
ejpam-5687	286	27	∗	∗	VERB
ejpam-5687	286	28	v	v	NOUN
ejpam-5687	286	29	)	)	PUNCT
ejpam-5687	287	1	=	=	SYM
ejpam-5687	287	2	(	(	PUNCT
ejpam-5687	287	3	λh	λh	ADP
ejpam-5687	287	4	µh	µh	NOUN
ejpam-5687	287	5	1	1	NUM
ejpam-5687	287	6	r0	r0	NOUN
ejpam-5687	287	7	,	,	PUNCT
ejpam-5687	287	8	λh(r0	λh(r0	ADP
ejpam-5687	287	9	−	−	PROPN
ejpam-5687	288	1	1)σh	1)σh	PROPN
ejpam-5687	289	1	+	+	CCONJ
ejpam-5687	289	2	µh	µh	INTJ
ejpam-5687	289	3	(	(	PUNCT
ejpam-5687	289	4	β1nv	β1nv	PUNCT
ejpam-5687	289	5	+	+	PUNCT
ejpam-5687	289	6	µhβ1s	µhβ1s	NOUN
ejpam-5687	289	7	∗	∗	NOUN
ejpam-5687	289	8	h)σh	h)σh	PROPN
ejpam-5687	289	9	,	,	PUNCT
ejpam-5687	289	10	λh(r0	λh(r0	ADP
ejpam-5687	289	11	−	−	PROPN
ejpam-5687	289	12	1	1	X
ejpam-5687	289	13	)	)	PUNCT
ejpam-5687	289	14	β1	β1	PROPN
ejpam-5687	289	15	nv	nv	PROPN
ejpam-5687	289	16	iv	iv	PROPN
ejpam-5687	290	1	+	+	CCONJ
ejpam-5687	290	2	µh	µh	ADV
ejpam-5687	290	3	,	,	PUNCT
ejpam-5687	290	4	γλh(r0	γλh(r0	ADJ
ejpam-5687	290	5	−	−	NOUN
ejpam-5687	290	6	1	1	NUM
ejpam-5687	290	7	)	)	PUNCT
ejpam-5687	290	8	(	(	PUNCT
ejpam-5687	290	9	β1nv	β1nv	PUNCT
ejpam-5687	290	10	+	+	PUNCT
ejpam-5687	290	11	µhβ1s	µhβ1s	NOUN
ejpam-5687	290	12	∗	∗	NOUN
ejpam-5687	290	13	h)µh	h)µh	PROPN
ejpam-5687	290	14	,	,	PUNCT
ejpam-5687	290	15	λv	λv	ADP
ejpam-5687	290	16	µv	µv	PROPN
ejpam-5687	290	17	1	1	NUM
ejpam-5687	290	18	r0	r0	NOUN
ejpam-5687	290	19	,	,	PUNCT
ejpam-5687	290	20	µvλv(r0	µvλv(r0	VERB
ejpam-5687	290	21	−	−	PROPN
ejpam-5687	290	22	1	1	NUM
ejpam-5687	290	23	)	)	PUNCT
ejpam-5687	290	24	(	(	PUNCT
ejpam-5687	290	25	β2nh	β2nh	PUNCT
ejpam-5687	290	26	+	+	NUM
ejpam-5687	290	27	µvβ2s∗	µvβ2s∗	PROPN
ejpam-5687	290	28	v)σv	v)σv	PROPN
ejpam-5687	290	29	,	,	PUNCT
ejpam-5687	290	30	λv(r0	λv(r0	ADP
ejpam-5687	290	31	−	−	PROPN
ejpam-5687	290	32	1	1	X
ejpam-5687	290	33	)	)	PUNCT
ejpam-5687	290	34	β2	β2	NOUN
ejpam-5687	290	35	nh	nh	PROPN
ejpam-5687	290	36	ih	ih	PROPN
ejpam-5687	290	37	+	+	CCONJ
ejpam-5687	290	38	µv	µv	PROPN
ejpam-5687	290	39	)	)	PUNCT
ejpam-5687	290	40	.	.	PUNCT
ejpam-5687	291	1	(	(	PUNCT
ejpam-5687	291	2	33	33	NUM
ejpam-5687	291	3	)	)	PUNCT
ejpam-5687	291	4	4	4	NUM
ejpam-5687	291	5	.	.	X
ejpam-5687	291	6	sensitivity	sensitivity	NOUN
ejpam-5687	291	7	index	index	NOUN
ejpam-5687	291	8	with	with	ADP
ejpam-5687	291	9	respect	respect	NOUN
ejpam-5687	291	10	to	to	PART
ejpam-5687	291	11	r0	r0	VERB
ejpam-5687	291	12	the	the	DET
ejpam-5687	291	13	section	section	NOUN
ejpam-5687	291	14	below	below	ADV
ejpam-5687	291	15	uses	use	VERB
ejpam-5687	291	16	a	a	DET
ejpam-5687	291	17	direct	direct	ADJ
ejpam-5687	291	18	sensitivity	sensitivity	NOUN
ejpam-5687	291	19	analysis	analysis	NOUN
ejpam-5687	291	20	to	to	PART
ejpam-5687	291	21	determine	determine	VERB
ejpam-5687	291	22	the	the	DET
ejpam-5687	291	23	significance	significance	NOUN
ejpam-5687	291	24	of	of	ADP
ejpam-5687	291	25	specific	specific	ADJ
ejpam-5687	291	26	biological	biological	ADJ
ejpam-5687	291	27	parameters	parameter	NOUN
ejpam-5687	291	28	that	that	PRON
ejpam-5687	291	29	are	be	AUX
ejpam-5687	291	30	linked	link	VERB
ejpam-5687	291	31	to	to	ADP
ejpam-5687	291	32	the	the	DET
ejpam-5687	291	33	basic	basic	ADJ
ejpam-5687	291	34	reproductive	reproductive	ADJ
ejpam-5687	291	35	number	number	NOUN
ejpam-5687	291	36	r0	r0	NOUN
ejpam-5687	291	37	in	in	ADP
ejpam-5687	291	38	decreasing	decrease	VERB
ejpam-5687	291	39	the	the	DET
ejpam-5687	291	40	spread	spread	NOUN
ejpam-5687	291	41	of	of	ADP
ejpam-5687	291	42	vector	vector	NOUN
ejpam-5687	291	43	-	-	PUNCT
ejpam-5687	291	44	borne	bear	VERB
ejpam-5687	291	45	illnesses	illness	NOUN
ejpam-5687	291	46	[	[	X
ejpam-5687	291	47	19	19	NUM
ejpam-5687	291	48	,	,	PUNCT
ejpam-5687	291	49	21	21	NUM
ejpam-5687	291	50	]	]	PUNCT
ejpam-5687	291	51	:	:	PUNCT
ejpam-5687	291	52	πr0	πr0	NOUN
ejpam-5687	291	53	ζ	ζ	NOUN
ejpam-5687	291	54	=	=	SYM
ejpam-5687	291	55	ζ	ζ	NOUN
ejpam-5687	291	56	r0	r0	NOUN
ejpam-5687	291	57	×	×	NOUN
ejpam-5687	291	58	∂r0	∂r0	ADP
ejpam-5687	291	59	∂ζ	∂ζ	PROPN
ejpam-5687	291	60	,	,	PUNCT
ejpam-5687	291	61	(	(	PUNCT
ejpam-5687	291	62	34	34	NUM
ejpam-5687	291	63	)	)	PUNCT
ejpam-5687	291	64	is	be	AUX
ejpam-5687	291	65	called	call	VERB
ejpam-5687	291	66	the	the	DET
ejpam-5687	291	67	sensitivity	sensitivity	NOUN
ejpam-5687	291	68	index	index	NOUN
ejpam-5687	291	69	of	of	ADP
ejpam-5687	291	70	the	the	DET
ejpam-5687	291	71	variable	variable	ADJ
ejpam-5687	291	72	ζ	ζ	PROPN
ejpam-5687	291	73	∈	∈	PROPN
ejpam-5687	291	74	{	{	PUNCT
ejpam-5687	291	75	β1	β1	PROPN
ejpam-5687	291	76	,	,	PUNCT
ejpam-5687	291	77	β2σh	β2σh	X
ejpam-5687	291	78	,	,	PUNCT
ejpam-5687	291	79	σv	σv	ADP
ejpam-5687	291	80	}	}	PUNCT
ejpam-5687	291	81	,	,	PUNCT
ejpam-5687	291	82	µh	µh	INTJ
ejpam-5687	291	83	,	,	PUNCT
ejpam-5687	291	84	µv	µv	PROPN
ejpam-5687	291	85	,	,	PUNCT
ejpam-5687	291	86	γ	γ	PROPN
ejpam-5687	291	87	,	,	PUNCT
ejpam-5687	291	88	which	which	PRON
ejpam-5687	291	89	depends	depend	VERB
ejpam-5687	291	90	on	on	ADP
ejpam-5687	291	91	the	the	DET
ejpam-5687	291	92	value	value	NOUN
ejpam-5687	291	93	r0	r0	NOUN
ejpam-5687	291	94	.	.	PUNCT
ejpam-5687	292	1	to	to	PART
ejpam-5687	292	2	ensure	ensure	VERB
ejpam-5687	292	3	the	the	DET
ejpam-5687	292	4	accuracy	accuracy	NOUN
ejpam-5687	292	5	of	of	ADP
ejpam-5687	292	6	model	model	NOUN
ejpam-5687	292	7	predictions	prediction	NOUN
ejpam-5687	292	8	for	for	ADP
ejpam-5687	292	9	parameter	parameter	NOUN
ejpam-5687	292	10	values	value	NOUN
ejpam-5687	292	11	,	,	PUNCT
ejpam-5687	292	12	it	it	PRON
ejpam-5687	292	13	is	be	AUX
ejpam-5687	292	14	frequently	frequently	ADV
ejpam-5687	292	15	utilized	utilize	VERB
ejpam-5687	292	16	as	as	ADP
ejpam-5687	292	17	errors	error	NOUN
ejpam-5687	292	18	and	and	CCONJ
ejpam-5687	292	19	changes	change	NOUN
ejpam-5687	292	20	in	in	ADP
ejpam-5687	292	21	expected	expected	ADJ
ejpam-5687	292	22	parameters	parameter	NOUN
ejpam-5687	292	23	are	be	AUX
ejpam-5687	292	24	likely	likely	ADJ
ejpam-5687	292	25	to	to	PART
ejpam-5687	292	26	occur	occur	VERB
ejpam-5687	292	27	during	during	ADP
ejpam-5687	292	28	data	data	PROPN
ejpam-5687	292	29	collection[21	collection[21	PROPN
ejpam-5687	292	30	]	]	PUNCT
ejpam-5687	292	31	.	.	PUNCT
ejpam-5687	293	1	in	in	ADP
ejpam-5687	293	2	the	the	DET
ejpam-5687	293	3	seir	seir	NOUN
ejpam-5687	293	4	model	model	NOUN
ejpam-5687	293	5	for	for	ADP
ejpam-5687	293	6	vector	vector	NOUN
ejpam-5687	293	7	-	-	PUNCT
ejpam-5687	293	8	borne	bear	VERB
ejpam-5687	293	9	diseases	disease	NOUN
ejpam-5687	293	10	,	,	PUNCT
ejpam-5687	293	11	several	several	ADJ
ejpam-5687	293	12	key	key	ADJ
ejpam-5687	293	13	parameters	parameter	NOUN
ejpam-5687	293	14	related	relate	VERB
ejpam-5687	293	15	to	to	ADP
ejpam-5687	293	16	disease	disease	NOUN
ejpam-5687	293	17	dynamics	dynamic	NOUN
ejpam-5687	293	18	are	be	AUX
ejpam-5687	293	19	listed	list	VERB
ejpam-5687	293	20	in	in	ADP
ejpam-5687	293	21	table	table	NOUN
ejpam-5687	293	22	2	2	NUM
ejpam-5687	293	23	:	:	PUNCT
ejpam-5687	293	24	β1	β1	PROPN
ejpam-5687	293	25	is	be	AUX
ejpam-5687	293	26	the	the	DET
ejpam-5687	293	27	human	human	ADJ
ejpam-5687	293	28	infectious	infectious	ADJ
ejpam-5687	293	29	rate	rate	NOUN
ejpam-5687	293	30	with	with	ADP
ejpam-5687	293	31	value	value	NOUN
ejpam-5687	293	32	0.4	0.4	NUM
ejpam-5687	293	33	,	,	PUNCT
ejpam-5687	293	34	eβ1	eβ1	NOUN
ejpam-5687	294	1	=	=	SYM
ejpam-5687	294	2	n.	n.	PROPN
ejpam-5687	294	3	ullah	ullah	PROPN
ejpam-5687	294	4	et	et	PROPN
ejpam-5687	294	5	al	al	PROPN
ejpam-5687	294	6	.	.	PUNCT
ejpam-5687	294	7	/	/	SYM
ejpam-5687	294	8	eur	eur	PROPN
ejpam-5687	294	9	.	.	PUNCT
ejpam-5687	295	1	j.	j.	PROPN
ejpam-5687	295	2	pure	pure	PROPN
ejpam-5687	295	3	appl	appl	PROPN
ejpam-5687	295	4	.	.	PROPN
ejpam-5687	295	5	math	math	PROPN
ejpam-5687	295	6	,	,	PUNCT
ejpam-5687	295	7	18	18	NUM
ejpam-5687	295	8	(	(	PUNCT
ejpam-5687	295	9	2	2	NUM
ejpam-5687	295	10	)	)	PUNCT
ejpam-5687	295	11	(	(	PUNCT
ejpam-5687	295	12	2025	2025	NUM
ejpam-5687	295	13	)	)	PUNCT
ejpam-5687	295	14	,	,	PUNCT
ejpam-5687	295	15	5687	5687	NUM
ejpam-5687	295	16	17	17	NUM
ejpam-5687	295	17	of	of	ADP
ejpam-5687	295	18	25	25	NUM
ejpam-5687	295	19	0.50	0.50	NUM
ejpam-5687	295	20	.	.	PUNCT
ejpam-5687	296	1	the	the	DET
ejpam-5687	296	2	elasticity	elasticity	NOUN
ejpam-5687	296	3	index	index	NOUN
ejpam-5687	296	4	indicate	indicate	VERB
ejpam-5687	296	5	that	that	SCONJ
ejpam-5687	296	6	an	an	DET
ejpam-5687	296	7	increase	increase	NOUN
ejpam-5687	296	8	in	in	ADP
ejpam-5687	296	9	β1	β1	PROPN
ejpam-5687	296	10	increases	increase	VERB
ejpam-5687	296	11	the	the	DET
ejpam-5687	296	12	number	number	NOUN
ejpam-5687	296	13	of	of	ADP
ejpam-5687	296	14	r0	r0	NOUN
ejpam-5687	296	15	.	.	PUNCT
ejpam-5687	297	1	β2	β2	VERB
ejpam-5687	297	2	the	the	DET
ejpam-5687	297	3	vector	vector	NOUN
ejpam-5687	297	4	rate	rate	NOUN
ejpam-5687	297	5	of	of	ADP
ejpam-5687	297	6	infection	infection	NOUN
ejpam-5687	297	7	having	have	VERB
ejpam-5687	297	8	value	value	NOUN
ejpam-5687	297	9	0.3	0.3	NUM
ejpam-5687	297	10	,	,	PUNCT
ejpam-5687	297	11	it	it	PRON
ejpam-5687	297	12	gives	give	VERB
ejpam-5687	297	13	elasticity	elasticity	NOUN
ejpam-5687	297	14	value	value	NOUN
ejpam-5687	297	15	eβ2	eβ2	PROPN
ejpam-5687	298	1	=	=	SYM
ejpam-5687	298	2	0.50	0.50	NUM
ejpam-5687	298	3	,	,	PUNCT
ejpam-5687	298	4	it	it	PRON
ejpam-5687	298	5	shows	show	VERB
ejpam-5687	298	6	that	that	SCONJ
ejpam-5687	298	7	with	with	ADP
ejpam-5687	298	8	increase	increase	NOUN
ejpam-5687	298	9	of	of	ADP
ejpam-5687	298	10	β2	β2	NOUN
ejpam-5687	298	11	the	the	DET
ejpam-5687	298	12	r0	r0	NOUN
ejpam-5687	298	13	would	would	AUX
ejpam-5687	298	14	be	be	AUX
ejpam-5687	298	15	increases.instead	increases.instead	PROPN
ejpam-5687	298	16	,	,	PUNCT
ejpam-5687	298	17	the	the	DET
ejpam-5687	298	18	human	human	ADJ
ejpam-5687	298	19	death	death	NOUN
ejpam-5687	298	20	rate	rate	NOUN
ejpam-5687	298	21	µh	µh	NOUN
ejpam-5687	298	22	was	be	AUX
ejpam-5687	298	23	set	set	VERB
ejpam-5687	298	24	to	to	ADP
ejpam-5687	298	25	0.01	0.01	NUM
ejpam-5687	298	26	and	and	CCONJ
ejpam-5687	298	27	the	the	DET
ejpam-5687	298	28	vector	vector	NOUN
ejpam-5687	298	29	death	death	NOUN
ejpam-5687	298	30	rate	rate	NOUN
ejpam-5687	298	31	µv	µv	PROPN
ejpam-5687	298	32	was	be	AUX
ejpam-5687	298	33	set	set	VERB
ejpam-5687	298	34	to	to	ADP
ejpam-5687	298	35	0.05	0.05	NUM
ejpam-5687	298	36	.	.	PUNCT
ejpam-5687	299	1	these	these	DET
ejpam-5687	299	2	parameters	parameter	NOUN
ejpam-5687	299	3	have	have	VERB
ejpam-5687	299	4	negative	negative	ADJ
ejpam-5687	299	5	elasticities	elasticity	NOUN
ejpam-5687	299	6	of	of	ADP
ejpam-5687	299	7	-0.15	-0.15	NUM
ejpam-5687	299	8	and	and	CCONJ
ejpam-5687	299	9	-0.20	-0.20	NUM
ejpam-5687	299	10	,	,	PUNCT
ejpam-5687	299	11	respectively	respectively	ADV
ejpam-5687	299	12	,	,	PUNCT
ejpam-5687	299	13	indicating	indicate	VERB
ejpam-5687	299	14	that	that	SCONJ
ejpam-5687	299	15	the	the	DET
ejpam-5687	299	16	death	death	NOUN
ejpam-5687	299	17	rate	rate	NOUN
ejpam-5687	299	18	decreases	decrease	VERB
ejpam-5687	299	19	to	to	PART
ejpam-5687	299	20	r0	r0	VERB
ejpam-5687	299	21	because	because	SCONJ
ejpam-5687	299	22	fewer	few	ADJ
ejpam-5687	299	23	people	people	NOUN
ejpam-5687	299	24	live	live	VERB
ejpam-5687	299	25	in	in	ADP
ejpam-5687	299	26	the	the	DET
ejpam-5687	299	27	population	population	NOUN
ejpam-5687	299	28	and	and	CCONJ
ejpam-5687	299	29	participate	participate	VERB
ejpam-5687	299	30	in	in	ADP
ejpam-5687	299	31	death	death	NOUN
ejpam-5687	299	32	.	.	PUNCT
ejpam-5687	300	1	the	the	DET
ejpam-5687	300	2	human	human	ADJ
ejpam-5687	300	3	recovery	recovery	NOUN
ejpam-5687	300	4	rate	rate	NOUN
ejpam-5687	300	5	σh	σh	ADP
ejpam-5687	300	6	and	and	CCONJ
ejpam-5687	300	7	the	the	DET
ejpam-5687	300	8	vector	vector	NOUN
ejpam-5687	300	9	recovery	recovery	NOUN
ejpam-5687	300	10	rate	rate	NOUN
ejpam-5687	300	11	σv	σv	NOUN
ejpam-5687	301	1	are	be	AUX
ejpam-5687	301	2	set	set	VERB
ejpam-5687	301	3	to	to	ADP
ejpam-5687	301	4	0.5	0.5	NUM
ejpam-5687	301	5	and	and	CCONJ
ejpam-5687	301	6	0.4	0.4	NUM
ejpam-5687	301	7	,	,	PUNCT
ejpam-5687	301	8	respectively	respectively	ADV
ejpam-5687	301	9	,	,	PUNCT
ejpam-5687	301	10	and	and	CCONJ
ejpam-5687	301	11	the	the	DET
ejpam-5687	301	12	elasticity	elasticity	NOUN
ejpam-5687	301	13	indices	index	NOUN
ejpam-5687	301	14	are	be	AUX
ejpam-5687	301	15	0.08	0.08	NUM
ejpam-5687	301	16	and	and	CCONJ
ejpam-5687	301	17	0.10	0.10	NUM
ejpam-5687	301	18	increase	increase	NOUN
ejpam-5687	301	19	the	the	DET
ejpam-5687	301	20	sensitivity	sensitivity	NOUN
ejpam-5687	301	21	and	and	CCONJ
ejpam-5687	301	22	γ	γ	NOUN
ejpam-5687	301	23	is	be	AUX
ejpam-5687	301	24	set	set	VERB
ejpam-5687	301	25	0.1	0.1	NUM
ejpam-5687	301	26	,	,	PUNCT
ejpam-5687	301	27	decrease	decrease	NOUN
ejpam-5687	301	28	to	to	ADP
ejpam-5687	301	29	-0.42	-0.42	NUM
ejpam-5687	301	30	.	.	PUNCT
ejpam-5687	302	1	this	this	PRON
ejpam-5687	302	2	means	mean	VERB
ejpam-5687	302	3	that	that	SCONJ
ejpam-5687	302	4	r0	r0	NOUN
ejpam-5687	302	5	decreases	decrease	VERB
ejpam-5687	302	6	with	with	ADP
ejpam-5687	302	7	higher	high	ADJ
ejpam-5687	302	8	recovery	recovery	NOUN
ejpam-5687	302	9	rates	rate	NOUN
ejpam-5687	302	10	because	because	SCONJ
ejpam-5687	302	11	survivors	survivor	NOUN
ejpam-5687	302	12	no	no	ADV
ejpam-5687	302	13	longer	long	ADV
ejpam-5687	302	14	die.in	die.in	PROPN
ejpam-5687	302	15	general	general	NOUN
ejpam-5687	302	16	,	,	PUNCT
ejpam-5687	302	17	these	these	DET
ejpam-5687	302	18	parameters	parameter	NOUN
ejpam-5687	302	19	and	and	CCONJ
ejpam-5687	302	20	elasticity	elasticity	NOUN
ejpam-5687	302	21	indices	index	NOUN
ejpam-5687	302	22	are	be	AUX
ejpam-5687	302	23	important	important	ADJ
ejpam-5687	302	24	for	for	ADP
ejpam-5687	302	25	understanding	understand	VERB
ejpam-5687	302	26	the	the	DET
ejpam-5687	302	27	epidemiology	epidemiology	NOUN
ejpam-5687	302	28	of	of	ADP
ejpam-5687	302	29	vector	vector	NOUN
ejpam-5687	302	30	-	-	PUNCT
ejpam-5687	302	31	borne	bear	VERB
ejpam-5687	302	32	diseases	disease	NOUN
ejpam-5687	302	33	and	and	CCONJ
ejpam-5687	302	34	the	the	DET
ejpam-5687	302	35	effect	effect	NOUN
ejpam-5687	302	36	of	of	ADP
ejpam-5687	302	37	various	various	ADJ
ejpam-5687	302	38	factors	factor	NOUN
ejpam-5687	302	39	on	on	ADP
ejpam-5687	302	40	the	the	DET
ejpam-5687	302	41	basic	basic	ADJ
ejpam-5687	302	42	reproduction	reproduction	NOUN
ejpam-5687	302	43	number	number	NOUN
ejpam-5687	302	44	r0	r0	NOUN
ejpam-5687	302	45	.	.	PUNCT
ejpam-5687	303	1	now	now	ADV
ejpam-5687	303	2	below	below	ADV
ejpam-5687	303	3	from	from	ADP
ejpam-5687	303	4	figure	figure	NOUN
ejpam-5687	303	5	1	1	NUM
ejpam-5687	303	6	:	:	PUNCT
ejpam-5687	303	7	β1	β1	PROPN
ejpam-5687	303	8	,	,	PUNCT
ejpam-5687	303	9	β2	β2	NOUN
ejpam-5687	303	10	,	,	PUNCT
ejpam-5687	303	11	λh	λh	ADP
ejpam-5687	303	12	,	,	PUNCT
ejpam-5687	303	13	and	and	CCONJ
ejpam-5687	303	14	λv	λv	X
ejpam-5687	303	15	,	,	PUNCT
ejpam-5687	303	16	it	it	PRON
ejpam-5687	303	17	parameter	parameter	NOUN
ejpam-5687	303	18	value	value	NOUN
ejpam-5687	303	19	elasticity	elasticity	NOUN
ejpam-5687	303	20	index	index	NOUN
ejpam-5687	303	21	effect	effect	NOUN
ejpam-5687	303	22	β1	β1	PROPN
ejpam-5687	303	23	0.4	0.4	NUM
ejpam-5687	303	24	0.50	0.50	NUM
ejpam-5687	303	25	increase	increase	NOUN
ejpam-5687	303	26	β2	β2	VERB
ejpam-5687	303	27	0.3	0.3	NUM
ejpam-5687	303	28	0.50	0.50	NUM
ejpam-5687	303	29	increase	increase	VERB
ejpam-5687	303	30	γ	γ	X
ejpam-5687	303	31	0.1	0.1	NUM
ejpam-5687	303	32	-0.42	-0.42	NUM
ejpam-5687	303	33	decrease	decrease	VERB
ejpam-5687	303	34	µh	µh	ADP
ejpam-5687	303	35	0.02	0.02	NUM
ejpam-5687	303	36	-0.17	-0.17	NOUN
ejpam-5687	303	37	decrease	decrease	NOUN
ejpam-5687	303	38	µv	µv	PROPN
ejpam-5687	303	39	0.03	0.03	NUM
ejpam-5687	303	40	-0.60	-0.60	NUM
ejpam-5687	303	41	decrease	decrease	NOUN
ejpam-5687	303	42	σh	σh	ADP
ejpam-5687	303	43	0.2	0.2	NUM
ejpam-5687	303	44	0.08	0.08	NUM
ejpam-5687	303	45	increase	increase	NOUN
ejpam-5687	303	46	σv	σv	ADP
ejpam-5687	303	47	0.2	0.2	NUM
ejpam-5687	303	48	0.10	0.10	NUM
ejpam-5687	303	49	increase	increase	NOUN
ejpam-5687	303	50	table	table	NOUN
ejpam-5687	303	51	2	2	NUM
ejpam-5687	303	52	:	:	PUNCT
ejpam-5687	303	53	parameter	parameter	NOUN
ejpam-5687	303	54	values	value	NOUN
ejpam-5687	303	55	,	,	PUNCT
ejpam-5687	303	56	elasticity	elasticity	NOUN
ejpam-5687	303	57	indices	index	NOUN
ejpam-5687	303	58	,	,	PUNCT
ejpam-5687	303	59	and	and	CCONJ
ejpam-5687	303	60	their	their	PRON
ejpam-5687	303	61	effects	effect	NOUN
ejpam-5687	303	62	on	on	ADP
ejpam-5687	303	63	r0	r0	NOUN
ejpam-5687	303	64	follows	follow	VERB
ejpam-5687	303	65	that	that	SCONJ
ejpam-5687	303	66	increasing	increase	VERB
ejpam-5687	303	67	these	these	DET
ejpam-5687	303	68	parameters	parameter	NOUN
ejpam-5687	303	69	increases	increase	VERB
ejpam-5687	303	70	r0	r0	NOUN
ejpam-5687	303	71	while	while	SCONJ
ejpam-5687	303	72	for	for	SCONJ
ejpam-5687	303	73	parameters	parameter	NOUN
ejpam-5687	303	74	µh	µh	ADP
ejpam-5687	303	75	,	,	PUNCT
ejpam-5687	303	76	µv	µv	PROPN
ejpam-5687	303	77	,	,	PUNCT
ejpam-5687	303	78	σh	σh	PROPN
ejpam-5687	303	79	,	,	PUNCT
ejpam-5687	303	80	and	and	CCONJ
ejpam-5687	303	81	σv	σv	ADV
ejpam-5687	303	82	,	,	PUNCT
ejpam-5687	303	83	increasing	increase	VERB
ejpam-5687	303	84	these	these	DET
ejpam-5687	303	85	parameters	parameter	NOUN
ejpam-5687	303	86	results	result	VERB
ejpam-5687	303	87	in	in	ADP
ejpam-5687	303	88	a	a	DET
ejpam-5687	303	89	decrease	decrease	NOUN
ejpam-5687	303	90	of	of	ADP
ejpam-5687	303	91	r0	r0	NOUN
ejpam-5687	303	92	.	.	PUNCT
ejpam-5687	304	1	n.	n.	PROPN
ejpam-5687	304	2	ullah	ullah	PROPN
ejpam-5687	304	3	et	et	PROPN
ejpam-5687	304	4	al	al	PROPN
ejpam-5687	304	5	.	.	PUNCT
ejpam-5687	304	6	/	/	SYM
ejpam-5687	304	7	eur	eur	PROPN
ejpam-5687	304	8	.	.	PUNCT
ejpam-5687	305	1	j.	j.	PROPN
ejpam-5687	305	2	pure	pure	PROPN
ejpam-5687	305	3	appl	appl	PROPN
ejpam-5687	305	4	.	.	PROPN
ejpam-5687	305	5	math	math	PROPN
ejpam-5687	305	6	,	,	PUNCT
ejpam-5687	305	7	18	18	NUM
ejpam-5687	305	8	(	(	PUNCT
ejpam-5687	305	9	2	2	NUM
ejpam-5687	305	10	)	)	PUNCT
ejpam-5687	305	11	(	(	PUNCT
ejpam-5687	305	12	2025	2025	NUM
ejpam-5687	305	13	)	)	PUNCT
ejpam-5687	305	14	,	,	PUNCT
ejpam-5687	305	15	5687	5687	NUM
ejpam-5687	305	16	18	18	NUM
ejpam-5687	305	17	of	of	ADP
ejpam-5687	305	18	25	25	NUM
ejpam-5687	305	19	figure	figure	NOUN
ejpam-5687	305	20	1	1	NUM
ejpam-5687	305	21	:	:	PUNCT
ejpam-5687	305	22	sensitivity	sensitivity	NOUN
ejpam-5687	305	23	analysis	analysis	NOUN
ejpam-5687	305	24	of	of	ADP
ejpam-5687	305	25	the	the	DET
ejpam-5687	305	26	basic	basic	ADJ
ejpam-5687	305	27	reproduction	reproduction	NOUN
ejpam-5687	305	28	number	number	NOUN
ejpam-5687	305	29	5	5	NUM
ejpam-5687	305	30	.	.	PUNCT
ejpam-5687	305	31	graphical	graphical	ADJ
ejpam-5687	305	32	analysis	analysis	NOUN
ejpam-5687	305	33	and	and	CCONJ
ejpam-5687	305	34	discussion	discussion	NOUN
ejpam-5687	305	35	to	to	PART
ejpam-5687	305	36	study	study	VERB
ejpam-5687	305	37	the	the	DET
ejpam-5687	305	38	dynamic	dynamic	ADJ
ejpam-5687	305	39	behavior	behavior	NOUN
ejpam-5687	305	40	of	of	ADP
ejpam-5687	305	41	the	the	DET
ejpam-5687	305	42	model	model	NOUN
ejpam-5687	305	43	,	,	PUNCT
ejpam-5687	305	44	we	we	PRON
ejpam-5687	305	45	may	may	AUX
ejpam-5687	305	46	use	use	VERB
ejpam-5687	305	47	an	an	DET
ejpam-5687	305	48	efficient	efficient	ADJ
ejpam-5687	305	49	numerical	numerical	ADJ
ejpam-5687	305	50	model	model	NOUN
ejpam-5687	305	51	that	that	PRON
ejpam-5687	305	52	is	be	AUX
ejpam-5687	305	53	stable	stable	ADJ
ejpam-5687	305	54	and	and	CCONJ
ejpam-5687	305	55	convergent	convergent	NOUN
ejpam-5687	305	56	,	,	PUNCT
ejpam-5687	305	57	see	see	VERB
ejpam-5687	305	58	[	[	X
ejpam-5687	305	59	24	24	NUM
ejpam-5687	305	60	]	]	PUNCT
ejpam-5687	305	61	.	.	PUNCT
ejpam-5687	306	1	the	the	DET
ejpam-5687	306	2	numerical	numerical	ADJ
ejpam-5687	306	3	scheme	scheme	NOUN
ejpam-5687	306	4	for	for	ADP
ejpam-5687	306	5	(	(	PUNCT
ejpam-5687	306	6	4	4	NUM
ejpam-5687	306	7	)	)	PUNCT
ejpam-5687	306	8	is	be	AUX
ejpam-5687	306	9	as	as	SCONJ
ejpam-5687	306	10	follows	follow	VERB
ejpam-5687	306	11	:	:	PUNCT
ejpam-5687	307	1	csh(k+1	csh(k+1	ADJ
ejpam-5687	307	2	)	)	PUNCT
ejpam-5687	307	3	=	=	SYM
ejpam-5687	307	4	b0	b0	NOUN
ejpam-5687	307	5	+	+	CCONJ
ejpam-5687	307	6	rl	rl	ADP
ejpam-5687	307	7	γ(l	γ(l	NOUN
ejpam-5687	307	8	+	+	CCONJ
ejpam-5687	307	9	1	1	X
ejpam-5687	307	10	)	)	PUNCT
ejpam-5687	307	11	k∑	k∑	NOUN
ejpam-5687	307	12	m=0	m=0	PROPN
ejpam-5687	307	13	(	(	PUNCT
ejpam-5687	307	14	(	(	PUNCT
ejpam-5687	307	15	k	k	X
ejpam-5687	307	16	−m+	−m+	PROPN
ejpam-5687	307	17	1)l	1)l	NUM
ejpam-5687	307	18	−	−	PROPN
ejpam-5687	307	19	(	(	PUNCT
ejpam-5687	307	20	k	k	X
ejpam-5687	307	21	−m)l	−m)l	PROPN
ejpam-5687	307	22	)	)	PUNCT
ejpam-5687	308	1	(	(	PUNCT
ejpam-5687	308	2	1−	1−	NUM
ejpam-5687	308	3	p)(λh	p)(λh	NOUN
ejpam-5687	308	4	−	−	PROPN
ejpam-5687	309	1	(	(	PUNCT
ejpam-5687	309	2	β1	β1	PROPN
ejpam-5687	309	3	iv	iv	NUM
ejpam-5687	309	4	nv	nv	PROPN
ejpam-5687	309	5	+	+	PROPN
ejpam-5687	309	6	µh)sh	µh)sh	PROPN
ejpam-5687	309	7	)	)	PUNCT
ejpam-5687	309	8	ceh(k+1	ceh(k+1	VERB
ejpam-5687	309	9	)	)	PUNCT
ejpam-5687	309	10	=	=	SYM
ejpam-5687	309	11	c0	c0	NOUN
ejpam-5687	309	12	+	+	CCONJ
ejpam-5687	309	13	rl	rl	VERB
ejpam-5687	309	14	γ(l	γ(l	NOUN
ejpam-5687	309	15	+	+	CCONJ
ejpam-5687	309	16	1	1	X
ejpam-5687	309	17	)	)	PUNCT
ejpam-5687	309	18	k∑	k∑	NOUN
ejpam-5687	310	1	m=0	m=0	PROPN
ejpam-5687	310	2	(	(	PUNCT
ejpam-5687	310	3	(	(	PUNCT
ejpam-5687	310	4	k	k	X
ejpam-5687	310	5	−m+	−m+	PROPN
ejpam-5687	310	6	1)l	1)l	NUM
ejpam-5687	310	7	−	−	PROPN
ejpam-5687	310	8	(	(	PUNCT
ejpam-5687	310	9	k	k	X
ejpam-5687	310	10	−m)l	−m)l	PROPN
ejpam-5687	310	11	)	)	PUNCT
ejpam-5687	310	12	(	(	PUNCT
ejpam-5687	310	13	β1sh	β1sh	PUNCT
ejpam-5687	310	14	iv	iv	X
ejpam-5687	310	15	nv	nv	PROPN
ejpam-5687	310	16	−	−	PROPN
ejpam-5687	310	17	(	(	PUNCT
ejpam-5687	310	18	σh	σh	PROPN
ejpam-5687	310	19	+	+	NOUN
ejpam-5687	310	20	µh)eh	µh)eh	NUM
ejpam-5687	310	21	)	)	PUNCT
ejpam-5687	310	22	cih(k+1	cih(k+1	NOUN
ejpam-5687	310	23	)	)	PUNCT
ejpam-5687	310	24	=	=	SYM
ejpam-5687	310	25	d0	d0	NOUN
ejpam-5687	310	26	+	+	CCONJ
ejpam-5687	310	27	rl	rl	ADP
ejpam-5687	310	28	γ(l	γ(l	NOUN
ejpam-5687	310	29	+	+	CCONJ
ejpam-5687	310	30	1	1	X
ejpam-5687	310	31	)	)	PUNCT
ejpam-5687	310	32	k∑	k∑	NOUN
ejpam-5687	310	33	m=0	m=0	PROPN
ejpam-5687	310	34	(	(	PUNCT
ejpam-5687	310	35	(	(	PUNCT
ejpam-5687	310	36	k	k	X
ejpam-5687	310	37	−m+	−m+	PROPN
ejpam-5687	310	38	1)l	1)l	NUM
ejpam-5687	310	39	−	−	PROPN
ejpam-5687	310	40	(	(	PUNCT
ejpam-5687	310	41	k	k	X
ejpam-5687	310	42	−m)l	−m)l	PROPN
ejpam-5687	310	43	)	)	PUNCT
ejpam-5687	310	44	(	(	PUNCT
ejpam-5687	310	45	σheh	σheh	ADJ
ejpam-5687	310	46	−	−	PROPN
ejpam-5687	310	47	(	(	PUNCT
ejpam-5687	310	48	γ	γ	X
ejpam-5687	310	49	+	+	SYM
ejpam-5687	310	50	µh)ih	µh)ih	SYM
ejpam-5687	310	51	)	)	PUNCT
ejpam-5687	310	52	crh(k+1	crh(k+1	NOUN
ejpam-5687	310	53	)	)	PUNCT
ejpam-5687	310	54	=	=	SYM
ejpam-5687	310	55	e0	e0	PROPN
ejpam-5687	310	56	+	+	CCONJ
ejpam-5687	310	57	rl	rl	ADP
ejpam-5687	310	58	γ(l	γ(l	NOUN
ejpam-5687	310	59	+	+	CCONJ
ejpam-5687	310	60	1	1	X
ejpam-5687	310	61	)	)	PUNCT
ejpam-5687	310	62	k∑	k∑	NOUN
ejpam-5687	310	63	m=0	m=0	PROPN
ejpam-5687	310	64	(	(	PUNCT
ejpam-5687	310	65	(	(	PUNCT
ejpam-5687	310	66	k	k	X
ejpam-5687	310	67	−m+	−m+	PROPN
ejpam-5687	310	68	1)l	1)l	NUM
ejpam-5687	310	69	−	−	PROPN
ejpam-5687	310	70	(	(	PUNCT
ejpam-5687	310	71	k	k	X
ejpam-5687	310	72	−m)l	−m)l	PROPN
ejpam-5687	310	73	)	)	PUNCT
ejpam-5687	310	74	(	(	PUNCT
ejpam-5687	310	75	γih	γih	NOUN
ejpam-5687	310	76	−	−	PROPN
ejpam-5687	310	77	µhrh	µhrh	NOUN
ejpam-5687	310	78	)	)	PUNCT
ejpam-5687	310	79	csv(k+1	csv(k+1	PROPN
ejpam-5687	310	80	)	)	PUNCT
ejpam-5687	310	81	=	=	SYM
ejpam-5687	310	82	f0	f0	PROPN
ejpam-5687	311	1	+	+	CCONJ
ejpam-5687	311	2	rl	rl	ADP
ejpam-5687	311	3	γ(l	γ(l	NOUN
ejpam-5687	311	4	+	+	CCONJ
ejpam-5687	311	5	1	1	X
ejpam-5687	311	6	)	)	PUNCT
ejpam-5687	311	7	k∑	k∑	NOUN
ejpam-5687	312	1	m=0	m=0	PROPN
ejpam-5687	312	2	(	(	PUNCT
ejpam-5687	312	3	(	(	PUNCT
ejpam-5687	312	4	k	k	X
ejpam-5687	312	5	−m+	−m+	PROPN
ejpam-5687	312	6	1)l	1)l	NUM
ejpam-5687	312	7	−	−	PROPN
ejpam-5687	312	8	(	(	PUNCT
ejpam-5687	312	9	k	k	X
ejpam-5687	312	10	−m)l	−m)l	PROPN
ejpam-5687	312	11	)	)	PUNCT
ejpam-5687	313	1	(	(	PUNCT
ejpam-5687	313	2	λv	λv	X
ejpam-5687	313	3	−	−	PROPN
ejpam-5687	313	4	(	(	PUNCT
ejpam-5687	313	5	β2	β2	VERB
ejpam-5687	313	6	ih	ih	PROPN
ejpam-5687	313	7	nh	nh	PROPN
ejpam-5687	313	8	+	+	CCONJ
ejpam-5687	313	9	µv)sv	µv)sv	NOUN
ejpam-5687	313	10	)	)	PUNCT
ejpam-5687	313	11	cev(k+1	cev(k+1	VERB
ejpam-5687	313	12	)	)	PUNCT
ejpam-5687	313	13	=	=	SYM
ejpam-5687	313	14	g0	g0	NOUN
ejpam-5687	313	15	+	+	CCONJ
ejpam-5687	313	16	rl	rl	PROPN
ejpam-5687	313	17	γ(l	γ(l	NOUN
ejpam-5687	313	18	+	+	CCONJ
ejpam-5687	313	19	1	1	X
ejpam-5687	313	20	)	)	PUNCT
ejpam-5687	313	21	k∑	k∑	NOUN
ejpam-5687	313	22	m=0	m=0	PROPN
ejpam-5687	313	23	(	(	PUNCT
ejpam-5687	313	24	(	(	PUNCT
ejpam-5687	313	25	k	k	X
ejpam-5687	313	26	−m+	−m+	PROPN
ejpam-5687	313	27	1)l	1)l	NUM
ejpam-5687	313	28	−	−	PROPN
ejpam-5687	314	1	(	(	PUNCT
ejpam-5687	314	2	k	k	X
ejpam-5687	314	3	−m)l	−m)l	PROPN
ejpam-5687	314	4	)	)	PUNCT
ejpam-5687	314	5	(	(	PUNCT
ejpam-5687	314	6	β2sv	β2sv	PUNCT
ejpam-5687	314	7	ih	ih	X
ejpam-5687	314	8	nh	nh	PROPN
ejpam-5687	314	9	−	−	PROPN
ejpam-5687	315	1	(	(	PUNCT
ejpam-5687	315	2	σv	σv	PROPN
ejpam-5687	315	3	+	+	NUM
ejpam-5687	315	4	µv)ev	µv)ev	NUM
ejpam-5687	315	5	)	)	PUNCT
ejpam-5687	315	6	civ(k+1	civ(k+1	NOUN
ejpam-5687	315	7	)	)	PUNCT
ejpam-5687	315	8	=	=	PUNCT
ejpam-5687	315	9	h0	h0	NOUN
ejpam-5687	315	10	+	+	CCONJ
ejpam-5687	315	11	rl	rl	PROPN
ejpam-5687	315	12	γ(l	γ(l	NOUN
ejpam-5687	315	13	+	+	CCONJ
ejpam-5687	315	14	1	1	X
ejpam-5687	315	15	)	)	PUNCT
ejpam-5687	315	16	k∑	k∑	NOUN
ejpam-5687	316	1	m=0	m=0	PROPN
ejpam-5687	316	2	(	(	PUNCT
ejpam-5687	316	3	(	(	PUNCT
ejpam-5687	316	4	k	k	X
ejpam-5687	316	5	−m+	−m+	PROPN
ejpam-5687	316	6	1)l	1)l	NUM
ejpam-5687	316	7	−	−	PROPN
ejpam-5687	316	8	(	(	PUNCT
ejpam-5687	316	9	k	k	X
ejpam-5687	316	10	−m)l	−m)l	PROPN
ejpam-5687	316	11	)	)	PUNCT
ejpam-5687	316	12	(	(	PUNCT
ejpam-5687	316	13	σvev	σvev	NOUN
ejpam-5687	316	14	−	−	PROPN
ejpam-5687	316	15	µviv	µviv	PROPN
ejpam-5687	316	16	)	)	PUNCT
ejpam-5687	316	17	.	.	PUNCT
ejpam-5687	317	1	(	(	PUNCT
ejpam-5687	317	2	35	35	NUM
ejpam-5687	317	3	)	)	PUNCT
ejpam-5687	317	4	n.	n.	PROPN
ejpam-5687	317	5	ullah	ullah	PROPN
ejpam-5687	317	6	et	et	PROPN
ejpam-5687	317	7	al	al	PROPN
ejpam-5687	317	8	.	.	PUNCT
ejpam-5687	317	9	/	/	SYM
ejpam-5687	317	10	eur	eur	PROPN
ejpam-5687	317	11	.	.	PUNCT
ejpam-5687	318	1	j.	j.	PROPN
ejpam-5687	318	2	pure	pure	PROPN
ejpam-5687	318	3	appl	appl	PROPN
ejpam-5687	318	4	.	.	PROPN
ejpam-5687	318	5	math	math	PROPN
ejpam-5687	318	6	,	,	PUNCT
ejpam-5687	318	7	18	18	NUM
ejpam-5687	318	8	(	(	PUNCT
ejpam-5687	318	9	2	2	NUM
ejpam-5687	318	10	)	)	PUNCT
ejpam-5687	318	11	(	(	PUNCT
ejpam-5687	318	12	2025	2025	NUM
ejpam-5687	318	13	)	)	PUNCT
ejpam-5687	318	14	,	,	PUNCT
ejpam-5687	318	15	5687	5687	NUM
ejpam-5687	318	16	19	19	NUM
ejpam-5687	318	17	of	of	ADP
ejpam-5687	318	18	25	25	NUM
ejpam-5687	318	19	understanding	understand	VERB
ejpam-5687	318	20	the	the	DET
ejpam-5687	318	21	dynamical	dynamical	ADJ
ejpam-5687	318	22	behavior	behavior	NOUN
ejpam-5687	318	23	of	of	ADP
ejpam-5687	318	24	an	an	DET
ejpam-5687	318	25	epidemic	epidemic	NOUN
ejpam-5687	318	26	model	model	NOUN
ejpam-5687	318	27	is	be	AUX
ejpam-5687	318	28	crucial	crucial	ADJ
ejpam-5687	318	29	for	for	ADP
ejpam-5687	318	30	predicting	predicting	NOUN
ejpam-5687	318	31	and	and	CCONJ
ejpam-5687	318	32	time	time	NOUN
ejpam-5687	318	33	t	t	PROPN
ejpam-5687	318	34	0	0	NUM
ejpam-5687	319	1	10	10	NUM
ejpam-5687	319	2	20	20	NUM
ejpam-5687	319	3	30	30	NUM
ejpam-5687	319	4	40	40	NUM
ejpam-5687	319	5	50	50	NUM
ejpam-5687	319	6	60	60	NUM
ejpam-5687	319	7	70	70	NUM
ejpam-5687	319	8	80	80	NUM
ejpam-5687	319	9	s	s	NOUN
ejpam-5687	319	10	u	u	NOUN
ejpam-5687	319	11	s	s	PRON
ejpam-5687	319	12	c	c	NOUN
ejpam-5687	319	13	e	e	NOUN
ejpam-5687	319	14	p	p	PROPN
ejpam-5687	319	15	t	t	PROPN
ejpam-5687	319	16	ib	ib	X
ejpam-5687	319	17	le	le	PROPN
ejpam-5687	319	18	p	p	X
ejpam-5687	319	19	o	o	X
ejpam-5687	319	20	p	p	X
ejpam-5687	319	21	u	u	X
ejpam-5687	319	22	la	la	PROPN
ejpam-5687	319	23	t	t	PROPN
ejpam-5687	319	24	io	io	PROPN
ejpam-5687	319	25	n	n	PRON
ejpam-5687	319	26	o	o	X
ejpam-5687	319	27	f	f	NOUN
ejpam-5687	319	28	h	h	NOUN
ejpam-5687	320	1	o	o	NOUN
ejpam-5687	320	2	s	s	PROPN
ejpam-5687	320	3	t	t	X
ejpam-5687	320	4	0	0	NUM
ejpam-5687	320	5	1	1	NUM
ejpam-5687	320	6	2	2	NUM
ejpam-5687	320	7	3	3	NUM
ejpam-5687	320	8	4	4	NUM
ejpam-5687	320	9	5	5	NUM
ejpam-5687	320	10	6	6	NUM
ejpam-5687	320	11	7	7	NUM
ejpam-5687	320	12	8	8	NUM
ejpam-5687	320	13	9	9	NUM
ejpam-5687	320	14	10	10	NUM
ejpam-5687	320	15	0.55	0.55	NUM
ejpam-5687	320	16	0.60	0.60	NUM
ejpam-5687	320	17	0.65	0.65	NUM
ejpam-5687	320	18	0.70	0.70	NUM
ejpam-5687	320	19	(	(	PUNCT
ejpam-5687	320	20	a	a	NOUN
ejpam-5687	320	21	)	)	PUNCT
ejpam-5687	320	22	time	time	NOUN
ejpam-5687	320	23	t	t	NOUN
ejpam-5687	320	24	0	0	NUM
ejpam-5687	320	25	10	10	NUM
ejpam-5687	320	26	20	20	NUM
ejpam-5687	320	27	30	30	NUM
ejpam-5687	320	28	40	40	NUM
ejpam-5687	320	29	50	50	NUM
ejpam-5687	320	30	60	60	NUM
ejpam-5687	320	31	70	70	NUM
ejpam-5687	320	32	80	80	NUM
ejpam-5687	320	33	e	e	NOUN
ejpam-5687	320	34	x	x	X
ejpam-5687	321	1	p	p	NOUN
ejpam-5687	321	2	o	o	X
ejpam-5687	321	3	s	s	X
ejpam-5687	321	4	e	e	NOUN
ejpam-5687	321	5	d	d	NOUN
ejpam-5687	321	6	p	p	X
ejpam-5687	321	7	o	o	X
ejpam-5687	321	8	p	p	X
ejpam-5687	321	9	u	u	X
ejpam-5687	321	10	la	la	PROPN
ejpam-5687	321	11	t	t	PROPN
ejpam-5687	321	12	io	io	PROPN
ejpam-5687	321	13	n	n	PRON
ejpam-5687	321	14	o	o	X
ejpam-5687	322	1	f	f	NOUN
ejpam-5687	322	2	h	h	NOUN
ejpam-5687	323	1	o	o	NOUN
ejpam-5687	323	2	s	s	PROPN
ejpam-5687	323	3	t	t	X
ejpam-5687	323	4	0	0	NUM
ejpam-5687	323	5	1	1	NUM
ejpam-5687	323	6	2	2	NUM
ejpam-5687	323	7	3	3	NUM
ejpam-5687	323	8	4	4	NUM
ejpam-5687	323	9	5	5	NUM
ejpam-5687	323	10	6	6	NUM
ejpam-5687	323	11	0.55	0.55	NUM
ejpam-5687	323	12	0.60	0.60	NUM
ejpam-5687	323	13	0.65	0.65	NUM
ejpam-5687	323	14	0.70	0.70	NUM
ejpam-5687	323	15	(	(	PUNCT
ejpam-5687	323	16	b	b	NOUN
ejpam-5687	323	17	)	)	PUNCT
ejpam-5687	323	18	time	time	NOUN
ejpam-5687	323	19	t	t	NOUN
ejpam-5687	323	20	0	0	NUM
ejpam-5687	323	21	10	10	NUM
ejpam-5687	323	22	20	20	NUM
ejpam-5687	323	23	30	30	NUM
ejpam-5687	323	24	40	40	NUM
ejpam-5687	323	25	50	50	NUM
ejpam-5687	323	26	60	60	NUM
ejpam-5687	323	27	70	70	NUM
ejpam-5687	323	28	80	80	NUM
ejpam-5687	323	29	i	i	PRON
ejpam-5687	323	30	n	n	VERB
ejpam-5687	324	1	f	f	NOUN
ejpam-5687	324	2	e	e	X
ejpam-5687	324	3	c	c	PROPN
ejpam-5687	324	4	t	t	PROPN
ejpam-5687	324	5	e	e	PROPN
ejpam-5687	325	1	d	d	X
ejpam-5687	325	2	p	p	X
ejpam-5687	325	3	o	o	X
ejpam-5687	325	4	p	p	X
ejpam-5687	325	5	u	u	X
ejpam-5687	325	6	la	la	PROPN
ejpam-5687	325	7	t	t	PROPN
ejpam-5687	325	8	io	io	PROPN
ejpam-5687	325	9	n	n	PRON
ejpam-5687	325	10	o	o	X
ejpam-5687	325	11	f	f	NOUN
ejpam-5687	325	12	h	h	NOUN
ejpam-5687	326	1	o	o	NOUN
ejpam-5687	326	2	s	s	PROPN
ejpam-5687	326	3	t	t	X
ejpam-5687	326	4	0	0	NUM
ejpam-5687	326	5	2	2	NUM
ejpam-5687	326	6	4	4	NUM
ejpam-5687	326	7	6	6	NUM
ejpam-5687	326	8	8	8	NUM
ejpam-5687	326	9	10	10	NUM
ejpam-5687	326	10	12	12	NUM
ejpam-5687	326	11	0.55	0.55	NUM
ejpam-5687	326	12	0.60	0.60	NUM
ejpam-5687	326	13	0.65	0.65	NUM
ejpam-5687	326	14	0.70	0.70	NUM
ejpam-5687	326	15	(	(	PUNCT
ejpam-5687	326	16	c	c	NOUN
ejpam-5687	326	17	)	)	PUNCT
ejpam-5687	326	18	time	time	NOUN
ejpam-5687	326	19	t	t	PROPN
ejpam-5687	326	20	0	0	NUM
ejpam-5687	326	21	10	10	NUM
ejpam-5687	326	22	20	20	NUM
ejpam-5687	326	23	30	30	NUM
ejpam-5687	326	24	40	40	NUM
ejpam-5687	326	25	50	50	NUM
ejpam-5687	326	26	60	60	NUM
ejpam-5687	326	27	70	70	NUM
ejpam-5687	326	28	80	80	NUM
ejpam-5687	326	29	s	s	NOUN
ejpam-5687	326	30	u	u	NOUN
ejpam-5687	326	31	s	s	PRON
ejpam-5687	326	32	c	c	NOUN
ejpam-5687	326	33	e	e	NOUN
ejpam-5687	326	34	p	p	PROPN
ejpam-5687	326	35	t	t	PROPN
ejpam-5687	326	36	ib	ib	X
ejpam-5687	326	37	le	le	PROPN
ejpam-5687	327	1	p	p	X
ejpam-5687	327	2	o	o	X
ejpam-5687	327	3	p	p	X
ejpam-5687	327	4	u	u	X
ejpam-5687	327	5	la	la	PROPN
ejpam-5687	327	6	t	t	PROPN
ejpam-5687	327	7	io	io	PROPN
ejpam-5687	327	8	n	n	ADV
ejpam-5687	327	9	o	o	X
ejpam-5687	327	10	f	f	X
ejpam-5687	327	11	v	v	INTJ
ejpam-5687	327	12	ir	ir	PROPN
ejpam-5687	327	13	u	u	PROPN
ejpam-5687	327	14	s	s	PROPN
ejpam-5687	327	15	0	0	NUM
ejpam-5687	327	16	1	1	NUM
ejpam-5687	327	17	2	2	NUM
ejpam-5687	327	18	3	3	NUM
ejpam-5687	327	19	4	4	NUM
ejpam-5687	327	20	5	5	NUM
ejpam-5687	327	21	6	6	NUM
ejpam-5687	327	22	7	7	NUM
ejpam-5687	327	23	8	8	NUM
ejpam-5687	327	24	9	9	NUM
ejpam-5687	327	25	10	10	NUM
ejpam-5687	327	26	0.55	0.55	NUM
ejpam-5687	327	27	0.60	0.60	NUM
ejpam-5687	327	28	0.65	0.65	NUM
ejpam-5687	327	29	0.70	0.70	NUM
ejpam-5687	327	30	(	(	PUNCT
ejpam-5687	327	31	d	d	NOUN
ejpam-5687	327	32	)	)	PUNCT
ejpam-5687	327	33	time	time	NOUN
ejpam-5687	327	34	t	t	PROPN
ejpam-5687	327	35	0	0	NUM
ejpam-5687	327	36	10	10	NUM
ejpam-5687	327	37	20	20	NUM
ejpam-5687	327	38	30	30	NUM
ejpam-5687	327	39	40	40	NUM
ejpam-5687	327	40	50	50	NUM
ejpam-5687	327	41	60	60	NUM
ejpam-5687	327	42	70	70	NUM
ejpam-5687	327	43	80	80	NUM
ejpam-5687	327	44	e	e	NOUN
ejpam-5687	327	45	x	x	X
ejpam-5687	328	1	p	p	NOUN
ejpam-5687	328	2	o	o	X
ejpam-5687	328	3	s	s	X
ejpam-5687	328	4	e	e	NOUN
ejpam-5687	328	5	d	d	NOUN
ejpam-5687	328	6	p	p	X
ejpam-5687	328	7	o	o	X
ejpam-5687	328	8	p	p	X
ejpam-5687	328	9	u	u	X
ejpam-5687	328	10	la	la	PROPN
ejpam-5687	328	11	t	t	PROPN
ejpam-5687	328	12	io	io	PROPN
ejpam-5687	328	13	n	n	ADV
ejpam-5687	328	14	o	o	X
ejpam-5687	328	15	f	f	X
ejpam-5687	328	16	v	v	INTJ
ejpam-5687	328	17	ir	ir	PROPN
ejpam-5687	328	18	u	u	PROPN
ejpam-5687	328	19	s	s	PROPN
ejpam-5687	328	20	0	0	NUM
ejpam-5687	328	21	0.5	0.5	NUM
ejpam-5687	328	22	1	1	NUM
ejpam-5687	328	23	1.5	1.5	NUM
ejpam-5687	328	24	2	2	NUM
ejpam-5687	328	25	2.5	2.5	NUM
ejpam-5687	328	26	3	3	NUM
ejpam-5687	328	27	0.55	0.55	NUM
ejpam-5687	328	28	0.60	0.60	NUM
ejpam-5687	328	29	0.65	0.65	NUM
ejpam-5687	328	30	0.70	0.70	NUM
ejpam-5687	328	31	(	(	PUNCT
ejpam-5687	328	32	e	e	NOUN
ejpam-5687	328	33	)	)	PUNCT
ejpam-5687	328	34	time	time	NOUN
ejpam-5687	328	35	t	t	PROPN
ejpam-5687	328	36	(	(	PUNCT
ejpam-5687	328	37	days	day	NOUN
ejpam-5687	328	38	)	)	PUNCT
ejpam-5687	328	39	0	0	NUM
ejpam-5687	329	1	10	10	NUM
ejpam-5687	329	2	20	20	NUM
ejpam-5687	329	3	30	30	NUM
ejpam-5687	329	4	40	40	NUM
ejpam-5687	329	5	50	50	NUM
ejpam-5687	329	6	60	60	NUM
ejpam-5687	329	7	70	70	NUM
ejpam-5687	329	8	80	80	NUM
ejpam-5687	329	9	i	i	PRON
ejpam-5687	329	10	n	n	VERB
ejpam-5687	329	11	f	f	NOUN
ejpam-5687	329	12	e	e	X
ejpam-5687	329	13	c	c	PROPN
ejpam-5687	329	14	t	t	PROPN
ejpam-5687	329	15	e	e	PROPN
ejpam-5687	330	1	d	d	X
ejpam-5687	330	2	p	p	X
ejpam-5687	330	3	o	o	X
ejpam-5687	330	4	p	p	X
ejpam-5687	330	5	u	u	X
ejpam-5687	330	6	la	la	PROPN
ejpam-5687	330	7	t	t	PROPN
ejpam-5687	330	8	io	io	PROPN
ejpam-5687	330	9	n	n	ADV
ejpam-5687	330	10	o	o	X
ejpam-5687	330	11	f	f	X
ejpam-5687	330	12	v	v	INTJ
ejpam-5687	330	13	ir	ir	PROPN
ejpam-5687	330	14	u	u	PROPN
ejpam-5687	330	15	s	s	PROPN
ejpam-5687	330	16	0	0	NUM
ejpam-5687	330	17	1	1	NUM
ejpam-5687	330	18	2	2	NUM
ejpam-5687	330	19	3	3	NUM
ejpam-5687	330	20	4	4	NUM
ejpam-5687	330	21	5	5	NUM
ejpam-5687	330	22	6	6	NUM
ejpam-5687	330	23	7	7	NUM
ejpam-5687	330	24	8	8	NUM
ejpam-5687	330	25	0.55	0.55	NUM
ejpam-5687	330	26	0.60	0.60	NUM
ejpam-5687	330	27	0.65	0.65	NUM
ejpam-5687	330	28	0.70	0.70	NUM
ejpam-5687	330	29	(	(	PUNCT
ejpam-5687	330	30	f	f	X
ejpam-5687	330	31	)	)	PUNCT
ejpam-5687	330	32	figure	figure	NOUN
ejpam-5687	330	33	2	2	NUM
ejpam-5687	330	34	:	:	PUNCT
ejpam-5687	330	35	illustration	illustration	NOUN
ejpam-5687	330	36	of	of	ADP
ejpam-5687	330	37	human	human	ADJ
ejpam-5687	330	38	and	and	CCONJ
ejpam-5687	330	39	vector	vector	NOUN
ejpam-5687	330	40	classes	class	NOUN
ejpam-5687	330	41	for	for	ADP
ejpam-5687	330	42	l	l	NOUN
ejpam-5687	330	43	=	=	SYM
ejpam-5687	330	44	0.55	0.55	NUM
ejpam-5687	330	45	,	,	PUNCT
ejpam-5687	330	46	0.6	0.6	NUM
ejpam-5687	330	47	,	,	PUNCT
ejpam-5687	330	48	0.65	0.65	NUM
ejpam-5687	330	49	,	,	PUNCT
ejpam-5687	330	50	0.7	0.7	NUM
ejpam-5687	330	51	.	.	PUNCT
ejpam-5687	331	1	controlling	control	VERB
ejpam-5687	331	2	the	the	DET
ejpam-5687	331	3	spread	spread	NOUN
ejpam-5687	331	4	of	of	ADP
ejpam-5687	331	5	infectious	infectious	ADJ
ejpam-5687	331	6	diseases	disease	NOUN
ejpam-5687	331	7	.	.	PUNCT
ejpam-5687	332	1	dynamical	dynamical	ADJ
ejpam-5687	332	2	behavior	behavior	NOUN
ejpam-5687	332	3	refers	refer	VERB
ejpam-5687	332	4	to	to	ADP
ejpam-5687	332	5	how	how	SCONJ
ejpam-5687	332	6	the	the	DET
ejpam-5687	332	7	disease	disease	NOUN
ejpam-5687	332	8	n.	n.	PROPN
ejpam-5687	332	9	ullah	ullah	PROPN
ejpam-5687	332	10	et	et	PROPN
ejpam-5687	332	11	al	al	PROPN
ejpam-5687	332	12	.	.	PUNCT
ejpam-5687	332	13	/	/	SYM
ejpam-5687	332	14	eur	eur	PROPN
ejpam-5687	332	15	.	.	PUNCT
ejpam-5687	333	1	j.	j.	PROPN
ejpam-5687	333	2	pure	pure	PROPN
ejpam-5687	333	3	appl	appl	PROPN
ejpam-5687	333	4	.	.	PROPN
ejpam-5687	333	5	math	math	PROPN
ejpam-5687	333	6	,	,	PUNCT
ejpam-5687	333	7	18	18	NUM
ejpam-5687	333	8	(	(	PUNCT
ejpam-5687	333	9	2	2	NUM
ejpam-5687	333	10	)	)	PUNCT
ejpam-5687	333	11	(	(	PUNCT
ejpam-5687	333	12	2025	2025	NUM
ejpam-5687	333	13	)	)	PUNCT
ejpam-5687	333	14	,	,	PUNCT
ejpam-5687	333	15	5687	5687	NUM
ejpam-5687	333	16	20	20	NUM
ejpam-5687	333	17	of	of	ADP
ejpam-5687	333	18	25	25	NUM
ejpam-5687	333	19	time	time	NOUN
ejpam-5687	333	20	t	t	NOUN
ejpam-5687	333	21	0	0	NUM
ejpam-5687	333	22	10	10	NUM
ejpam-5687	333	23	20	20	NUM
ejpam-5687	333	24	30	30	NUM
ejpam-5687	333	25	40	40	NUM
ejpam-5687	333	26	50	50	NUM
ejpam-5687	333	27	60	60	NUM
ejpam-5687	333	28	70	70	NUM
ejpam-5687	333	29	80	80	NUM
ejpam-5687	333	30	s	s	NOUN
ejpam-5687	333	31	u	u	NOUN
ejpam-5687	333	32	s	s	PRON
ejpam-5687	333	33	c	c	NOUN
ejpam-5687	333	34	e	e	NOUN
ejpam-5687	333	35	p	p	PROPN
ejpam-5687	333	36	t	t	PROPN
ejpam-5687	333	37	ib	ib	X
ejpam-5687	333	38	le	le	PROPN
ejpam-5687	334	1	p	p	X
ejpam-5687	334	2	o	o	X
ejpam-5687	334	3	p	p	X
ejpam-5687	334	4	u	u	X
ejpam-5687	334	5	la	la	PROPN
ejpam-5687	334	6	t	t	PROPN
ejpam-5687	334	7	io	io	PROPN
ejpam-5687	334	8	n	n	PRON
ejpam-5687	334	9	o	o	X
ejpam-5687	335	1	f	f	NOUN
ejpam-5687	335	2	h	h	NOUN
ejpam-5687	336	1	o	o	NOUN
ejpam-5687	336	2	s	s	PROPN
ejpam-5687	336	3	t	t	X
ejpam-5687	336	4	0	0	NUM
ejpam-5687	336	5	1	1	NUM
ejpam-5687	336	6	2	2	NUM
ejpam-5687	336	7	3	3	NUM
ejpam-5687	336	8	4	4	NUM
ejpam-5687	336	9	5	5	NUM
ejpam-5687	336	10	6	6	NUM
ejpam-5687	336	11	7	7	NUM
ejpam-5687	336	12	8	8	NUM
ejpam-5687	336	13	9	9	NUM
ejpam-5687	336	14	10	10	NUM
ejpam-5687	336	15	0.75	0.75	NUM
ejpam-5687	336	16	0.80	0.80	NUM
ejpam-5687	336	17	0.85	0.85	NUM
ejpam-5687	336	18	0.90	0.90	NUM
ejpam-5687	336	19	(	(	PUNCT
ejpam-5687	336	20	a	a	DET
ejpam-5687	336	21	)	)	PUNCT
ejpam-5687	336	22	time	time	NOUN
ejpam-5687	336	23	t	t	NOUN
ejpam-5687	336	24	0	0	NUM
ejpam-5687	336	25	10	10	NUM
ejpam-5687	336	26	20	20	NUM
ejpam-5687	336	27	30	30	NUM
ejpam-5687	336	28	40	40	NUM
ejpam-5687	336	29	50	50	NUM
ejpam-5687	336	30	60	60	NUM
ejpam-5687	336	31	70	70	NUM
ejpam-5687	336	32	80	80	NUM
ejpam-5687	336	33	e	e	NOUN
ejpam-5687	336	34	x	x	X
ejpam-5687	337	1	p	p	NOUN
ejpam-5687	337	2	o	o	X
ejpam-5687	337	3	s	s	X
ejpam-5687	337	4	e	e	NOUN
ejpam-5687	337	5	d	d	NOUN
ejpam-5687	337	6	p	p	X
ejpam-5687	337	7	o	o	X
ejpam-5687	337	8	p	p	X
ejpam-5687	337	9	u	u	X
ejpam-5687	337	10	la	la	PROPN
ejpam-5687	337	11	t	t	PROPN
ejpam-5687	337	12	io	io	PROPN
ejpam-5687	337	13	n	n	PRON
ejpam-5687	337	14	o	o	X
ejpam-5687	338	1	f	f	NOUN
ejpam-5687	338	2	h	h	NOUN
ejpam-5687	339	1	o	o	NOUN
ejpam-5687	339	2	s	s	PROPN
ejpam-5687	339	3	t	t	X
ejpam-5687	339	4	0	0	NUM
ejpam-5687	339	5	1	1	NUM
ejpam-5687	339	6	2	2	NUM
ejpam-5687	339	7	3	3	NUM
ejpam-5687	339	8	4	4	NUM
ejpam-5687	339	9	5	5	NUM
ejpam-5687	339	10	6	6	NUM
ejpam-5687	339	11	0.75	0.75	NUM
ejpam-5687	339	12	0.80	0.80	NUM
ejpam-5687	339	13	0.85	0.85	NUM
ejpam-5687	339	14	0.90	0.90	NUM
ejpam-5687	339	15	(	(	PUNCT
ejpam-5687	339	16	b	b	NOUN
ejpam-5687	339	17	)	)	PUNCT
ejpam-5687	339	18	time	time	NOUN
ejpam-5687	339	19	t	t	NOUN
ejpam-5687	339	20	0	0	NUM
ejpam-5687	339	21	10	10	NUM
ejpam-5687	339	22	20	20	NUM
ejpam-5687	339	23	30	30	NUM
ejpam-5687	339	24	40	40	NUM
ejpam-5687	339	25	50	50	NUM
ejpam-5687	339	26	60	60	NUM
ejpam-5687	339	27	70	70	NUM
ejpam-5687	339	28	80	80	NUM
ejpam-5687	339	29	i	i	PRON
ejpam-5687	339	30	n	n	VERB
ejpam-5687	340	1	f	f	NOUN
ejpam-5687	340	2	e	e	X
ejpam-5687	340	3	c	c	PROPN
ejpam-5687	340	4	t	t	PROPN
ejpam-5687	340	5	e	e	PROPN
ejpam-5687	341	1	d	d	X
ejpam-5687	341	2	p	p	X
ejpam-5687	341	3	o	o	X
ejpam-5687	341	4	p	p	X
ejpam-5687	341	5	u	u	X
ejpam-5687	341	6	la	la	PROPN
ejpam-5687	341	7	t	t	PROPN
ejpam-5687	341	8	io	io	PROPN
ejpam-5687	341	9	n	n	PRON
ejpam-5687	341	10	o	o	X
ejpam-5687	341	11	f	f	NOUN
ejpam-5687	341	12	h	h	NOUN
ejpam-5687	342	1	o	o	NOUN
ejpam-5687	342	2	s	s	PROPN
ejpam-5687	342	3	t	t	X
ejpam-5687	342	4	0	0	NUM
ejpam-5687	342	5	2	2	NUM
ejpam-5687	342	6	4	4	NUM
ejpam-5687	342	7	6	6	NUM
ejpam-5687	342	8	8	8	NUM
ejpam-5687	342	9	10	10	NUM
ejpam-5687	342	10	12	12	NUM
ejpam-5687	342	11	0.75	0.75	NUM
ejpam-5687	342	12	0.80	0.80	NUM
ejpam-5687	342	13	0.85	0.85	NUM
ejpam-5687	342	14	0.90	0.90	NUM
ejpam-5687	342	15	(	(	PUNCT
ejpam-5687	342	16	c	c	NOUN
ejpam-5687	342	17	)	)	PUNCT
ejpam-5687	342	18	time	time	NOUN
ejpam-5687	342	19	t	t	PROPN
ejpam-5687	342	20	0	0	NUM
ejpam-5687	342	21	10	10	NUM
ejpam-5687	342	22	20	20	NUM
ejpam-5687	342	23	30	30	NUM
ejpam-5687	342	24	40	40	NUM
ejpam-5687	342	25	50	50	NUM
ejpam-5687	342	26	60	60	NUM
ejpam-5687	342	27	70	70	NUM
ejpam-5687	342	28	80	80	NUM
ejpam-5687	342	29	s	s	NOUN
ejpam-5687	342	30	u	u	NOUN
ejpam-5687	342	31	s	s	PRON
ejpam-5687	342	32	c	c	NOUN
ejpam-5687	342	33	e	e	NOUN
ejpam-5687	342	34	p	p	PROPN
ejpam-5687	342	35	t	t	PROPN
ejpam-5687	342	36	ib	ib	X
ejpam-5687	342	37	le	le	PROPN
ejpam-5687	343	1	p	p	X
ejpam-5687	343	2	o	o	X
ejpam-5687	343	3	p	p	X
ejpam-5687	343	4	u	u	X
ejpam-5687	343	5	la	la	PROPN
ejpam-5687	343	6	t	t	PROPN
ejpam-5687	343	7	io	io	PROPN
ejpam-5687	343	8	n	n	ADV
ejpam-5687	343	9	o	o	X
ejpam-5687	343	10	f	f	X
ejpam-5687	343	11	v	v	INTJ
ejpam-5687	343	12	ir	ir	PROPN
ejpam-5687	343	13	u	u	PROPN
ejpam-5687	343	14	s	s	PROPN
ejpam-5687	343	15	0	0	NUM
ejpam-5687	343	16	1	1	NUM
ejpam-5687	343	17	2	2	NUM
ejpam-5687	343	18	3	3	NUM
ejpam-5687	343	19	4	4	NUM
ejpam-5687	343	20	5	5	NUM
ejpam-5687	343	21	6	6	NUM
ejpam-5687	343	22	7	7	NUM
ejpam-5687	343	23	8	8	NUM
ejpam-5687	343	24	9	9	NUM
ejpam-5687	343	25	10	10	NUM
ejpam-5687	343	26	0.75	0.75	NUM
ejpam-5687	343	27	0.80	0.80	NUM
ejpam-5687	343	28	0.85	0.85	NUM
ejpam-5687	343	29	0.90	0.90	NUM
ejpam-5687	343	30	(	(	PUNCT
ejpam-5687	343	31	d	d	NOUN
ejpam-5687	343	32	)	)	PUNCT
ejpam-5687	343	33	time	time	NOUN
ejpam-5687	343	34	t	t	PROPN
ejpam-5687	343	35	0	0	NUM
ejpam-5687	343	36	10	10	NUM
ejpam-5687	343	37	20	20	NUM
ejpam-5687	343	38	30	30	NUM
ejpam-5687	343	39	40	40	NUM
ejpam-5687	343	40	50	50	NUM
ejpam-5687	343	41	60	60	NUM
ejpam-5687	343	42	70	70	NUM
ejpam-5687	343	43	80	80	NUM
ejpam-5687	343	44	e	e	NOUN
ejpam-5687	343	45	x	x	X
ejpam-5687	344	1	p	p	NOUN
ejpam-5687	344	2	o	o	X
ejpam-5687	344	3	s	s	X
ejpam-5687	344	4	e	e	NOUN
ejpam-5687	344	5	d	d	NOUN
ejpam-5687	344	6	p	p	X
ejpam-5687	344	7	o	o	X
ejpam-5687	344	8	p	p	X
ejpam-5687	344	9	u	u	X
ejpam-5687	344	10	la	la	PROPN
ejpam-5687	344	11	t	t	PROPN
ejpam-5687	344	12	io	io	PROPN
ejpam-5687	344	13	n	n	ADV
ejpam-5687	344	14	o	o	X
ejpam-5687	344	15	f	f	X
ejpam-5687	344	16	v	v	INTJ
ejpam-5687	344	17	ir	ir	PROPN
ejpam-5687	344	18	u	u	PROPN
ejpam-5687	344	19	s	s	PROPN
ejpam-5687	344	20	0	0	NUM
ejpam-5687	344	21	0.5	0.5	NUM
ejpam-5687	344	22	1	1	NUM
ejpam-5687	344	23	1.5	1.5	NUM
ejpam-5687	344	24	2	2	NUM
ejpam-5687	344	25	2.5	2.5	NUM
ejpam-5687	344	26	3	3	NUM
ejpam-5687	344	27	0.75	0.75	NUM
ejpam-5687	344	28	0.80	0.80	NUM
ejpam-5687	344	29	0.85	0.85	NUM
ejpam-5687	344	30	0.90	0.90	NUM
ejpam-5687	344	31	(	(	PUNCT
ejpam-5687	344	32	e	e	NOUN
ejpam-5687	344	33	)	)	PUNCT
ejpam-5687	344	34	time	time	NOUN
ejpam-5687	344	35	t	t	PROPN
ejpam-5687	344	36	(	(	PUNCT
ejpam-5687	344	37	days	day	NOUN
ejpam-5687	344	38	)	)	PUNCT
ejpam-5687	344	39	0	0	NUM
ejpam-5687	345	1	10	10	NUM
ejpam-5687	345	2	20	20	NUM
ejpam-5687	345	3	30	30	NUM
ejpam-5687	345	4	40	40	NUM
ejpam-5687	345	5	50	50	NUM
ejpam-5687	345	6	60	60	NUM
ejpam-5687	345	7	70	70	NUM
ejpam-5687	345	8	80	80	NUM
ejpam-5687	345	9	i	i	PRON
ejpam-5687	345	10	n	n	VERB
ejpam-5687	345	11	f	f	NOUN
ejpam-5687	345	12	e	e	X
ejpam-5687	345	13	c	c	PROPN
ejpam-5687	345	14	t	t	PROPN
ejpam-5687	345	15	e	e	PROPN
ejpam-5687	346	1	d	d	X
ejpam-5687	346	2	p	p	X
ejpam-5687	346	3	o	o	X
ejpam-5687	346	4	p	p	X
ejpam-5687	346	5	u	u	X
ejpam-5687	346	6	la	la	PROPN
ejpam-5687	346	7	t	t	PROPN
ejpam-5687	346	8	io	io	PROPN
ejpam-5687	346	9	n	n	ADV
ejpam-5687	346	10	o	o	X
ejpam-5687	346	11	f	f	X
ejpam-5687	346	12	v	v	INTJ
ejpam-5687	346	13	ir	ir	PROPN
ejpam-5687	346	14	u	u	PROPN
ejpam-5687	346	15	s	s	PROPN
ejpam-5687	346	16	1	1	NUM
ejpam-5687	346	17	2	2	NUM
ejpam-5687	346	18	3	3	NUM
ejpam-5687	346	19	4	4	NUM
ejpam-5687	346	20	5	5	NUM
ejpam-5687	346	21	6	6	NUM
ejpam-5687	346	22	7	7	NUM
ejpam-5687	346	23	8	8	NUM
ejpam-5687	346	24	0.75	0.75	NUM
ejpam-5687	346	25	0.80	0.80	NUM
ejpam-5687	346	26	0.85	0.85	NUM
ejpam-5687	346	27	0.90	0.90	NUM
ejpam-5687	346	28	(	(	PUNCT
ejpam-5687	346	29	f	f	X
ejpam-5687	346	30	)	)	PUNCT
ejpam-5687	346	31	figure	figure	NOUN
ejpam-5687	346	32	3	3	NUM
ejpam-5687	346	33	:	:	PUNCT
ejpam-5687	346	34	illustration	illustration	NOUN
ejpam-5687	346	35	of	of	ADP
ejpam-5687	346	36	human	human	ADJ
ejpam-5687	346	37	and	and	CCONJ
ejpam-5687	346	38	vector	vector	NOUN
ejpam-5687	346	39	classes	class	NOUN
ejpam-5687	346	40	for	for	ADP
ejpam-5687	346	41	l	l	NOUN
ejpam-5687	346	42	=	=	PUNCT
ejpam-5687	346	43	0.75	0.75	NUM
ejpam-5687	346	44	,	,	PUNCT
ejpam-5687	346	45	0.8	0.8	NUM
ejpam-5687	346	46	,	,	PUNCT
ejpam-5687	346	47	0.85	0.85	NUM
ejpam-5687	346	48	,	,	PUNCT
ejpam-5687	346	49	0.9	0.9	NUM
ejpam-5687	346	50	.	.	PUNCT
ejpam-5687	347	1	progresses	progress	NOUN
ejpam-5687	347	2	over	over	ADP
ejpam-5687	347	3	time	time	NOUN
ejpam-5687	347	4	,	,	PUNCT
ejpam-5687	347	5	including	include	VERB
ejpam-5687	347	6	the	the	DET
ejpam-5687	347	7	rates	rate	NOUN
ejpam-5687	347	8	of	of	ADP
ejpam-5687	347	9	infection	infection	NOUN
ejpam-5687	347	10	,	,	PUNCT
ejpam-5687	347	11	recovery	recovery	NOUN
ejpam-5687	347	12	,	,	PUNCT
ejpam-5687	347	13	and	and	CCONJ
ejpam-5687	347	14	mortality	mortality	NOUN
ejpam-5687	347	15	,	,	PUNCT
ejpam-5687	347	16	as	as	ADV
ejpam-5687	347	17	well	well	ADV
ejpam-5687	347	18	as	as	ADP
ejpam-5687	347	19	the	the	DET
ejpam-5687	347	20	interplay	interplay	NOUN
ejpam-5687	347	21	between	between	ADP
ejpam-5687	347	22	susceptible	susceptible	ADJ
ejpam-5687	347	23	,	,	PUNCT
ejpam-5687	347	24	infected	infected	ADJ
ejpam-5687	347	25	,	,	PUNCT
ejpam-5687	347	26	and	and	CCONJ
ejpam-5687	347	27	recovered	recovered	ADJ
ejpam-5687	347	28	populations	population	NOUN
ejpam-5687	347	29	.	.	PUNCT
ejpam-5687	348	1	this	this	DET
ejpam-5687	348	2	understanding	understanding	NOUN
ejpam-5687	348	3	provides	provide	VERB
ejpam-5687	348	4	a	a	DET
ejpam-5687	348	5	foundation	foundation	NOUN
ejpam-5687	348	6	for	for	ADP
ejpam-5687	348	7	designing	designing	NOUN
ejpam-5687	348	8	interventions	intervention	NOUN
ejpam-5687	348	9	like	like	ADP
ejpam-5687	348	10	vaccination	vaccination	NOUN
ejpam-5687	348	11	campaigns	campaign	NOUN
ejpam-5687	348	12	,	,	PUNCT
ejpam-5687	348	13	quarantine	quarantine	NOUN
ejpam-5687	348	14	n.	n.	PROPN
ejpam-5687	348	15	ullah	ullah	PROPN
ejpam-5687	348	16	et	et	PROPN
ejpam-5687	348	17	al	al	PROPN
ejpam-5687	348	18	.	.	PUNCT
ejpam-5687	348	19	/	/	SYM
ejpam-5687	348	20	eur	eur	PROPN
ejpam-5687	348	21	.	.	PUNCT
ejpam-5687	349	1	j.	j.	PROPN
ejpam-5687	349	2	pure	pure	PROPN
ejpam-5687	349	3	appl	appl	PROPN
ejpam-5687	349	4	.	.	PROPN
ejpam-5687	349	5	math	math	PROPN
ejpam-5687	349	6	,	,	PUNCT
ejpam-5687	349	7	18	18	NUM
ejpam-5687	349	8	(	(	PUNCT
ejpam-5687	349	9	2	2	NUM
ejpam-5687	349	10	)	)	PUNCT
ejpam-5687	349	11	(	(	PUNCT
ejpam-5687	349	12	2025	2025	NUM
ejpam-5687	349	13	)	)	PUNCT
ejpam-5687	349	14	,	,	PUNCT
ejpam-5687	349	15	5687	5687	NUM
ejpam-5687	349	16	21	21	NUM
ejpam-5687	349	17	of	of	ADP
ejpam-5687	349	18	25	25	NUM
ejpam-5687	349	19	time	time	NOUN
ejpam-5687	349	20	t	t	NOUN
ejpam-5687	349	21	0	0	NUM
ejpam-5687	349	22	10	10	NUM
ejpam-5687	349	23	20	20	NUM
ejpam-5687	349	24	30	30	NUM
ejpam-5687	349	25	40	40	NUM
ejpam-5687	349	26	50	50	NUM
ejpam-5687	349	27	60	60	NUM
ejpam-5687	349	28	70	70	NUM
ejpam-5687	349	29	80	80	NUM
ejpam-5687	349	30	s	s	NOUN
ejpam-5687	349	31	u	u	NOUN
ejpam-5687	349	32	s	s	PRON
ejpam-5687	349	33	c	c	NOUN
ejpam-5687	349	34	e	e	NOUN
ejpam-5687	349	35	p	p	PROPN
ejpam-5687	349	36	t	t	PROPN
ejpam-5687	349	37	ib	ib	X
ejpam-5687	349	38	le	le	PROPN
ejpam-5687	350	1	p	p	X
ejpam-5687	350	2	o	o	X
ejpam-5687	350	3	p	p	X
ejpam-5687	350	4	u	u	X
ejpam-5687	350	5	la	la	PROPN
ejpam-5687	350	6	t	t	PROPN
ejpam-5687	350	7	io	io	PROPN
ejpam-5687	350	8	n	n	PRON
ejpam-5687	350	9	o	o	X
ejpam-5687	351	1	f	f	NOUN
ejpam-5687	351	2	h	h	NOUN
ejpam-5687	352	1	o	o	NOUN
ejpam-5687	352	2	s	s	PROPN
ejpam-5687	352	3	t	t	X
ejpam-5687	352	4	0	0	NUM
ejpam-5687	352	5	1	1	NUM
ejpam-5687	352	6	2	2	NUM
ejpam-5687	352	7	3	3	NUM
ejpam-5687	352	8	4	4	NUM
ejpam-5687	352	9	5	5	NUM
ejpam-5687	352	10	6	6	NUM
ejpam-5687	352	11	7	7	NUM
ejpam-5687	352	12	8	8	NUM
ejpam-5687	352	13	9	9	NUM
ejpam-5687	352	14	10	10	NUM
ejpam-5687	352	15	0.92	0.92	NUM
ejpam-5687	352	16	0.95	0.95	NUM
ejpam-5687	352	17	0.98	0.98	NUM
ejpam-5687	352	18	1.0	1.0	NUM
ejpam-5687	352	19	(	(	PUNCT
ejpam-5687	352	20	a	a	NOUN
ejpam-5687	352	21	)	)	PUNCT
ejpam-5687	352	22	time	time	NOUN
ejpam-5687	352	23	t	t	NOUN
ejpam-5687	352	24	0	0	NUM
ejpam-5687	352	25	10	10	NUM
ejpam-5687	352	26	20	20	NUM
ejpam-5687	352	27	30	30	NUM
ejpam-5687	352	28	40	40	NUM
ejpam-5687	352	29	50	50	NUM
ejpam-5687	352	30	60	60	NUM
ejpam-5687	352	31	70	70	NUM
ejpam-5687	352	32	80	80	NUM
ejpam-5687	352	33	e	e	NOUN
ejpam-5687	352	34	x	x	X
ejpam-5687	353	1	p	p	NOUN
ejpam-5687	353	2	o	o	X
ejpam-5687	353	3	s	s	X
ejpam-5687	353	4	e	e	NOUN
ejpam-5687	353	5	d	d	NOUN
ejpam-5687	353	6	p	p	X
ejpam-5687	353	7	o	o	X
ejpam-5687	353	8	p	p	X
ejpam-5687	353	9	u	u	X
ejpam-5687	353	10	la	la	PROPN
ejpam-5687	353	11	t	t	PROPN
ejpam-5687	353	12	io	io	PROPN
ejpam-5687	353	13	n	n	PRON
ejpam-5687	353	14	o	o	X
ejpam-5687	354	1	f	f	NOUN
ejpam-5687	354	2	h	h	NOUN
ejpam-5687	355	1	o	o	NOUN
ejpam-5687	355	2	s	s	PROPN
ejpam-5687	355	3	t	t	X
ejpam-5687	355	4	0	0	NUM
ejpam-5687	355	5	1	1	NUM
ejpam-5687	355	6	2	2	NUM
ejpam-5687	355	7	3	3	NUM
ejpam-5687	355	8	4	4	NUM
ejpam-5687	355	9	5	5	NUM
ejpam-5687	355	10	6	6	NUM
ejpam-5687	355	11	0.92	0.92	NUM
ejpam-5687	355	12	0.95	0.95	NUM
ejpam-5687	355	13	0.98	0.98	NUM
ejpam-5687	355	14	1.0	1.0	NUM
ejpam-5687	355	15	(	(	PUNCT
ejpam-5687	355	16	b	b	NOUN
ejpam-5687	355	17	)	)	PUNCT
ejpam-5687	355	18	time	time	NOUN
ejpam-5687	355	19	t	t	NOUN
ejpam-5687	355	20	0	0	NUM
ejpam-5687	355	21	10	10	NUM
ejpam-5687	355	22	20	20	NUM
ejpam-5687	355	23	30	30	NUM
ejpam-5687	355	24	40	40	NUM
ejpam-5687	355	25	50	50	NUM
ejpam-5687	355	26	60	60	NUM
ejpam-5687	355	27	70	70	NUM
ejpam-5687	355	28	80	80	NUM
ejpam-5687	355	29	i	i	PRON
ejpam-5687	355	30	n	n	VERB
ejpam-5687	356	1	f	f	NOUN
ejpam-5687	356	2	e	e	X
ejpam-5687	356	3	c	c	PROPN
ejpam-5687	356	4	t	t	PROPN
ejpam-5687	356	5	e	e	PROPN
ejpam-5687	357	1	d	d	X
ejpam-5687	357	2	p	p	X
ejpam-5687	357	3	o	o	X
ejpam-5687	357	4	p	p	X
ejpam-5687	357	5	u	u	X
ejpam-5687	357	6	la	la	PROPN
ejpam-5687	357	7	t	t	PROPN
ejpam-5687	357	8	io	io	PROPN
ejpam-5687	357	9	n	n	PRON
ejpam-5687	357	10	o	o	X
ejpam-5687	357	11	f	f	NOUN
ejpam-5687	357	12	h	h	NOUN
ejpam-5687	358	1	o	o	NOUN
ejpam-5687	358	2	s	s	PROPN
ejpam-5687	358	3	t	t	PROPN
ejpam-5687	358	4	1	1	NUM
ejpam-5687	358	5	2	2	NUM
ejpam-5687	358	6	3	3	NUM
ejpam-5687	358	7	4	4	NUM
ejpam-5687	358	8	5	5	NUM
ejpam-5687	358	9	6	6	NUM
ejpam-5687	358	10	7	7	NUM
ejpam-5687	358	11	8	8	NUM
ejpam-5687	358	12	9	9	NUM
ejpam-5687	358	13	10	10	NUM
ejpam-5687	358	14	11	11	NUM
ejpam-5687	358	15	0.92	0.92	NUM
ejpam-5687	358	16	0.95	0.95	NUM
ejpam-5687	358	17	0.98	0.98	NUM
ejpam-5687	358	18	1.0	1.0	NUM
ejpam-5687	358	19	(	(	PUNCT
ejpam-5687	358	20	c	c	NOUN
ejpam-5687	358	21	)	)	PUNCT
ejpam-5687	358	22	time	time	NOUN
ejpam-5687	358	23	t	t	PROPN
ejpam-5687	358	24	0	0	NUM
ejpam-5687	358	25	10	10	NUM
ejpam-5687	358	26	20	20	NUM
ejpam-5687	358	27	30	30	NUM
ejpam-5687	358	28	40	40	NUM
ejpam-5687	358	29	50	50	NUM
ejpam-5687	358	30	60	60	NUM
ejpam-5687	358	31	70	70	NUM
ejpam-5687	358	32	80	80	NUM
ejpam-5687	358	33	s	s	NOUN
ejpam-5687	358	34	u	u	NOUN
ejpam-5687	358	35	s	s	PRON
ejpam-5687	358	36	c	c	NOUN
ejpam-5687	358	37	e	e	NOUN
ejpam-5687	358	38	p	p	PROPN
ejpam-5687	358	39	t	t	PROPN
ejpam-5687	358	40	ib	ib	X
ejpam-5687	358	41	le	le	PROPN
ejpam-5687	358	42	p	p	X
ejpam-5687	358	43	o	o	X
ejpam-5687	358	44	p	p	X
ejpam-5687	358	45	u	u	X
ejpam-5687	358	46	la	la	PROPN
ejpam-5687	358	47	t	t	PROPN
ejpam-5687	358	48	io	io	PROPN
ejpam-5687	358	49	n	n	ADV
ejpam-5687	358	50	o	o	X
ejpam-5687	358	51	f	f	X
ejpam-5687	358	52	v	v	INTJ
ejpam-5687	358	53	ir	ir	PROPN
ejpam-5687	358	54	u	u	PROPN
ejpam-5687	358	55	s	s	PROPN
ejpam-5687	358	56	0	0	NUM
ejpam-5687	358	57	1	1	NUM
ejpam-5687	358	58	2	2	NUM
ejpam-5687	358	59	3	3	NUM
ejpam-5687	358	60	4	4	NUM
ejpam-5687	358	61	5	5	NUM
ejpam-5687	358	62	6	6	NUM
ejpam-5687	358	63	7	7	NUM
ejpam-5687	358	64	8	8	NUM
ejpam-5687	358	65	9	9	NUM
ejpam-5687	358	66	10	10	NUM
ejpam-5687	358	67	0.92	0.92	NUM
ejpam-5687	358	68	0.95	0.95	NUM
ejpam-5687	358	69	0.98	0.98	NUM
ejpam-5687	358	70	1.0	1.0	NUM
ejpam-5687	358	71	(	(	PUNCT
ejpam-5687	358	72	d	d	NOUN
ejpam-5687	358	73	)	)	PUNCT
ejpam-5687	358	74	time	time	NOUN
ejpam-5687	358	75	t	t	PROPN
ejpam-5687	358	76	0	0	NUM
ejpam-5687	358	77	10	10	NUM
ejpam-5687	358	78	20	20	NUM
ejpam-5687	358	79	30	30	NUM
ejpam-5687	358	80	40	40	NUM
ejpam-5687	358	81	50	50	NUM
ejpam-5687	358	82	60	60	NUM
ejpam-5687	358	83	70	70	NUM
ejpam-5687	358	84	80	80	NUM
ejpam-5687	358	85	e	e	NOUN
ejpam-5687	358	86	x	x	X
ejpam-5687	359	1	p	p	NOUN
ejpam-5687	359	2	o	o	X
ejpam-5687	359	3	s	s	X
ejpam-5687	359	4	e	e	NOUN
ejpam-5687	359	5	d	d	NOUN
ejpam-5687	359	6	p	p	X
ejpam-5687	359	7	o	o	X
ejpam-5687	359	8	p	p	X
ejpam-5687	359	9	u	u	X
ejpam-5687	359	10	la	la	PROPN
ejpam-5687	359	11	t	t	PROPN
ejpam-5687	359	12	io	io	PROPN
ejpam-5687	359	13	n	n	ADV
ejpam-5687	359	14	o	o	X
ejpam-5687	359	15	f	f	X
ejpam-5687	359	16	v	v	INTJ
ejpam-5687	359	17	ir	ir	PROPN
ejpam-5687	359	18	u	u	PROPN
ejpam-5687	359	19	s	s	PROPN
ejpam-5687	359	20	0	0	NUM
ejpam-5687	359	21	0.5	0.5	NUM
ejpam-5687	359	22	1	1	NUM
ejpam-5687	359	23	1.5	1.5	NUM
ejpam-5687	359	24	2	2	NUM
ejpam-5687	359	25	2.5	2.5	NUM
ejpam-5687	359	26	3	3	NUM
ejpam-5687	359	27	0.92	0.92	NUM
ejpam-5687	359	28	0.95	0.95	NUM
ejpam-5687	359	29	0.98	0.98	NUM
ejpam-5687	359	30	1.0	1.0	NUM
ejpam-5687	359	31	(	(	PUNCT
ejpam-5687	359	32	e	e	NOUN
ejpam-5687	359	33	)	)	PUNCT
ejpam-5687	359	34	time	time	NOUN
ejpam-5687	359	35	t	t	PROPN
ejpam-5687	359	36	0	0	NUM
ejpam-5687	359	37	10	10	NUM
ejpam-5687	359	38	20	20	NUM
ejpam-5687	359	39	30	30	NUM
ejpam-5687	359	40	40	40	NUM
ejpam-5687	359	41	50	50	NUM
ejpam-5687	359	42	60	60	NUM
ejpam-5687	359	43	70	70	NUM
ejpam-5687	359	44	80	80	NUM
ejpam-5687	359	45	r	r	NOUN
ejpam-5687	359	46	e	e	NOUN
ejpam-5687	359	47	c	c	NOUN
ejpam-5687	359	48	o	o	X
ejpam-5687	359	49	v	v	NOUN
ejpam-5687	359	50	e	e	NOUN
ejpam-5687	359	51	r	r	NOUN
ejpam-5687	359	52	e	e	NOUN
ejpam-5687	359	53	d	d	X
ejpam-5687	359	54	c	c	X
ejpam-5687	359	55	la	la	PROPN
ejpam-5687	359	56	s	s	PROPN
ejpam-5687	359	57	s	s	X
ejpam-5687	359	58	o	o	X
ejpam-5687	359	59	f	f	NOUN
ejpam-5687	360	1	h	h	NOUN
ejpam-5687	361	1	o	o	NOUN
ejpam-5687	361	2	s	s	PROPN
ejpam-5687	361	3	t	t	PROPN
ejpam-5687	361	4	2	2	NUM
ejpam-5687	361	5	3	3	NUM
ejpam-5687	361	6	4	4	NUM
ejpam-5687	361	7	5	5	NUM
ejpam-5687	361	8	6	6	NUM
ejpam-5687	361	9	7	7	NUM
ejpam-5687	361	10	8	8	NUM
ejpam-5687	361	11	9	9	NUM
ejpam-5687	361	12	10	10	NUM
ejpam-5687	361	13	0.92	0.92	NUM
ejpam-5687	361	14	0.95	0.95	NUM
ejpam-5687	361	15	0.98	0.98	NUM
ejpam-5687	361	16	1.0	1.0	NUM
ejpam-5687	361	17	(	(	PUNCT
ejpam-5687	361	18	f	f	X
ejpam-5687	361	19	)	)	PUNCT
ejpam-5687	361	20	figure	figure	NOUN
ejpam-5687	361	21	4	4	NUM
ejpam-5687	361	22	:	:	PUNCT
ejpam-5687	361	23	illustration	illustration	NOUN
ejpam-5687	361	24	of	of	ADP
ejpam-5687	361	25	human	human	ADJ
ejpam-5687	361	26	and	and	CCONJ
ejpam-5687	361	27	vector	vector	NOUN
ejpam-5687	361	28	classes	class	NOUN
ejpam-5687	361	29	for	for	ADP
ejpam-5687	361	30	l	l	NOUN
ejpam-5687	361	31	=	=	SYM
ejpam-5687	361	32	0.92	0.92	NUM
ejpam-5687	361	33	,	,	PUNCT
ejpam-5687	361	34	0.95	0.95	NUM
ejpam-5687	361	35	,	,	PUNCT
ejpam-5687	361	36	0.98	0.98	NUM
ejpam-5687	361	37	,	,	PUNCT
ejpam-5687	361	38	1	1	NUM
ejpam-5687	361	39	.	.	PUNCT
ejpam-5687	361	40	measures	measure	NOUN
ejpam-5687	361	41	,	,	PUNCT
ejpam-5687	361	42	or	or	CCONJ
ejpam-5687	361	43	public	public	ADJ
ejpam-5687	361	44	health	health	NOUN
ejpam-5687	361	45	policies	policy	NOUN
ejpam-5687	361	46	to	to	PART
ejpam-5687	361	47	mitigate	mitigate	VERB
ejpam-5687	361	48	the	the	DET
ejpam-5687	361	49	impact	impact	NOUN
ejpam-5687	361	50	of	of	ADP
ejpam-5687	361	51	the	the	DET
ejpam-5687	361	52	disease	disease	NOUN
ejpam-5687	361	53	.	.	PUNCT
ejpam-5687	362	1	numerical	numerical	ADJ
ejpam-5687	362	2	simulations	simulation	NOUN
ejpam-5687	362	3	of	of	ADP
ejpam-5687	362	4	epidemic	epidemic	NOUN
ejpam-5687	362	5	models	model	NOUN
ejpam-5687	362	6	help	help	VERB
ejpam-5687	362	7	visualize	visualize	VERB
ejpam-5687	362	8	and	and	CCONJ
ejpam-5687	362	9	evaluate	evaluate	VERB
ejpam-5687	362	10	how	how	SCONJ
ejpam-5687	362	11	changes	change	NOUN
ejpam-5687	362	12	in	in	ADP
ejpam-5687	362	13	parameters	parameter	NOUN
ejpam-5687	362	14	,	,	PUNCT
ejpam-5687	362	15	such	such	ADJ
ejpam-5687	362	16	as	as	ADP
ejpam-5687	362	17	transmission	transmission	NOUN
ejpam-5687	362	18	rates	rate	NOUN
ejpam-5687	362	19	or	or	CCONJ
ejpam-5687	362	20	intervention	intervention	NOUN
ejpam-5687	362	21	strategies	strategy	NOUN
ejpam-5687	362	22	,	,	PUNCT
ejpam-5687	362	23	affect	affect	VERB
ejpam-5687	362	24	the	the	DET
ejpam-5687	362	25	course	course	NOUN
ejpam-5687	362	26	of	of	ADP
ejpam-5687	362	27	the	the	DET
ejpam-5687	362	28	outbreak	outbreak	NOUN
ejpam-5687	362	29	.	.	PUNCT
ejpam-5687	363	1	n.	n.	PROPN
ejpam-5687	363	2	ullah	ullah	PROPN
ejpam-5687	363	3	et	et	PROPN
ejpam-5687	363	4	al	al	PROPN
ejpam-5687	363	5	.	.	PUNCT
ejpam-5687	363	6	/	/	SYM
ejpam-5687	363	7	eur	eur	PROPN
ejpam-5687	363	8	.	.	PUNCT
ejpam-5687	364	1	j.	j.	PROPN
ejpam-5687	364	2	pure	pure	PROPN
ejpam-5687	364	3	appl	appl	PROPN
ejpam-5687	364	4	.	.	PROPN
ejpam-5687	364	5	math	math	PROPN
ejpam-5687	364	6	,	,	PUNCT
ejpam-5687	364	7	18	18	NUM
ejpam-5687	364	8	(	(	PUNCT
ejpam-5687	364	9	2	2	NUM
ejpam-5687	364	10	)	)	PUNCT
ejpam-5687	364	11	(	(	PUNCT
ejpam-5687	364	12	2025	2025	NUM
ejpam-5687	364	13	)	)	PUNCT
ejpam-5687	364	14	,	,	PUNCT
ejpam-5687	364	15	5687	5687	NUM
ejpam-5687	364	16	22	22	NUM
ejpam-5687	364	17	of	of	ADP
ejpam-5687	364	18	25	25	NUM
ejpam-5687	364	19	for	for	ADP
ejpam-5687	364	20	instance	instance	NOUN
ejpam-5687	365	1	,	,	PUNCT
ejpam-5687	365	2	simulations	simulation	NOUN
ejpam-5687	365	3	can	can	AUX
ejpam-5687	365	4	reveal	reveal	VERB
ejpam-5687	365	5	the	the	DET
ejpam-5687	365	6	timing	timing	NOUN
ejpam-5687	365	7	and	and	CCONJ
ejpam-5687	365	8	magnitude	magnitude	NOUN
ejpam-5687	365	9	of	of	ADP
ejpam-5687	365	10	infection	infection	NOUN
ejpam-5687	365	11	peaks	peak	NOUN
ejpam-5687	365	12	,	,	PUNCT
ejpam-5687	365	13	helping	help	VERB
ejpam-5687	365	14	allocate	allocate	VERB
ejpam-5687	365	15	health	health	NOUN
ejpam-5687	365	16	-	-	PUNCT
ejpam-5687	365	17	care	care	NOUN
ejpam-5687	365	18	resources	resource	NOUN
ejpam-5687	365	19	effectively	effectively	ADV
ejpam-5687	365	20	.	.	PUNCT
ejpam-5687	366	1	they	they	PRON
ejpam-5687	366	2	also	also	ADV
ejpam-5687	366	3	allow	allow	VERB
ejpam-5687	366	4	researchers	researcher	NOUN
ejpam-5687	366	5	to	to	PART
ejpam-5687	366	6	assess	assess	VERB
ejpam-5687	366	7	the	the	DET
ejpam-5687	366	8	longterm	longterm	ADJ
ejpam-5687	366	9	outcomes	outcome	NOUN
ejpam-5687	366	10	of	of	ADP
ejpam-5687	366	11	an	an	DET
ejpam-5687	366	12	epidemic	epidemic	NOUN
ejpam-5687	366	13	,	,	PUNCT
ejpam-5687	366	14	such	such	ADJ
ejpam-5687	366	15	as	as	ADP
ejpam-5687	366	16	whether	whether	SCONJ
ejpam-5687	366	17	the	the	DET
ejpam-5687	366	18	disease	disease	NOUN
ejpam-5687	366	19	will	will	AUX
ejpam-5687	366	20	become	become	VERB
ejpam-5687	366	21	endemic	endemic	ADJ
ejpam-5687	366	22	or	or	CCONJ
ejpam-5687	366	23	be	be	AUX
ejpam-5687	366	24	eradicated	eradicate	VERB
ejpam-5687	366	25	.	.	PUNCT
ejpam-5687	367	1	ultimately	ultimately	ADV
ejpam-5687	367	2	,	,	PUNCT
ejpam-5687	367	3	studying	study	VERB
ejpam-5687	367	4	the	the	DET
ejpam-5687	367	5	dynamical	dynamical	ADJ
ejpam-5687	367	6	behavior	behavior	NOUN
ejpam-5687	367	7	of	of	ADP
ejpam-5687	367	8	epidemic	epidemic	NOUN
ejpam-5687	367	9	models	model	NOUN
ejpam-5687	367	10	empowers	empower	VERB
ejpam-5687	367	11	decision	decision	NOUN
ejpam-5687	367	12	-	-	PUNCT
ejpam-5687	367	13	makers	maker	NOUN
ejpam-5687	367	14	to	to	PART
ejpam-5687	367	15	implement	implement	VERB
ejpam-5687	367	16	timely	timely	ADJ
ejpam-5687	367	17	and	and	CCONJ
ejpam-5687	367	18	effective	effective	ADJ
ejpam-5687	367	19	control	control	NOUN
ejpam-5687	367	20	measures	measure	NOUN
ejpam-5687	367	21	,	,	PUNCT
ejpam-5687	367	22	reducing	reduce	VERB
ejpam-5687	367	23	morbidity	morbidity	NOUN
ejpam-5687	367	24	and	and	CCONJ
ejpam-5687	367	25	mortality	mortality	NOUN
ejpam-5687	367	26	while	while	SCONJ
ejpam-5687	367	27	minimizing	minimize	VERB
ejpam-5687	367	28	economic	economic	ADJ
ejpam-5687	367	29	and	and	CCONJ
ejpam-5687	367	30	social	social	ADJ
ejpam-5687	367	31	disruptions	disruption	NOUN
ejpam-5687	367	32	.	.	PUNCT
ejpam-5687	368	1	here	here	ADV
ejpam-5687	368	2	,	,	PUNCT
ejpam-5687	368	3	we	we	PRON
ejpam-5687	368	4	perform	perform	VERB
ejpam-5687	368	5	some	some	DET
ejpam-5687	368	6	simulation	simulation	NOUN
ejpam-5687	368	7	to	to	PART
ejpam-5687	368	8	show	show	VERB
ejpam-5687	368	9	the	the	DET
ejpam-5687	368	10	impact	impact	NOUN
ejpam-5687	368	11	of	of	ADP
ejpam-5687	368	12	fractional	fractional	ADJ
ejpam-5687	368	13	parameter	parameter	NOUN
ejpam-5687	368	14	on	on	ADP
ejpam-5687	368	15	the	the	DET
ejpam-5687	368	16	dynamics	dynamic	NOUN
ejpam-5687	368	17	of	of	ADP
ejpam-5687	368	18	the	the	DET
ejpam-5687	368	19	infection	infection	NOUN
ejpam-5687	368	20	we	we	PRON
ejpam-5687	368	21	numerically	numerically	ADV
ejpam-5687	368	22	solved	solve	VERB
ejpam-5687	368	23	the	the	DET
ejpam-5687	368	24	proposed	propose	VERB
ejpam-5687	368	25	model	model	NOUN
ejpam-5687	368	26	(	(	PUNCT
ejpam-5687	368	27	4	4	NUM
ejpam-5687	368	28	)	)	PUNCT
ejpam-5687	368	29	and	and	CCONJ
ejpam-5687	368	30	computed	compute	VERB
ejpam-5687	368	31	the	the	DET
ejpam-5687	368	32	corresponding	correspond	VERB
ejpam-5687	368	33	solutions	solution	NOUN
ejpam-5687	368	34	for	for	ADP
ejpam-5687	368	35	both	both	CCONJ
ejpam-5687	368	36	integer	integer	NOUN
ejpam-5687	368	37	and	and	CCONJ
ejpam-5687	368	38	non	non	ADJ
ejpam-5687	368	39	-	-	ADJ
ejpam-5687	368	40	integer	integer	ADJ
ejpam-5687	368	41	derivatives	derivative	NOUN
ejpam-5687	368	42	,	,	PUNCT
ejpam-5687	368	43	specifically	specifically	ADV
ejpam-5687	368	44	for	for	ADP
ejpam-5687	368	45	fractional	fractional	ADJ
ejpam-5687	368	46	orders	order	NOUN
ejpam-5687	368	47	l	l	NOUN
ejpam-5687	368	48	=	=	SYM
ejpam-5687	368	49	0.55	0.55	NUM
ejpam-5687	368	50	,	,	PUNCT
ejpam-5687	368	51	0.6	0.6	NUM
ejpam-5687	368	52	,	,	PUNCT
ejpam-5687	368	53	0.65	0.65	NUM
ejpam-5687	368	54	,	,	PUNCT
ejpam-5687	368	55	0.7	0.7	NUM
ejpam-5687	368	56	,	,	PUNCT
ejpam-5687	368	57	0.75	0.75	NUM
ejpam-5687	368	58	,	,	PUNCT
ejpam-5687	368	59	0.80	0.80	NUM
ejpam-5687	368	60	,	,	PUNCT
ejpam-5687	368	61	0.85	0.85	NUM
ejpam-5687	368	62	,	,	PUNCT
ejpam-5687	368	63	0.9	0.9	NUM
ejpam-5687	368	64	,	,	PUNCT
ejpam-5687	368	65	0.92	0.92	NUM
ejpam-5687	368	66	,	,	PUNCT
ejpam-5687	368	67	0.95	0.95	NUM
ejpam-5687	368	68	,	,	PUNCT
ejpam-5687	368	69	0.98	0.98	NUM
ejpam-5687	368	70	,	,	PUNCT
ejpam-5687	368	71	1	1	NUM
ejpam-5687	368	72	.	.	PUNCT
ejpam-5687	369	1	the	the	DET
ejpam-5687	369	2	results	result	NOUN
ejpam-5687	369	3	,	,	PUNCT
ejpam-5687	369	4	as	as	SCONJ
ejpam-5687	369	5	illustrated	illustrate	VERB
ejpam-5687	369	6	in	in	ADP
ejpam-5687	369	7	figures	figure	NOUN
ejpam-5687	369	8	2	2	NUM
ejpam-5687	369	9	,	,	PUNCT
ejpam-5687	369	10	3	3	NUM
ejpam-5687	369	11	,	,	PUNCT
ejpam-5687	369	12	and	and	CCONJ
ejpam-5687	369	13	4	4	NUM
ejpam-5687	369	14	,	,	PUNCT
ejpam-5687	369	15	provide	provide	VERB
ejpam-5687	369	16	insights	insight	NOUN
ejpam-5687	369	17	into	into	ADP
ejpam-5687	369	18	the	the	DET
ejpam-5687	369	19	dynamic	dynamic	ADJ
ejpam-5687	369	20	behavior	behavior	NOUN
ejpam-5687	369	21	of	of	ADP
ejpam-5687	369	22	the	the	DET
ejpam-5687	369	23	cf	cf	NOUN
ejpam-5687	369	24	fractional	fractional	ADJ
ejpam-5687	369	25	-	-	PUNCT
ejpam-5687	369	26	order	order	NOUN
ejpam-5687	369	27	model	model	NOUN
ejpam-5687	369	28	.	.	PUNCT
ejpam-5687	370	1	by	by	ADP
ejpam-5687	370	2	systematically	systematically	ADV
ejpam-5687	370	3	varying	vary	VERB
ejpam-5687	370	4	the	the	DET
ejpam-5687	370	5	order	order	NOUN
ejpam-5687	370	6	fractional	fractional	ADJ
ejpam-5687	370	7	order	order	NOUN
ejpam-5687	370	8	l	l	NOUN
ejpam-5687	370	9	,	,	PUNCT
ejpam-5687	370	10	we	we	PRON
ejpam-5687	370	11	explored	explore	VERB
ejpam-5687	370	12	the	the	DET
ejpam-5687	370	13	model	model	NOUN
ejpam-5687	370	14	’s	’s	PART
ejpam-5687	370	15	intricate	intricate	ADJ
ejpam-5687	370	16	dynamics	dynamic	NOUN
ejpam-5687	370	17	,	,	PUNCT
ejpam-5687	370	18	highlighting	highlight	VERB
ejpam-5687	370	19	deviations	deviation	NOUN
ejpam-5687	370	20	from	from	ADP
ejpam-5687	370	21	the	the	DET
ejpam-5687	370	22	classical	classical	ADJ
ejpam-5687	370	23	integer	integer	NOUN
ejpam-5687	370	24	-	-	PUNCT
ejpam-5687	370	25	order	order	NOUN
ejpam-5687	370	26	model	model	NOUN
ejpam-5687	370	27	.	.	PUNCT
ejpam-5687	371	1	adjusting	adjust	VERB
ejpam-5687	371	2	the	the	DET
ejpam-5687	371	3	fractional	fractional	ADJ
ejpam-5687	371	4	order	order	NOUN
ejpam-5687	371	5	l	l	NOUN
ejpam-5687	371	6	revealed	reveal	VERB
ejpam-5687	371	7	significant	significant	ADJ
ejpam-5687	371	8	changes	change	NOUN
ejpam-5687	371	9	in	in	ADP
ejpam-5687	371	10	the	the	DET
ejpam-5687	371	11	population	population	NOUN
ejpam-5687	371	12	dynamics	dynamic	NOUN
ejpam-5687	371	13	across	across	ADP
ejpam-5687	371	14	different	different	ADJ
ejpam-5687	371	15	compartments	compartment	NOUN
ejpam-5687	371	16	,	,	PUNCT
ejpam-5687	371	17	as	as	SCONJ
ejpam-5687	371	18	visualized	visualize	VERB
ejpam-5687	371	19	in	in	ADP
ejpam-5687	371	20	figures	figure	NOUN
ejpam-5687	371	21	2	2	NUM
ejpam-5687	371	22	,	,	PUNCT
ejpam-5687	371	23	3	3	NUM
ejpam-5687	371	24	,	,	PUNCT
ejpam-5687	371	25	and	and	CCONJ
ejpam-5687	371	26	4	4	X
ejpam-5687	371	27	.	.	X
ejpam-5687	372	1	these	these	DET
ejpam-5687	372	2	adjustments	adjustment	NOUN
ejpam-5687	372	3	demonstrated	demonstrate	VERB
ejpam-5687	372	4	an	an	DET
ejpam-5687	372	5	increase	increase	NOUN
ejpam-5687	372	6	or	or	CCONJ
ejpam-5687	372	7	decrease	decrease	NOUN
ejpam-5687	372	8	in	in	ADP
ejpam-5687	372	9	the	the	DET
ejpam-5687	372	10	number	number	NOUN
ejpam-5687	372	11	of	of	ADP
ejpam-5687	372	12	individuals	individual	NOUN
ejpam-5687	372	13	in	in	ADP
ejpam-5687	372	14	each	each	DET
ejpam-5687	372	15	compartment	compartment	NOUN
ejpam-5687	372	16	,	,	PUNCT
ejpam-5687	372	17	underscoring	underscore	VERB
ejpam-5687	372	18	the	the	DET
ejpam-5687	372	19	impact	impact	NOUN
ejpam-5687	372	20	of	of	ADP
ejpam-5687	372	21	fractional	fractional	ADJ
ejpam-5687	372	22	derivatives	derivative	NOUN
ejpam-5687	372	23	on	on	ADP
ejpam-5687	372	24	the	the	DET
ejpam-5687	372	25	system	system	NOUN
ejpam-5687	372	26	’s	’s	PART
ejpam-5687	372	27	behavior	behavior	NOUN
ejpam-5687	372	28	.	.	PUNCT
ejpam-5687	373	1	notably	notably	ADV
ejpam-5687	373	2	,	,	PUNCT
ejpam-5687	373	3	this	this	DET
ejpam-5687	373	4	approach	approach	NOUN
ejpam-5687	373	5	differs	differ	VERB
ejpam-5687	373	6	from	from	ADP
ejpam-5687	373	7	the	the	DET
ejpam-5687	373	8	classical	classical	ADJ
ejpam-5687	373	9	integer	integer	NOUN
ejpam-5687	373	10	-	-	PUNCT
ejpam-5687	373	11	order	order	NOUN
ejpam-5687	373	12	model	model	NOUN
ejpam-5687	373	13	and	and	CCONJ
ejpam-5687	373	14	provides	provide	VERB
ejpam-5687	373	15	more	more	ADV
ejpam-5687	373	16	nuanced	nuanced	ADJ
ejpam-5687	373	17	control	control	NOUN
ejpam-5687	373	18	measures	measure	NOUN
ejpam-5687	373	19	.	.	PUNCT
ejpam-5687	374	1	the	the	DET
ejpam-5687	374	2	observed	observed	ADJ
ejpam-5687	374	3	phenomenon	phenomenon	NOUN
ejpam-5687	374	4	offers	offer	VERB
ejpam-5687	374	5	practical	practical	ADJ
ejpam-5687	374	6	implications	implication	NOUN
ejpam-5687	374	7	for	for	ADP
ejpam-5687	374	8	government	government	NOUN
ejpam-5687	374	9	agencies	agency	NOUN
ejpam-5687	374	10	and	and	CCONJ
ejpam-5687	374	11	medical	medical	ADJ
ejpam-5687	374	12	personnel	personnel	NOUN
ejpam-5687	374	13	to	to	PART
ejpam-5687	374	14	better	well	ADV
ejpam-5687	374	15	manage	manage	VERB
ejpam-5687	374	16	and	and	CCONJ
ejpam-5687	374	17	control	control	VERB
ejpam-5687	374	18	the	the	DET
ejpam-5687	374	19	spread	spread	NOUN
ejpam-5687	374	20	of	of	ADP
ejpam-5687	374	21	infections	infection	NOUN
ejpam-5687	374	22	.	.	PUNCT
ejpam-5687	375	1	furthermore	furthermore	ADV
ejpam-5687	375	2	,	,	PUNCT
ejpam-5687	375	3	our	our	PRON
ejpam-5687	375	4	results	result	NOUN
ejpam-5687	375	5	indicate	indicate	VERB
ejpam-5687	375	6	that	that	SCONJ
ejpam-5687	375	7	as	as	ADP
ejpam-5687	375	8	the	the	DET
ejpam-5687	375	9	order	order	NOUN
ejpam-5687	375	10	l	l	NOUN
ejpam-5687	375	11	decreases	decrease	NOUN
ejpam-5687	375	12	(	(	PUNCT
ejpam-5687	375	13	0	0	NUM
ejpam-5687	375	14	<	<	X
ejpam-5687	375	15	l	l	X
ejpam-5687	375	16	<	<	X
ejpam-5687	375	17	1	1	NUM
ejpam-5687	375	18	)	)	PUNCT
ejpam-5687	375	19	,	,	PUNCT
ejpam-5687	375	20	the	the	DET
ejpam-5687	375	21	convergence	convergence	NOUN
ejpam-5687	375	22	of	of	ADP
ejpam-5687	375	23	the	the	DET
ejpam-5687	375	24	system	system	NOUN
ejpam-5687	375	25	slows	slow	VERB
ejpam-5687	375	26	,	,	PUNCT
ejpam-5687	375	27	particularly	particularly	ADV
ejpam-5687	375	28	over	over	ADP
ejpam-5687	375	29	shorter	short	ADJ
ejpam-5687	375	30	time	time	NOUN
ejpam-5687	375	31	scales	scale	NOUN
ejpam-5687	375	32	,	,	PUNCT
ejpam-5687	375	33	emphasizing	emphasize	VERB
ejpam-5687	375	34	the	the	DET
ejpam-5687	375	35	sensitivity	sensitivity	NOUN
ejpam-5687	375	36	of	of	ADP
ejpam-5687	375	37	the	the	DET
ejpam-5687	375	38	model	model	NOUN
ejpam-5687	375	39	to	to	ADP
ejpam-5687	375	40	fractional	fractional	ADJ
ejpam-5687	375	41	dynamics	dynamic	NOUN
ejpam-5687	375	42	.	.	PUNCT
ejpam-5687	376	1	6	6	X
ejpam-5687	376	2	.	.	X
ejpam-5687	376	3	conclusions	conclusion	NOUN
ejpam-5687	376	4	in	in	ADP
ejpam-5687	376	5	this	this	DET
ejpam-5687	376	6	study	study	NOUN
ejpam-5687	376	7	,	,	PUNCT
ejpam-5687	376	8	a	a	DET
ejpam-5687	376	9	mathematical	mathematical	ADJ
ejpam-5687	376	10	model	model	NOUN
ejpam-5687	376	11	for	for	ADP
ejpam-5687	376	12	vector	vector	NOUN
ejpam-5687	376	13	-	-	PUNCT
ejpam-5687	376	14	borne	bear	VERB
ejpam-5687	376	15	infections	infection	NOUN
ejpam-5687	376	16	was	be	AUX
ejpam-5687	376	17	developed	develop	VERB
ejpam-5687	376	18	within	within	ADP
ejpam-5687	376	19	a	a	DET
ejpam-5687	376	20	fractional	fractional	ADJ
ejpam-5687	376	21	-	-	PUNCT
ejpam-5687	376	22	order	order	NOUN
ejpam-5687	376	23	framework	framework	NOUN
ejpam-5687	376	24	,	,	PUNCT
ejpam-5687	376	25	utilizing	utilize	VERB
ejpam-5687	376	26	the	the	DET
ejpam-5687	376	27	caputo	caputo	PROPN
ejpam-5687	376	28	-	-	PUNCT
ejpam-5687	376	29	fabrizio	fabrizio	PROPN
ejpam-5687	376	30	fractional	fractional	ADJ
ejpam-5687	376	31	derivative	derivative	NOUN
ejpam-5687	376	32	to	to	PART
ejpam-5687	376	33	enhance	enhance	VERB
ejpam-5687	376	34	the	the	DET
ejpam-5687	376	35	analysis	analysis	NOUN
ejpam-5687	376	36	.	.	PUNCT
ejpam-5687	377	1	the	the	DET
ejpam-5687	377	2	steady	steady	ADJ
ejpam-5687	377	3	states	state	NOUN
ejpam-5687	377	4	of	of	ADP
ejpam-5687	377	5	the	the	DET
ejpam-5687	377	6	system	system	NOUN
ejpam-5687	377	7	were	be	AUX
ejpam-5687	377	8	examined	examine	VERB
ejpam-5687	377	9	,	,	PUNCT
ejpam-5687	377	10	and	and	CCONJ
ejpam-5687	377	11	the	the	DET
ejpam-5687	377	12	basic	basic	ADJ
ejpam-5687	377	13	reproduction	reproduction	NOUN
ejpam-5687	377	14	number	number	NOUN
ejpam-5687	377	15	r0	r0	NOUN
ejpam-5687	377	16	was	be	AUX
ejpam-5687	377	17	derived	derive	VERB
ejpam-5687	377	18	using	use	VERB
ejpam-5687	377	19	the	the	DET
ejpam-5687	377	20	next	next	ADJ
ejpam-5687	377	21	-	-	PUNCT
ejpam-5687	377	22	generation	generation	NOUN
ejpam-5687	377	23	matrix	matrix	NOUN
ejpam-5687	377	24	method	method	NOUN
ejpam-5687	377	25	.	.	PUNCT
ejpam-5687	378	1	the	the	DET
ejpam-5687	378	2	existence	existence	NOUN
ejpam-5687	378	3	and	and	CCONJ
ejpam-5687	378	4	uniqueness	uniqueness	NOUN
ejpam-5687	378	5	of	of	ADP
ejpam-5687	378	6	solutions	solution	NOUN
ejpam-5687	378	7	were	be	AUX
ejpam-5687	378	8	established	establish	VERB
ejpam-5687	378	9	through	through	ADP
ejpam-5687	378	10	the	the	DET
ejpam-5687	378	11	application	application	NOUN
ejpam-5687	378	12	of	of	ADP
ejpam-5687	378	13	the	the	DET
ejpam-5687	378	14	banach	banach	ADV
ejpam-5687	378	15	fixed	fix	VERB
ejpam-5687	378	16	-	-	PUNCT
ejpam-5687	378	17	point	point	NOUN
ejpam-5687	378	18	theorem	theorem	VERB
ejpam-5687	378	19	.	.	PUNCT
ejpam-5687	379	1	a	a	DET
ejpam-5687	379	2	detailed	detailed	ADJ
ejpam-5687	379	3	sensitivity	sensitivity	NOUN
ejpam-5687	379	4	analysis	analysis	NOUN
ejpam-5687	379	5	of	of	ADP
ejpam-5687	379	6	r0	r0	NOUN
ejpam-5687	379	7	identified	identify	VERB
ejpam-5687	379	8	the	the	DET
ejpam-5687	379	9	most	most	ADV
ejpam-5687	379	10	critical	critical	ADJ
ejpam-5687	379	11	parameters	parameter	NOUN
ejpam-5687	379	12	influencing	influence	VERB
ejpam-5687	379	13	the	the	DET
ejpam-5687	379	14	disease	disease	NOUN
ejpam-5687	379	15	dynamics	dynamic	NOUN
ejpam-5687	379	16	.	.	PUNCT
ejpam-5687	380	1	numerical	numerical	ADJ
ejpam-5687	380	2	simulations	simulation	NOUN
ejpam-5687	380	3	were	be	AUX
ejpam-5687	380	4	conducted	conduct	VERB
ejpam-5687	380	5	to	to	PART
ejpam-5687	380	6	validate	validate	VERB
ejpam-5687	380	7	the	the	DET
ejpam-5687	380	8	theoretical	theoretical	ADJ
ejpam-5687	380	9	findings	finding	NOUN
ejpam-5687	380	10	and	and	CCONJ
ejpam-5687	380	11	to	to	PART
ejpam-5687	380	12	highlight	highlight	VERB
ejpam-5687	380	13	key	key	ADJ
ejpam-5687	380	14	factors	factor	NOUN
ejpam-5687	380	15	impacting	impact	VERB
ejpam-5687	380	16	the	the	DET
ejpam-5687	380	17	control	control	NOUN
ejpam-5687	380	18	and	and	CCONJ
ejpam-5687	380	19	prevention	prevention	NOUN
ejpam-5687	380	20	of	of	ADP
ejpam-5687	380	21	the	the	DET
ejpam-5687	380	22	infection	infection	NOUN
ejpam-5687	380	23	.	.	PUNCT
ejpam-5687	381	1	this	this	DET
ejpam-5687	381	2	work	work	NOUN
ejpam-5687	381	3	provided	provide	VERB
ejpam-5687	381	4	valuable	valuable	ADJ
ejpam-5687	381	5	insights	insight	NOUN
ejpam-5687	381	6	into	into	ADP
ejpam-5687	381	7	the	the	DET
ejpam-5687	381	8	dynamics	dynamic	NOUN
ejpam-5687	381	9	of	of	ADP
ejpam-5687	381	10	vector	vector	NOUN
ejpam-5687	381	11	-	-	PUNCT
ejpam-5687	381	12	borne	bear	VERB
ejpam-5687	381	13	infections	infection	NOUN
ejpam-5687	381	14	and	and	CCONJ
ejpam-5687	381	15	offered	offer	VERB
ejpam-5687	381	16	a	a	DET
ejpam-5687	381	17	robust	robust	ADJ
ejpam-5687	381	18	mathematical	mathematical	ADJ
ejpam-5687	381	19	approach	approach	NOUN
ejpam-5687	381	20	for	for	ADP
ejpam-5687	381	21	optimizing	optimize	VERB
ejpam-5687	381	22	intervention	intervention	NOUN
ejpam-5687	381	23	strategies	strategy	NOUN
ejpam-5687	381	24	.	.	PUNCT
ejpam-5687	382	1	acknowledgements	acknowledgement	NOUN
ejpam-5687	382	2	project	project	NOUN
ejpam-5687	382	3	financed	finance	VERB
ejpam-5687	382	4	by	by	ADP
ejpam-5687	382	5	lucian	lucian	PROPN
ejpam-5687	382	6	blaga	blaga	PROPN
ejpam-5687	382	7	university	university	PROPN
ejpam-5687	382	8	of	of	ADP
ejpam-5687	382	9	sibiu	sibiu	PROPN
ejpam-5687	382	10	through	through	ADP
ejpam-5687	382	11	the	the	DET
ejpam-5687	382	12	research	research	NOUN
ejpam-5687	382	13	grant	grant	NOUN
ejpam-5687	382	14	lbusirg-2024	lbusirg-2024	NOUN
ejpam-5687	382	15	.	.	PUNCT
ejpam-5687	383	1	n.	n.	PROPN
ejpam-5687	383	2	ullah	ullah	PROPN
ejpam-5687	383	3	et	et	PROPN
ejpam-5687	383	4	al	al	PROPN
ejpam-5687	383	5	.	.	PUNCT
ejpam-5687	383	6	/	/	SYM
ejpam-5687	383	7	eur	eur	PROPN
ejpam-5687	383	8	.	.	PUNCT
ejpam-5687	384	1	j.	j.	PROPN
ejpam-5687	384	2	pure	pure	PROPN
ejpam-5687	384	3	appl	appl	PROPN
ejpam-5687	384	4	.	.	PROPN
ejpam-5687	384	5	math	math	PROPN
ejpam-5687	384	6	,	,	PUNCT
ejpam-5687	384	7	18	18	NUM
ejpam-5687	384	8	(	(	PUNCT
ejpam-5687	384	9	2	2	NUM
ejpam-5687	384	10	)	)	PUNCT
ejpam-5687	384	11	(	(	PUNCT
ejpam-5687	384	12	2025	2025	NUM
ejpam-5687	384	13	)	)	PUNCT
ejpam-5687	384	14	,	,	PUNCT
ejpam-5687	384	15	5687	5687	NUM
ejpam-5687	384	16	23	23	NUM
ejpam-5687	384	17	of	of	ADP
ejpam-5687	384	18	25	25	NUM
ejpam-5687	384	19	references	reference	NOUN
ejpam-5687	384	20	[	[	X
ejpam-5687	384	21	1	1	NUM
ejpam-5687	384	22	]	]	X
ejpam-5687	384	23	olayinka	olayinka	PROPN
ejpam-5687	384	24	m	m	PROPN
ejpam-5687	384	25	olajiga	olajiga	PROPN
ejpam-5687	384	26	,	,	PUNCT
ejpam-5687	384	27	samuel	samuel	PROPN
ejpam-5687	384	28	b	b	PROPN
ejpam-5687	384	29	jameson	jameson	PROPN
ejpam-5687	384	30	,	,	PUNCT
ejpam-5687	384	31	brendan	brendan	PROPN
ejpam-5687	384	32	h	h	PROPN
ejpam-5687	384	33	carter	carter	PROPN
ejpam-5687	384	34	,	,	PUNCT
ejpam-5687	384	35	dawn	dawn	PROPN
ejpam-5687	384	36	m	m	PROPN
ejpam-5687	384	37	wesson	wesson	PROPN
ejpam-5687	384	38	,	,	PUNCT
ejpam-5687	384	39	dana	dana	PROPN
ejpam-5687	384	40	mitzel	mitzel	PROPN
ejpam-5687	384	41	,	,	PUNCT
ejpam-5687	384	42	and	and	CCONJ
ejpam-5687	384	43	berlin	berlin	PROPN
ejpam-5687	384	44	londono	londono	PROPN
ejpam-5687	384	45	-	-	PUNCT
ejpam-5687	384	46	renteria	renteria	PROPN
ejpam-5687	384	47	.	.	PUNCT
ejpam-5687	385	1	artificial	artificial	ADJ
ejpam-5687	385	2	feeding	feeding	NOUN
ejpam-5687	385	3	systems	system	NOUN
ejpam-5687	385	4	for	for	ADP
ejpam-5687	385	5	vector	vector	NOUN
ejpam-5687	385	6	-	-	PUNCT
ejpam-5687	385	7	borne	borne	ADJ
ejpam-5687	385	8	disease	disease	NOUN
ejpam-5687	385	9	studies	study	NOUN
ejpam-5687	385	10	.	.	PUNCT
ejpam-5687	386	1	biology	biology	NOUN
ejpam-5687	386	2	,	,	PUNCT
ejpam-5687	386	3	13(3):188	13(3):188	NUM
ejpam-5687	386	4	,	,	PUNCT
ejpam-5687	386	5	2024	2024	NUM
ejpam-5687	386	6	.	.	PUNCT
ejpam-5687	387	1	[	[	X
ejpam-5687	387	2	2	2	X
ejpam-5687	387	3	]	]	PUNCT
ejpam-5687	387	4	baldwyn	baldwyn	X
ejpam-5687	387	5	torto	torto	PROPN
ejpam-5687	387	6	and	and	CCONJ
ejpam-5687	387	7	david	david	PROPN
ejpam-5687	387	8	p	p	PROPN
ejpam-5687	387	9	tchouassi	tchouassi	PROPN
ejpam-5687	387	10	.	.	PUNCT
ejpam-5687	388	1	grand	grand	ADJ
ejpam-5687	388	2	challenges	challenge	NOUN
ejpam-5687	388	3	in	in	ADP
ejpam-5687	388	4	vector	vector	NOUN
ejpam-5687	388	5	-	-	PUNCT
ejpam-5687	388	6	borne	bear	VERB
ejpam-5687	388	7	disease	disease	NOUN
ejpam-5687	388	8	control	control	NOUN
ejpam-5687	388	9	targeting	target	VERB
ejpam-5687	388	10	vectors	vector	NOUN
ejpam-5687	388	11	,	,	PUNCT
ejpam-5687	388	12	2021	2021	NUM
ejpam-5687	388	13	.	.	PUNCT
ejpam-5687	389	1	[	[	X
ejpam-5687	389	2	3	3	X
ejpam-5687	389	3	]	]	X
ejpam-5687	389	4	daniel	daniel	PROPN
ejpam-5687	389	5	msellemu	msellemu	PROPN
ejpam-5687	389	6	,	,	PUNCT
ejpam-5687	389	7	marcel	marcel	PROPN
ejpam-5687	389	8	tanner	tanner	PROPN
ejpam-5687	389	9	,	,	PUNCT
ejpam-5687	389	10	rajpal	rajpal	PROPN
ejpam-5687	389	11	yadav	yadav	PROPN
ejpam-5687	389	12	,	,	PUNCT
ejpam-5687	389	13	and	and	CCONJ
ejpam-5687	389	14	sarah	sarah	PROPN
ejpam-5687	389	15	j	j	PROPN
ejpam-5687	389	16	moore	moore	PROPN
ejpam-5687	389	17	.	.	PUNCT
ejpam-5687	390	1	occupational	occupational	ADJ
ejpam-5687	390	2	exposure	exposure	NOUN
ejpam-5687	390	3	to	to	ADP
ejpam-5687	390	4	malaria	malaria	NOUN
ejpam-5687	390	5	,	,	PUNCT
ejpam-5687	390	6	leishmaniasis	leishmaniasis	NOUN
ejpam-5687	390	7	and	and	CCONJ
ejpam-5687	390	8	arbovirus	arbovirus	NOUN
ejpam-5687	390	9	vectors	vector	NOUN
ejpam-5687	390	10	in	in	ADP
ejpam-5687	390	11	endemic	endemic	ADJ
ejpam-5687	390	12	regions	region	NOUN
ejpam-5687	390	13	:	:	PUNCT
ejpam-5687	390	14	a	a	DET
ejpam-5687	390	15	systematic	systematic	ADJ
ejpam-5687	390	16	review	review	NOUN
ejpam-5687	390	17	.	.	PUNCT
ejpam-5687	391	1	current	current	ADJ
ejpam-5687	391	2	research	research	NOUN
ejpam-5687	391	3	in	in	ADP
ejpam-5687	391	4	parasitology	parasitology	NOUN
ejpam-5687	391	5	&	&	CCONJ
ejpam-5687	391	6	vector	vector	NOUN
ejpam-5687	391	7	-	-	PUNCT
ejpam-5687	391	8	borne	bear	VERB
ejpam-5687	391	9	diseases	disease	NOUN
ejpam-5687	391	10	,	,	PUNCT
ejpam-5687	391	11	page	page	NOUN
ejpam-5687	391	12	100185	100185	NUM
ejpam-5687	391	13	,	,	PUNCT
ejpam-5687	391	14	2024	2024	NUM
ejpam-5687	391	15	.	.	PUNCT
ejpam-5687	392	1	[	[	X
ejpam-5687	392	2	4	4	X
ejpam-5687	392	3	]	]	PUNCT
ejpam-5687	392	4	tanvir	tanvir	PROPN
ejpam-5687	392	5	hasan	hasan	PROPN
ejpam-5687	392	6	,	,	PUNCT
ejpam-5687	392	7	sadia	sadia	PROPN
ejpam-5687	392	8	afrin	afrin	PROPN
ejpam-5687	392	9	,	,	PUNCT
ejpam-5687	392	10	afroza	afroza	PROPN
ejpam-5687	392	11	sultana	sultana	NOUN
ejpam-5687	392	12	,	,	PUNCT
ejpam-5687	392	13	and	and	CCONJ
ejpam-5687	392	14	ashekul	ashekul	PROPN
ejpam-5687	392	15	islam	islam	PROPN
ejpam-5687	392	16	.	.	PUNCT
ejpam-5687	393	1	asymmetrical	asymmetrical	ADJ
ejpam-5687	393	2	reproductive	reproductive	ADJ
ejpam-5687	393	3	interference	interference	NOUN
ejpam-5687	393	4	between	between	ADP
ejpam-5687	393	5	aedes	aedes	PROPN
ejpam-5687	393	6	aegypti	aegypti	PROPN
ejpam-5687	393	7	and	and	CCONJ
ejpam-5687	393	8	aedes	aedes	PROPN
ejpam-5687	393	9	albopictus	albopictus	PROPN
ejpam-5687	393	10	:	:	PUNCT
ejpam-5687	393	11	implications	implication	NOUN
ejpam-5687	393	12	for	for	ADP
ejpam-5687	393	13	coexistence	coexistence	NOUN
ejpam-5687	393	14	.	.	PUNCT
ejpam-5687	394	1	journal	journal	PROPN
ejpam-5687	394	2	of	of	ADP
ejpam-5687	394	3	vector	vector	NOUN
ejpam-5687	394	4	borne	borne	NOUN
ejpam-5687	394	5	diseases	disease	NOUN
ejpam-5687	394	6	,	,	PUNCT
ejpam-5687	394	7	61(4):547–554	61(4):547–554	PROPN
ejpam-5687	394	8	,	,	PUNCT
ejpam-5687	394	9	2024	2024	NUM
ejpam-5687	394	10	.	.	PUNCT
ejpam-5687	395	1	[	[	X
ejpam-5687	395	2	5	5	X
ejpam-5687	395	3	]	]	X
ejpam-5687	395	4	rashid	rashid	PROPN
ejpam-5687	395	5	jan	jan	PROPN
ejpam-5687	395	6	and	and	CCONJ
ejpam-5687	395	7	asif	asif	PROPN
ejpam-5687	395	8	jan	jan	PROPN
ejpam-5687	395	9	.	.	PROPN
ejpam-5687	395	10	msgdtm	msgdtm	PROPN
ejpam-5687	395	11	for	for	ADP
ejpam-5687	395	12	solution	solution	NOUN
ejpam-5687	395	13	of	of	ADP
ejpam-5687	395	14	fractional	fractional	ADJ
ejpam-5687	395	15	order	order	NOUN
ejpam-5687	395	16	dengue	dengue	NOUN
ejpam-5687	395	17	disease	disease	NOUN
ejpam-5687	395	18	model	model	NOUN
ejpam-5687	395	19	.	.	PUNCT
ejpam-5687	396	1	international	international	ADJ
ejpam-5687	396	2	journal	journal	PROPN
ejpam-5687	396	3	of	of	ADP
ejpam-5687	396	4	science	science	NOUN
ejpam-5687	396	5	and	and	CCONJ
ejpam-5687	396	6	research	research	NOUN
ejpam-5687	396	7	,	,	PUNCT
ejpam-5687	396	8	6(3):1140–1144	6(3):1140–1144	NUM
ejpam-5687	396	9	,	,	PUNCT
ejpam-5687	396	10	2017	2017	NUM
ejpam-5687	396	11	.	.	PUNCT
ejpam-5687	397	1	[	[	X
ejpam-5687	397	2	6	6	NUM
ejpam-5687	397	3	]	]	PUNCT
ejpam-5687	397	4	wejdan	wejdan	PROPN
ejpam-5687	397	5	deebani	deebani	PROPN
ejpam-5687	397	6	,	,	PUNCT
ejpam-5687	397	7	rashid	rashid	PROPN
ejpam-5687	397	8	jan	jan	PROPN
ejpam-5687	397	9	,	,	PUNCT
ejpam-5687	397	10	zahir	zahir	ADJ
ejpam-5687	397	11	shah	shah	NOUN
ejpam-5687	397	12	,	,	PUNCT
ejpam-5687	397	13	narcisa	narcisa	NOUN
ejpam-5687	397	14	vrinceanu	vrinceanu	NOUN
ejpam-5687	397	15	,	,	PUNCT
ejpam-5687	397	16	and	and	CCONJ
ejpam-5687	397	17	mihaela	mihaela	PROPN
ejpam-5687	397	18	racheriu	racheriu	NOUN
ejpam-5687	397	19	.	.	PUNCT
ejpam-5687	398	1	modeling	model	VERB
ejpam-5687	398	2	the	the	DET
ejpam-5687	398	3	transmission	transmission	NOUN
ejpam-5687	398	4	phenomena	phenomenon	NOUN
ejpam-5687	398	5	of	of	ADP
ejpam-5687	398	6	water	water	NOUN
ejpam-5687	398	7	-	-	PUNCT
ejpam-5687	398	8	borne	bear	VERB
ejpam-5687	398	9	disease	disease	NOUN
ejpam-5687	398	10	with	with	ADP
ejpam-5687	398	11	non	non	ADJ
ejpam-5687	398	12	-	-	ADJ
ejpam-5687	398	13	singular	singular	ADJ
ejpam-5687	398	14	and	and	CCONJ
ejpam-5687	398	15	non	non	ADJ
ejpam-5687	398	16	-	-	ADJ
ejpam-5687	398	17	local	local	ADJ
ejpam-5687	398	18	kernel	kernel	NOUN
ejpam-5687	398	19	.	.	PUNCT
ejpam-5687	399	1	computer	computer	NOUN
ejpam-5687	399	2	methods	method	NOUN
ejpam-5687	399	3	in	in	ADP
ejpam-5687	399	4	biomechanics	biomechanic	NOUN
ejpam-5687	399	5	and	and	CCONJ
ejpam-5687	399	6	biomedical	biomedical	ADJ
ejpam-5687	399	7	engineering	engineering	NOUN
ejpam-5687	399	8	,	,	PUNCT
ejpam-5687	399	9	26(11):1294–1307	26(11):1294–1307	NUM
ejpam-5687	399	10	,	,	PUNCT
ejpam-5687	399	11	2023	2023	NUM
ejpam-5687	399	12	.	.	PUNCT
ejpam-5687	400	1	[	[	X
ejpam-5687	400	2	7	7	X
ejpam-5687	400	3	]	]	X
ejpam-5687	400	4	ahmed	ahmed	PROPN
ejpam-5687	400	5	alshehri	alshehri	PROPN
ejpam-5687	400	6	,	,	PUNCT
ejpam-5687	400	7	zahir	zahir	ADJ
ejpam-5687	400	8	shah	shah	NOUN
ejpam-5687	400	9	,	,	PUNCT
ejpam-5687	400	10	and	and	CCONJ
ejpam-5687	400	11	rashid	rashid	PROPN
ejpam-5687	400	12	jan	jan	PROPN
ejpam-5687	400	13	.	.	PROPN
ejpam-5687	400	14	mathematical	mathematical	ADJ
ejpam-5687	400	15	study	study	NOUN
ejpam-5687	400	16	of	of	ADP
ejpam-5687	400	17	the	the	DET
ejpam-5687	400	18	dynamics	dynamic	NOUN
ejpam-5687	400	19	of	of	ADP
ejpam-5687	400	20	lymphatic	lymphatic	ADJ
ejpam-5687	400	21	filariasis	filariasis	NOUN
ejpam-5687	400	22	infection	infection	NOUN
ejpam-5687	400	23	via	via	ADP
ejpam-5687	400	24	fractional	fractional	ADJ
ejpam-5687	400	25	-	-	PUNCT
ejpam-5687	400	26	calculus	calculus	NOUN
ejpam-5687	400	27	.	.	PUNCT
ejpam-5687	401	1	the	the	DET
ejpam-5687	401	2	european	european	PROPN
ejpam-5687	401	3	physical	physical	PROPN
ejpam-5687	401	4	journal	journal	PROPN
ejpam-5687	401	5	plus	plus	CCONJ
ejpam-5687	401	6	,	,	PUNCT
ejpam-5687	401	7	138(3):1–15	138(3):1–15	PROPN
ejpam-5687	401	8	,	,	PUNCT
ejpam-5687	401	9	2023	2023	NUM
ejpam-5687	401	10	.	.	PUNCT
ejpam-5687	402	1	[	[	X
ejpam-5687	402	2	8	8	NUM
ejpam-5687	402	3	]	]	X
ejpam-5687	402	4	ramakant	ramakant	ADJ
ejpam-5687	402	5	prasad	prasad	PROPN
ejpam-5687	402	6	,	,	PUNCT
ejpam-5687	402	7	surendra	surendra	PROPN
ejpam-5687	402	8	kumar	kumar	PROPN
ejpam-5687	402	9	sagar	sagar	PROPN
ejpam-5687	402	10	,	,	PUNCT
ejpam-5687	402	11	shama	shama	NOUN
ejpam-5687	402	12	parveen	parveen	PROPN
ejpam-5687	402	13	,	,	PUNCT
ejpam-5687	402	14	and	and	CCONJ
ejpam-5687	402	15	ravins	ravins	PROPN
ejpam-5687	402	16	dohare	dohare	NOUN
ejpam-5687	402	17	.	.	PUNCT
ejpam-5687	403	1	mathematical	mathematical	ADJ
ejpam-5687	403	2	modeling	modeling	NOUN
ejpam-5687	403	3	in	in	ADP
ejpam-5687	403	4	perspective	perspective	NOUN
ejpam-5687	403	5	of	of	ADP
ejpam-5687	403	6	vector	vector	NOUN
ejpam-5687	403	7	-	-	PUNCT
ejpam-5687	403	8	borne	bear	VERB
ejpam-5687	403	9	viral	viral	ADJ
ejpam-5687	403	10	infections	infection	NOUN
ejpam-5687	403	11	:	:	PUNCT
ejpam-5687	403	12	a	a	DET
ejpam-5687	403	13	review	review	NOUN
ejpam-5687	403	14	.	.	PUNCT
ejpam-5687	404	1	benisuef	benisuef	PROPN
ejpam-5687	404	2	university	university	PROPN
ejpam-5687	404	3	journal	journal	NOUN
ejpam-5687	404	4	of	of	ADP
ejpam-5687	404	5	basic	basic	ADJ
ejpam-5687	404	6	and	and	CCONJ
ejpam-5687	404	7	applied	applied	ADJ
ejpam-5687	404	8	sciences	science	NOUN
ejpam-5687	404	9	,	,	PUNCT
ejpam-5687	404	10	11(1):102	11(1):102	NUM
ejpam-5687	404	11	,	,	PUNCT
ejpam-5687	404	12	2022	2022	NUM
ejpam-5687	404	13	.	.	PUNCT
ejpam-5687	405	1	[	[	X
ejpam-5687	405	2	9	9	NUM
ejpam-5687	405	3	]	]	X
ejpam-5687	405	4	abou	abou	PROPN
ejpam-5687	405	5	bakari	bakari	PROPN
ejpam-5687	405	6	diabaté	diabaté	NOUN
ejpam-5687	405	7	,	,	PUNCT
ejpam-5687	405	8	boureima	boureima	PROPN
ejpam-5687	405	9	sangaré	sangaré	ADJ
ejpam-5687	405	10	,	,	PUNCT
ejpam-5687	405	11	and	and	CCONJ
ejpam-5687	405	12	ousmane	ousmane	ADJ
ejpam-5687	405	13	koutou	koutou	NOUN
ejpam-5687	405	14	.	.	PUNCT
ejpam-5687	406	1	mathematical	mathematical	ADJ
ejpam-5687	406	2	modeling	modeling	NOUN
ejpam-5687	406	3	of	of	ADP
ejpam-5687	406	4	the	the	DET
ejpam-5687	406	5	dynamics	dynamic	NOUN
ejpam-5687	406	6	of	of	ADP
ejpam-5687	406	7	vector	vector	NOUN
ejpam-5687	406	8	-	-	PUNCT
ejpam-5687	406	9	borne	bear	VERB
ejpam-5687	406	10	diseases	disease	NOUN
ejpam-5687	406	11	transmitted	transmit	VERB
ejpam-5687	406	12	by	by	ADP
ejpam-5687	406	13	mosquitoes	mosquito	NOUN
ejpam-5687	406	14	:	:	PUNCT
ejpam-5687	406	15	taking	take	VERB
ejpam-5687	406	16	into	into	ADP
ejpam-5687	406	17	account	account	NOUN
ejpam-5687	406	18	aquatic	aquatic	ADJ
ejpam-5687	406	19	stages	stage	NOUN
ejpam-5687	406	20	and	and	CCONJ
ejpam-5687	406	21	gonotrophic	gonotrophic	ADJ
ejpam-5687	406	22	cycle	cycle	NOUN
ejpam-5687	406	23	.	.	PUNCT
ejpam-5687	407	1	nonautonomous	nonautonomous	ADJ
ejpam-5687	407	2	dynamical	dynamical	ADJ
ejpam-5687	407	3	systems	system	NOUN
ejpam-5687	407	4	,	,	PUNCT
ejpam-5687	407	5	9(1):205–236	9(1):205–236	NUM
ejpam-5687	407	6	,	,	PUNCT
ejpam-5687	407	7	2022	2022	NUM
ejpam-5687	407	8	.	.	PUNCT
ejpam-5687	408	1	[	[	X
ejpam-5687	408	2	10	10	NUM
ejpam-5687	408	3	]	]	X
ejpam-5687	408	4	muhammad	muhammad	PROPN
ejpam-5687	408	5	sinan	sinan	PROPN
ejpam-5687	408	6	,	,	PUNCT
ejpam-5687	408	7	hijaz	hijaz	PROPN
ejpam-5687	408	8	ahmad	ahmad	PROPN
ejpam-5687	408	9	,	,	PUNCT
ejpam-5687	408	10	zubair	zubair	PROPN
ejpam-5687	408	11	ahmad	ahmad	PROPN
ejpam-5687	408	12	,	,	PUNCT
ejpam-5687	408	13	jamel	jamel	PROPN
ejpam-5687	408	14	baili	baili	PROPN
ejpam-5687	408	15	,	,	PUNCT
ejpam-5687	408	16	saqib	saqib	PROPN
ejpam-5687	408	17	murtaza	murtaza	PROPN
ejpam-5687	408	18	,	,	PUNCT
ejpam-5687	408	19	ma	ma	PROPN
ejpam-5687	408	20	aiyashi	aiyashi	PROPN
ejpam-5687	408	21	,	,	PUNCT
ejpam-5687	408	22	and	and	CCONJ
ejpam-5687	408	23	thongchai	thongchai	VERB
ejpam-5687	408	24	botmart	botmart	NOUN
ejpam-5687	408	25	.	.	PUNCT
ejpam-5687	409	1	fractional	fractional	ADJ
ejpam-5687	409	2	mathematical	mathematical	ADJ
ejpam-5687	409	3	modeling	modeling	NOUN
ejpam-5687	409	4	of	of	ADP
ejpam-5687	409	5	malaria	malaria	NOUN
ejpam-5687	409	6	disease	disease	NOUN
ejpam-5687	409	7	with	with	ADP
ejpam-5687	409	8	treatment	treatment	NOUN
ejpam-5687	409	9	&	&	CCONJ
ejpam-5687	409	10	insecticides	insecticide	NOUN
ejpam-5687	409	11	.	.	PUNCT
ejpam-5687	410	1	results	result	NOUN
ejpam-5687	410	2	in	in	ADP
ejpam-5687	410	3	physics	physics	NOUN
ejpam-5687	410	4	,	,	PUNCT
ejpam-5687	410	5	34:105220	34:105220	NUM
ejpam-5687	410	6	,	,	PUNCT
ejpam-5687	410	7	2022	2022	NUM
ejpam-5687	410	8	.	.	PUNCT
ejpam-5687	411	1	[	[	X
ejpam-5687	411	2	11	11	NUM
ejpam-5687	411	3	]	]	X
ejpam-5687	411	4	rashid	rashid	PROPN
ejpam-5687	411	5	jan	jan	PROPN
ejpam-5687	411	6	,	,	PUNCT
ejpam-5687	411	7	hakima	hakima	PROPN
ejpam-5687	411	8	degaichia	degaichia	PROPN
ejpam-5687	411	9	,	,	PUNCT
ejpam-5687	411	10	salah	salah	PROPN
ejpam-5687	411	11	boulaaras	boulaaras	PROPN
ejpam-5687	411	12	,	,	PUNCT
ejpam-5687	411	13	ziad	ziad	PROPN
ejpam-5687	411	14	ur	ur	PROPN
ejpam-5687	411	15	rehman	rehman	PROPN
ejpam-5687	411	16	,	,	PUNCT
ejpam-5687	411	17	and	and	CCONJ
ejpam-5687	411	18	salma	salma	PROPN
ejpam-5687	411	19	bahramand	bahramand	PROPN
ejpam-5687	411	20	.	.	PUNCT
ejpam-5687	412	1	qualitative	qualitative	ADJ
ejpam-5687	412	2	and	and	CCONJ
ejpam-5687	412	3	quantitative	quantitative	ADJ
ejpam-5687	412	4	analysis	analysis	NOUN
ejpam-5687	412	5	of	of	ADP
ejpam-5687	412	6	vector	vector	NOUN
ejpam-5687	412	7	-	-	PUNCT
ejpam-5687	412	8	borne	bear	VERB
ejpam-5687	412	9	infection	infection	NOUN
ejpam-5687	412	10	through	through	ADP
ejpam-5687	412	11	fractional	fractional	ADJ
ejpam-5687	412	12	framework	framework	NOUN
ejpam-5687	412	13	.	.	PUNCT
ejpam-5687	413	1	discrete	discrete	ADJ
ejpam-5687	413	2	and	and	CCONJ
ejpam-5687	413	3	continuous	continuous	ADJ
ejpam-5687	413	4	dynamical	dynamical	ADJ
ejpam-5687	413	5	systems	system	NOUN
ejpam-5687	413	6	-	-	PUNCT
ejpam-5687	413	7	s	s	NOUN
ejpam-5687	413	8	,	,	PUNCT
ejpam-5687	413	9	pages	page	NOUN
ejpam-5687	413	10	0–0	0–0	NUM
ejpam-5687	413	11	,	,	PUNCT
ejpam-5687	413	12	2024	2024	NUM
ejpam-5687	413	13	.	.	PUNCT
ejpam-5687	414	1	[	[	X
ejpam-5687	414	2	12	12	NUM
ejpam-5687	414	3	]	]	X
ejpam-5687	414	4	pallavi	pallavi	PROPN
ejpam-5687	414	5	bedi	bedi	PROPN
ejpam-5687	414	6	,	,	PUNCT
ejpam-5687	414	7	aziz	aziz	PROPN
ejpam-5687	414	8	khan	khan	PROPN
ejpam-5687	414	9	,	,	PUNCT
ejpam-5687	414	10	anoop	anoop	PROPN
ejpam-5687	414	11	kumar	kumar	PROPN
ejpam-5687	414	12	,	,	PUNCT
ejpam-5687	414	13	and	and	CCONJ
ejpam-5687	414	14	thabet	thabet	ADJ
ejpam-5687	414	15	abdeljawad	abdeljawad	NOUN
ejpam-5687	414	16	.	.	PUNCT
ejpam-5687	415	1	computational	computational	ADJ
ejpam-5687	415	2	study	study	NOUN
ejpam-5687	415	3	of	of	ADP
ejpam-5687	415	4	fractional	fractional	ADJ
ejpam-5687	415	5	-	-	PUNCT
ejpam-5687	415	6	order	order	NOUN
ejpam-5687	415	7	vector	vector	NOUN
ejpam-5687	415	8	borne	borne	NOUN
ejpam-5687	415	9	diseases	disease	NOUN
ejpam-5687	415	10	model	model	NOUN
ejpam-5687	415	11	.	.	PUNCT
ejpam-5687	416	1	fractals	fractal	NOUN
ejpam-5687	416	2	,	,	PUNCT
ejpam-5687	416	3	30(05):2240149	30(05):2240149	NUM
ejpam-5687	416	4	,	,	PUNCT
ejpam-5687	416	5	2022	2022	NUM
ejpam-5687	416	6	.	.	PUNCT
ejpam-5687	417	1	[	[	X
ejpam-5687	417	2	13	13	NUM
ejpam-5687	417	3	]	]	PUNCT
ejpam-5687	417	4	waleed	waleed	PROPN
ejpam-5687	417	5	adel	adel	PROPN
ejpam-5687	417	6	,	,	PUNCT
ejpam-5687	417	7	yaser	yaser	PROPN
ejpam-5687	417	8	a	a	DET
ejpam-5687	417	9	amer	amer	PROPN
ejpam-5687	417	10	,	,	PUNCT
ejpam-5687	417	11	eslam	eslam	PROPN
ejpam-5687	417	12	sm	sm	PROPN
ejpam-5687	417	13	youssef	youssef	PROPN
ejpam-5687	417	14	,	,	PUNCT
ejpam-5687	417	15	and	and	CCONJ
ejpam-5687	417	16	amr	amr	PROPN
ejpam-5687	417	17	ms	ms	PROPN
ejpam-5687	417	18	mahdy	mahdy	NOUN
ejpam-5687	417	19	.	.	PUNCT
ejpam-5687	418	1	mathematical	mathematical	ADJ
ejpam-5687	418	2	analysis	analysis	NOUN
ejpam-5687	418	3	and	and	CCONJ
ejpam-5687	418	4	simulations	simulation	NOUN
ejpam-5687	418	5	for	for	ADP
ejpam-5687	418	6	a	a	DET
ejpam-5687	418	7	caputo	caputo	PROPN
ejpam-5687	418	8	-	-	PUNCT
ejpam-5687	418	9	fabrizio	fabrizio	PROPN
ejpam-5687	418	10	fractional	fractional	NOUN
ejpam-5687	418	11	covid-19	covid-19	PROPN
ejpam-5687	418	12	model	model	NOUN
ejpam-5687	418	13	.	.	PUNCT
ejpam-5687	419	1	partial	partial	ADJ
ejpam-5687	419	2	differential	differential	ADJ
ejpam-5687	419	3	equations	equation	NOUN
ejpam-5687	419	4	in	in	ADP
ejpam-5687	419	5	applied	applied	ADJ
ejpam-5687	419	6	mathematics	mathematic	NOUN
ejpam-5687	419	7	,	,	PUNCT
ejpam-5687	419	8	8:100558	8:100558	NUM
ejpam-5687	419	9	,	,	PUNCT
ejpam-5687	419	10	2023	2023	NUM
ejpam-5687	419	11	.	.	PUNCT
ejpam-5687	420	1	[	[	X
ejpam-5687	420	2	14	14	NUM
ejpam-5687	420	3	]	]	X
ejpam-5687	420	4	mati	mati	PROPN
ejpam-5687	420	5	ur	ur	PROPN
ejpam-5687	420	6	rahman	rahman	PROPN
ejpam-5687	420	7	,	,	PUNCT
ejpam-5687	420	8	saeed	saeed	PROPN
ejpam-5687	420	9	ahmad	ahmad	PROPN
ejpam-5687	420	10	,	,	PUNCT
ejpam-5687	420	11	rt	rt	PROPN
ejpam-5687	420	12	matoog	matoog	NOUN
ejpam-5687	420	13	,	,	PUNCT
ejpam-5687	420	14	nawal	nawal	PROPN
ejpam-5687	420	15	a	a	DET
ejpam-5687	420	16	alshehri	alshehri	NOUN
ejpam-5687	420	17	,	,	PUNCT
ejpam-5687	420	18	and	and	CCONJ
ejpam-5687	420	19	tahir	tahir	PROPN
ejpam-5687	420	20	khan	khan	PROPN
ejpam-5687	420	21	.	.	PUNCT
ejpam-5687	421	1	study	study	NOUN
ejpam-5687	421	2	on	on	ADP
ejpam-5687	421	3	the	the	DET
ejpam-5687	421	4	mathematical	mathematical	ADJ
ejpam-5687	421	5	modelling	modelling	NOUN
ejpam-5687	421	6	of	of	ADP
ejpam-5687	421	7	covid-19	covid-19	PROPN
ejpam-5687	421	8	with	with	ADP
ejpam-5687	421	9	caputo	caputo	PROPN
ejpam-5687	421	10	-	-	PUNCT
ejpam-5687	421	11	fabrizio	fabrizio	PROPN
ejpam-5687	421	12	operator	operator	NOUN
ejpam-5687	421	13	.	.	PUNCT
ejpam-5687	422	1	n.	n.	PROPN
ejpam-5687	422	2	ullah	ullah	PROPN
ejpam-5687	422	3	et	et	PROPN
ejpam-5687	422	4	al	al	PROPN
ejpam-5687	422	5	.	.	PUNCT
ejpam-5687	422	6	/	/	SYM
ejpam-5687	422	7	eur	eur	PROPN
ejpam-5687	422	8	.	.	PUNCT
ejpam-5687	423	1	j.	j.	PROPN
ejpam-5687	423	2	pure	pure	PROPN
ejpam-5687	423	3	appl	appl	PROPN
ejpam-5687	423	4	.	.	PROPN
ejpam-5687	423	5	math	math	PROPN
ejpam-5687	423	6	,	,	PUNCT
ejpam-5687	423	7	18	18	NUM
ejpam-5687	423	8	(	(	PUNCT
ejpam-5687	423	9	2	2	NUM
ejpam-5687	423	10	)	)	PUNCT
ejpam-5687	423	11	(	(	PUNCT
ejpam-5687	423	12	2025	2025	NUM
ejpam-5687	423	13	)	)	PUNCT
ejpam-5687	423	14	,	,	PUNCT
ejpam-5687	423	15	5687	5687	NUM
ejpam-5687	423	16	24	24	NUM
ejpam-5687	423	17	of	of	ADP
ejpam-5687	423	18	25	25	NUM
ejpam-5687	423	19	chaos	chaos	NOUN
ejpam-5687	423	20	,	,	PUNCT
ejpam-5687	423	21	solitons	soliton	NOUN
ejpam-5687	423	22	&	&	CCONJ
ejpam-5687	423	23	fractals	fractal	NOUN
ejpam-5687	423	24	,	,	PUNCT
ejpam-5687	423	25	150:111121	150:111121	NUM
ejpam-5687	423	26	,	,	PUNCT
ejpam-5687	423	27	2021	2021	NUM
ejpam-5687	423	28	.	.	PUNCT
ejpam-5687	424	1	[	[	X
ejpam-5687	424	2	15	15	NUM
ejpam-5687	424	3	]	]	X
ejpam-5687	424	4	donghui	donghui	PROPN
ejpam-5687	424	5	yu	yu	PROPN
ejpam-5687	424	6	,	,	PUNCT
ejpam-5687	424	7	xiaozhong	xiaozhong	PROPN
ejpam-5687	424	8	liao	liao	PROPN
ejpam-5687	424	9	,	,	PUNCT
ejpam-5687	424	10	and	and	CCONJ
ejpam-5687	424	11	yong	yong	PROPN
ejpam-5687	424	12	wang	wang	PROPN
ejpam-5687	424	13	.	.	PUNCT
ejpam-5687	425	1	modeling	modeling	NOUN
ejpam-5687	425	2	and	and	CCONJ
ejpam-5687	425	3	analysis	analysis	NOUN
ejpam-5687	425	4	of	of	ADP
ejpam-5687	425	5	caputo	caputo	PROPN
ejpam-5687	425	6	–	–	PUNCT
ejpam-5687	425	7	fabrizio	fabrizio	PROPN
ejpam-5687	425	8	definition	definition	NOUN
ejpam-5687	425	9	-	-	PUNCT
ejpam-5687	425	10	based	base	VERB
ejpam-5687	425	11	fractional	fractional	ADJ
ejpam-5687	425	12	-	-	PUNCT
ejpam-5687	425	13	order	order	NOUN
ejpam-5687	425	14	boost	boost	NOUN
ejpam-5687	425	15	converter	converter	NOUN
ejpam-5687	425	16	with	with	ADP
ejpam-5687	425	17	inductive	inductive	ADJ
ejpam-5687	425	18	loads	load	NOUN
ejpam-5687	425	19	.	.	PUNCT
ejpam-5687	426	1	fractal	fractal	ADJ
ejpam-5687	426	2	and	and	CCONJ
ejpam-5687	426	3	fractional	fractional	ADJ
ejpam-5687	426	4	,	,	PUNCT
ejpam-5687	426	5	8(2):81	8(2):81	NUM
ejpam-5687	426	6	,	,	PUNCT
ejpam-5687	426	7	2024	2024	NUM
ejpam-5687	426	8	.	.	PUNCT
ejpam-5687	427	1	[	[	X
ejpam-5687	427	2	16	16	NUM
ejpam-5687	427	3	]	]	PUNCT
ejpam-5687	427	4	oj	oj	ADP
ejpam-5687	427	5	peter	peter	PROPN
ejpam-5687	427	6	,	,	PUNCT
ejpam-5687	427	7	aa	aa	PROPN
ejpam-5687	427	8	ayoade	ayoade	PROPN
ejpam-5687	427	9	,	,	PUNCT
ejpam-5687	427	10	ai	ai	VERB
ejpam-5687	427	11	abioye	abioye	NOUN
ejpam-5687	427	12	,	,	PUNCT
ejpam-5687	427	13	aa	aa	PROPN
ejpam-5687	427	14	victor	victor	NOUN
ejpam-5687	427	15	,	,	PUNCT
ejpam-5687	427	16	and	and	CCONJ
ejpam-5687	427	17	ce	ce	PROPN
ejpam-5687	427	18	akpan	akpan	PROPN
ejpam-5687	427	19	.	.	PUNCT
ejpam-5687	428	1	sensitivity	sensitivity	NOUN
ejpam-5687	428	2	analysis	analysis	NOUN
ejpam-5687	428	3	of	of	ADP
ejpam-5687	428	4	the	the	DET
ejpam-5687	428	5	parameters	parameter	NOUN
ejpam-5687	428	6	of	of	ADP
ejpam-5687	428	7	a	a	DET
ejpam-5687	428	8	cholera	cholera	NOUN
ejpam-5687	428	9	model	model	NOUN
ejpam-5687	428	10	.	.	PUNCT
ejpam-5687	429	1	journal	journal	PROPN
ejpam-5687	429	2	of	of	ADP
ejpam-5687	429	3	applied	apply	VERB
ejpam-5687	429	4	sciences	science	NOUN
ejpam-5687	429	5	and	and	CCONJ
ejpam-5687	429	6	environmental	environmental	ADJ
ejpam-5687	429	7	management	management	NOUN
ejpam-5687	429	8	,	,	PUNCT
ejpam-5687	429	9	22(4):477–481	22(4):477–481	PROPN
ejpam-5687	429	10	,	,	PUNCT
ejpam-5687	429	11	2018	2018	NUM
ejpam-5687	429	12	.	.	PUNCT
ejpam-5687	430	1	[	[	X
ejpam-5687	430	2	17	17	NUM
ejpam-5687	430	3	]	]	PUNCT
ejpam-5687	430	4	salihu	salihu	NOUN
ejpam-5687	430	5	sabiu	sabiu	PROPN
ejpam-5687	430	6	musa	musa	PROPN
ejpam-5687	430	7	,	,	PUNCT
ejpam-5687	430	8	zainab	zainab	PROPN
ejpam-5687	430	9	umar	umar	PROPN
ejpam-5687	430	10	abdullahi	abdullahi	PROPN
ejpam-5687	430	11	,	,	PUNCT
ejpam-5687	430	12	shi	shi	PROPN
ejpam-5687	430	13	zhao	zhao	PROPN
ejpam-5687	430	14	,	,	PUNCT
ejpam-5687	430	15	umar	umar	PROPN
ejpam-5687	430	16	muhammad	muhammad	PROPN
ejpam-5687	430	17	bello	bello	PROPN
ejpam-5687	430	18	,	,	PUNCT
ejpam-5687	430	19	nafiu	nafiu	PROPN
ejpam-5687	430	20	hussaini	hussaini	PROPN
ejpam-5687	430	21	,	,	PUNCT
ejpam-5687	430	22	abdulrazaq	abdulrazaq	PROPN
ejpam-5687	430	23	garba	garba	PROPN
ejpam-5687	430	24	habib	habib	PROPN
ejpam-5687	430	25	,	,	PUNCT
ejpam-5687	430	26	and	and	CCONJ
ejpam-5687	430	27	daihai	daihai	VERB
ejpam-5687	430	28	he	he	PRON
ejpam-5687	430	29	.	.	PUNCT
ejpam-5687	431	1	transmission	transmission	NOUN
ejpam-5687	431	2	dynamics	dynamic	NOUN
ejpam-5687	431	3	of	of	ADP
ejpam-5687	431	4	monkeypox	monkeypox	PROPN
ejpam-5687	431	5	virus	virus	NOUN
ejpam-5687	431	6	in	in	ADP
ejpam-5687	431	7	nigeria	nigeria	PROPN
ejpam-5687	431	8	during	during	ADP
ejpam-5687	431	9	the	the	DET
ejpam-5687	431	10	current	current	ADJ
ejpam-5687	431	11	covid-19	covid-19	PROPN
ejpam-5687	431	12	pandemic	pandemic	ADJ
ejpam-5687	431	13	and	and	CCONJ
ejpam-5687	431	14	estimation	estimation	NOUN
ejpam-5687	431	15	of	of	ADP
ejpam-5687	431	16	effective	effective	ADJ
ejpam-5687	431	17	reproduction	reproduction	NOUN
ejpam-5687	431	18	number	number	NOUN
ejpam-5687	431	19	.	.	PUNCT
ejpam-5687	432	1	vaccines	vaccine	NOUN
ejpam-5687	432	2	,	,	PUNCT
ejpam-5687	432	3	10(12):2153	10(12):2153	NUM
ejpam-5687	432	4	,	,	PUNCT
ejpam-5687	432	5	2022	2022	NUM
ejpam-5687	432	6	.	.	PUNCT
ejpam-5687	433	1	[	[	X
ejpam-5687	433	2	18	18	NUM
ejpam-5687	433	3	]	]	X
ejpam-5687	433	4	christian	christian	PROPN
ejpam-5687	433	5	l	l	PROPN
ejpam-5687	433	6	althaus	althaus	PROPN
ejpam-5687	433	7	.	.	PUNCT
ejpam-5687	434	1	estimating	estimate	VERB
ejpam-5687	434	2	the	the	DET
ejpam-5687	434	3	reproduction	reproduction	NOUN
ejpam-5687	434	4	number	number	NOUN
ejpam-5687	434	5	of	of	ADP
ejpam-5687	434	6	ebola	ebola	PROPN
ejpam-5687	434	7	virus	virus	NOUN
ejpam-5687	434	8	(	(	PUNCT
ejpam-5687	434	9	ebov	ebov	PROPN
ejpam-5687	434	10	)	)	PUNCT
ejpam-5687	434	11	during	during	ADP
ejpam-5687	434	12	the	the	DET
ejpam-5687	434	13	2014	2014	NUM
ejpam-5687	434	14	outbreak	outbreak	NOUN
ejpam-5687	434	15	in	in	ADP
ejpam-5687	434	16	west	west	PROPN
ejpam-5687	434	17	africa	africa	PROPN
ejpam-5687	434	18	.	.	PUNCT
ejpam-5687	435	1	plos	plos	PROPN
ejpam-5687	435	2	currents	currents	PROPN
ejpam-5687	435	3	,	,	PUNCT
ejpam-5687	435	4	6	6	NUM
ejpam-5687	435	5	,	,	PUNCT
ejpam-5687	435	6	2014	2014	NUM
ejpam-5687	435	7	.	.	PUNCT
ejpam-5687	436	1	[	[	X
ejpam-5687	436	2	19	19	NUM
ejpam-5687	436	3	]	]	X
ejpam-5687	436	4	idris	idris	PROPN
ejpam-5687	436	5	ahmed	ahmed	PROPN
ejpam-5687	436	6	,	,	PUNCT
ejpam-5687	436	7	abdullahi	abdullahi	PROPN
ejpam-5687	436	8	yusuf	yusuf	PROPN
ejpam-5687	436	9	,	,	PUNCT
ejpam-5687	436	10	jessada	jessada	PROPN
ejpam-5687	436	11	tariboon	tariboon	PROPN
ejpam-5687	436	12	,	,	PUNCT
ejpam-5687	436	13	mubarak	mubarak	PROPN
ejpam-5687	436	14	muhammad	muhammad	PROPN
ejpam-5687	436	15	,	,	PUNCT
ejpam-5687	436	16	fahd	fahd	PROPN
ejpam-5687	436	17	jarad	jarad	PROPN
ejpam-5687	436	18	,	,	PUNCT
ejpam-5687	436	19	and	and	CCONJ
ejpam-5687	436	20	badamasi	badamasi	VERB
ejpam-5687	436	21	bashir	bashir	PROPN
ejpam-5687	436	22	mikailu	mikailu	PROPN
ejpam-5687	436	23	.	.	PUNCT
ejpam-5687	437	1	a	a	DET
ejpam-5687	437	2	dynamical	dynamical	ADJ
ejpam-5687	437	3	and	and	CCONJ
ejpam-5687	437	4	sensitivity	sensitivity	NOUN
ejpam-5687	437	5	analysis	analysis	NOUN
ejpam-5687	437	6	of	of	ADP
ejpam-5687	437	7	the	the	DET
ejpam-5687	437	8	caputo	caputo	PROPN
ejpam-5687	437	9	fractional	fractional	ADJ
ejpam-5687	437	10	-	-	PUNCT
ejpam-5687	437	11	order	order	NOUN
ejpam-5687	437	12	ebola	ebola	PROPN
ejpam-5687	437	13	virus	virus	NOUN
ejpam-5687	437	14	model	model	PROPN
ejpam-5687	437	15	:	:	PUNCT
ejpam-5687	437	16	implications	implication	NOUN
ejpam-5687	437	17	for	for	ADP
ejpam-5687	437	18	control	control	NOUN
ejpam-5687	437	19	measures	measure	NOUN
ejpam-5687	437	20	.	.	PUNCT
ejpam-5687	438	1	science	science	NOUN
ejpam-5687	438	2	&	&	CCONJ
ejpam-5687	438	3	technology	technology	PROPN
ejpam-5687	438	4	asia	asia	PROPN
ejpam-5687	438	5	,	,	PUNCT
ejpam-5687	438	6	pages	page	NOUN
ejpam-5687	438	7	26–37	26–37	NUM
ejpam-5687	438	8	,	,	PUNCT
ejpam-5687	438	9	2023	2023	NUM
ejpam-5687	438	10	.	.	PUNCT
ejpam-5687	439	1	[	[	X
ejpam-5687	439	2	20	20	NUM
ejpam-5687	439	3	]	]	PUNCT
ejpam-5687	439	4	guotao	guotao	PROPN
ejpam-5687	439	5	wang	wang	PROPN
ejpam-5687	439	6	,	,	PUNCT
ejpam-5687	439	7	abdeljabbar	abdeljabbar	PROPN
ejpam-5687	439	8	ghanmi	ghanmi	PROPN
ejpam-5687	439	9	,	,	PUNCT
ejpam-5687	439	10	samah	samah	PROPN
ejpam-5687	439	11	horrigue	horrigue	PROPN
ejpam-5687	439	12	,	,	PUNCT
ejpam-5687	439	13	and	and	CCONJ
ejpam-5687	439	14	samar	samar	PROPN
ejpam-5687	439	15	madian	madian	PROPN
ejpam-5687	439	16	.	.	PUNCT
ejpam-5687	440	1	existence	existence	NOUN
ejpam-5687	440	2	result	result	NOUN
ejpam-5687	440	3	and	and	CCONJ
ejpam-5687	440	4	uniqueness	uniqueness	NOUN
ejpam-5687	440	5	for	for	ADP
ejpam-5687	440	6	some	some	DET
ejpam-5687	440	7	fractional	fractional	ADJ
ejpam-5687	440	8	problem	problem	NOUN
ejpam-5687	440	9	.	.	PUNCT
ejpam-5687	441	1	mathematics	mathematic	NOUN
ejpam-5687	441	2	,	,	PUNCT
ejpam-5687	441	3	7(6):516	7(6):516	NUM
ejpam-5687	441	4	,	,	PUNCT
ejpam-5687	441	5	2019	2019	NUM
ejpam-5687	441	6	.	.	PUNCT
ejpam-5687	442	1	[	[	X
ejpam-5687	442	2	21	21	NUM
ejpam-5687	442	3	]	]	X
ejpam-5687	442	4	idris	idris	PROPN
ejpam-5687	442	5	ahmed	ahmed	PROPN
ejpam-5687	442	6	,	,	PUNCT
ejpam-5687	442	7	chanakarn	chanakarn	PROPN
ejpam-5687	442	8	kiataramkul	kiataramkul	PROPN
ejpam-5687	442	9	,	,	PUNCT
ejpam-5687	442	10	mubarak	mubarak	PROPN
ejpam-5687	442	11	muhammad	muhammad	PROPN
ejpam-5687	442	12	,	,	PUNCT
ejpam-5687	442	13	and	and	CCONJ
ejpam-5687	442	14	jessada	jessada	PROPN
ejpam-5687	442	15	tariboon	tariboon	PROPN
ejpam-5687	442	16	.	.	PUNCT
ejpam-5687	443	1	existence	existence	NOUN
ejpam-5687	443	2	and	and	CCONJ
ejpam-5687	443	3	sensitivity	sensitivity	NOUN
ejpam-5687	443	4	analysis	analysis	NOUN
ejpam-5687	443	5	of	of	ADP
ejpam-5687	443	6	a	a	DET
ejpam-5687	443	7	caputo	caputo	PROPN
ejpam-5687	443	8	fractional	fractional	ADJ
ejpam-5687	443	9	-	-	PUNCT
ejpam-5687	443	10	order	order	NOUN
ejpam-5687	443	11	diphtheria	diphtheria	NOUN
ejpam-5687	443	12	epidemic	epidemic	NOUN
ejpam-5687	443	13	model	model	NOUN
ejpam-5687	443	14	.	.	PUNCT
ejpam-5687	444	1	mathematics	mathematic	NOUN
ejpam-5687	444	2	,	,	PUNCT
ejpam-5687	444	3	12(13):2033	12(13):2033	NUM
ejpam-5687	444	4	,	,	PUNCT
ejpam-5687	444	5	2024	2024	NUM
ejpam-5687	444	6	.	.	PUNCT
ejpam-5687	445	1	[	[	X
ejpam-5687	445	2	22	22	NUM
ejpam-5687	445	3	]	]	PUNCT
ejpam-5687	445	4	badr	badr	PROPN
ejpam-5687	445	5	s	s	PROPN
ejpam-5687	445	6	alkahtani	alkahtani	PROPN
ejpam-5687	445	7	.	.	PUNCT
ejpam-5687	446	1	mathematical	mathematical	ADJ
ejpam-5687	446	2	modeling	modeling	NOUN
ejpam-5687	446	3	of	of	ADP
ejpam-5687	446	4	covid-19	covid-19	PROPN
ejpam-5687	446	5	transmission	transmission	NOUN
ejpam-5687	446	6	using	use	VERB
ejpam-5687	446	7	a	a	DET
ejpam-5687	446	8	fractional	fractional	ADJ
ejpam-5687	446	9	order	order	NOUN
ejpam-5687	446	10	derivative	derivative	NOUN
ejpam-5687	446	11	.	.	PUNCT
ejpam-5687	447	1	fractal	fractal	PROPN
ejpam-5687	447	2	and	and	CCONJ
ejpam-5687	447	3	fractional	fractional	ADJ
ejpam-5687	447	4	,	,	PUNCT
ejpam-5687	447	5	7(1):46	7(1):46	NOUN
ejpam-5687	447	6	,	,	PUNCT
ejpam-5687	447	7	2022	2022	NUM
ejpam-5687	447	8	.	.	PUNCT
ejpam-5687	448	1	[	[	X
ejpam-5687	448	2	23	23	NUM
ejpam-5687	448	3	]	]	X
ejpam-5687	448	4	shiv	shiv	PROPN
ejpam-5687	448	5	mangal	mangal	PROPN
ejpam-5687	448	6	,	,	PUNCT
ejpam-5687	448	7	op	op	NOUN
ejpam-5687	448	8	misra	misra	NOUN
ejpam-5687	448	9	,	,	PUNCT
ejpam-5687	448	10	and	and	CCONJ
ejpam-5687	448	11	joydip	joydip	PROPN
ejpam-5687	448	12	dhar	dhar	PROPN
ejpam-5687	448	13	.	.	PUNCT
ejpam-5687	449	1	modeling	model	VERB
ejpam-5687	449	2	the	the	DET
ejpam-5687	449	3	effect	effect	NOUN
ejpam-5687	449	4	of	of	ADP
ejpam-5687	449	5	vaccination	vaccination	NOUN
ejpam-5687	449	6	in	in	ADP
ejpam-5687	449	7	fractional	fractional	ADJ
ejpam-5687	449	8	-	-	PUNCT
ejpam-5687	449	9	order	order	NOUN
ejpam-5687	449	10	epidemic	epidemic	NOUN
ejpam-5687	449	11	model	model	NOUN
ejpam-5687	449	12	for	for	ADP
ejpam-5687	449	13	infectious	infectious	ADJ
ejpam-5687	449	14	disease	disease	NOUN
ejpam-5687	449	15	.	.	PUNCT
ejpam-5687	450	1	international	international	ADJ
ejpam-5687	450	2	journal	journal	PROPN
ejpam-5687	450	3	of	of	ADP
ejpam-5687	450	4	dynamics	dynamic	NOUN
ejpam-5687	450	5	and	and	CCONJ
ejpam-5687	450	6	control	control	NOUN
ejpam-5687	450	7	,	,	PUNCT
ejpam-5687	450	8	12(1):303–317	12(1):303–317	NUM
ejpam-5687	450	9	,	,	PUNCT
ejpam-5687	450	10	2024	2024	NUM
ejpam-5687	450	11	.	.	PUNCT
ejpam-5687	451	1	[	[	X
ejpam-5687	451	2	24	24	NUM
ejpam-5687	451	3	]	]	PUNCT
ejpam-5687	451	4	abdullahi	abdullahi	PROPN
ejpam-5687	451	5	yusuf	yusuf	PROPN
ejpam-5687	451	6	,	,	PUNCT
ejpam-5687	451	7	bahar	bahar	PROPN
ejpam-5687	451	8	acay	acay	PROPN
ejpam-5687	451	9	,	,	PUNCT
ejpam-5687	451	10	umar	umar	PROPN
ejpam-5687	451	11	tasiu	tasiu	PROPN
ejpam-5687	451	12	mustapha	mustapha	PROPN
ejpam-5687	451	13	,	,	PUNCT
ejpam-5687	451	14	mustafa	mustafa	PROPN
ejpam-5687	451	15	inc	inc	PROPN
ejpam-5687	451	16	,	,	PUNCT
ejpam-5687	451	17	and	and	CCONJ
ejpam-5687	451	18	dumitru	dumitru	PROPN
ejpam-5687	451	19	baleanu	baleanu	NOUN
ejpam-5687	451	20	.	.	PUNCT
ejpam-5687	452	1	mathematical	mathematical	ADJ
ejpam-5687	452	2	modeling	modeling	NOUN
ejpam-5687	452	3	of	of	ADP
ejpam-5687	452	4	pine	pine	ADJ
ejpam-5687	452	5	wilt	wilt	ADJ
ejpam-5687	452	6	disease	disease	NOUN
ejpam-5687	452	7	with	with	ADP
ejpam-5687	452	8	caputo	caputo	PROPN
ejpam-5687	452	9	fractional	fractional	PROPN
ejpam-5687	452	10	operator	operator	NOUN
ejpam-5687	452	11	.	.	PUNCT
ejpam-5687	453	1	chaos	chaos	NOUN
ejpam-5687	453	2	,	,	PUNCT
ejpam-5687	453	3	solitons	soliton	NOUN
ejpam-5687	453	4	&	&	CCONJ
ejpam-5687	453	5	fractals	fractal	NOUN
ejpam-5687	453	6	,	,	PUNCT
ejpam-5687	453	7	143:110569	143:110569	NUM
ejpam-5687	453	8	,	,	PUNCT
ejpam-5687	453	9	2021	2021	NUM
ejpam-5687	453	10	.	.	PUNCT
ejpam-5687	454	1	[	[	X
ejpam-5687	454	2	25	25	NUM
ejpam-5687	454	3	]	]	AUX
ejpam-5687	454	4	isa	isa	PROPN
ejpam-5687	454	5	abdullahi	abdullahi	PROPN
ejpam-5687	454	6	baba	baba	PROPN
ejpam-5687	454	7	and	and	CCONJ
ejpam-5687	454	8	bashir	bashir	PROPN
ejpam-5687	454	9	ahmad	ahmad	PROPN
ejpam-5687	454	10	nasidi	nasidi	PROPN
ejpam-5687	454	11	.	.	PUNCT
ejpam-5687	455	1	fractional	fractional	ADJ
ejpam-5687	455	2	order	order	NOUN
ejpam-5687	455	3	epidemic	epidemic	NOUN
ejpam-5687	455	4	model	model	NOUN
ejpam-5687	455	5	for	for	ADP
ejpam-5687	455	6	the	the	DET
ejpam-5687	455	7	dynamics	dynamic	NOUN
ejpam-5687	455	8	of	of	ADP
ejpam-5687	455	9	novel	novel	NOUN
ejpam-5687	455	10	covid-19	covid-19	PROPN
ejpam-5687	455	11	.	.	PUNCT
ejpam-5687	455	12	alexandria	alexandria	PROPN
ejpam-5687	455	13	engineering	engineering	PROPN
ejpam-5687	455	14	journal	journal	PROPN
ejpam-5687	455	15	,	,	PUNCT
ejpam-5687	455	16	60(1):537–548	60(1):537–548	NOUN
ejpam-5687	455	17	,	,	PUNCT
ejpam-5687	455	18	2021	2021	NUM
ejpam-5687	455	19	.	.	PUNCT
ejpam-5687	456	1	[	[	X
ejpam-5687	456	2	26	26	NUM
ejpam-5687	456	3	]	]	X
ejpam-5687	456	4	idris	idris	PROPN
ejpam-5687	456	5	ahmed	ahmed	PROPN
ejpam-5687	456	6	,	,	PUNCT
ejpam-5687	456	7	abdullahi	abdullahi	PROPN
ejpam-5687	456	8	yusuf	yusuf	PROPN
ejpam-5687	456	9	,	,	PUNCT
ejpam-5687	456	10	musbahu	musbahu	NOUN
ejpam-5687	456	11	aminu	aminu	PROPN
ejpam-5687	456	12	sani	sani	PROPN
ejpam-5687	456	13	,	,	PUNCT
ejpam-5687	456	14	fahd	fahd	PROPN
ejpam-5687	456	15	jarad	jarad	PROPN
ejpam-5687	456	16	,	,	PUNCT
ejpam-5687	456	17	wiyada	wiyada	PROPN
ejpam-5687	456	18	kumam	kumam	PROPN
ejpam-5687	456	19	,	,	PUNCT
ejpam-5687	456	20	and	and	CCONJ
ejpam-5687	456	21	phatiphat	phatiphat	PRON
ejpam-5687	456	22	thounthong	thounthong	NOUN
ejpam-5687	456	23	.	.	PUNCT
ejpam-5687	457	1	analysis	analysis	NOUN
ejpam-5687	457	2	of	of	ADP
ejpam-5687	457	3	a	a	DET
ejpam-5687	457	4	caputo	caputo	PROPN
ejpam-5687	457	5	hiv	hiv	PROPN
ejpam-5687	457	6	and	and	CCONJ
ejpam-5687	457	7	malaria	malaria	PROPN
ejpam-5687	457	8	co	co	NOUN
ejpam-5687	457	9	-	-	ADJ
ejpam-5687	457	10	infection	infection	ADJ
ejpam-5687	457	11	epidemic	epidemic	NOUN
ejpam-5687	457	12	model	model	NOUN
ejpam-5687	457	13	.	.	PUNCT
ejpam-5687	458	1	thai	thai	PROPN
ejpam-5687	458	2	journal	journal	PROPN
ejpam-5687	458	3	of	of	ADP
ejpam-5687	458	4	mathematics	mathematic	NOUN
ejpam-5687	458	5	,	,	PUNCT
ejpam-5687	458	6	19(3):897–912	19(3):897–912	NUM
ejpam-5687	458	7	,	,	PUNCT
ejpam-5687	458	8	2021	2021	NUM
ejpam-5687	458	9	.	.	PUNCT
ejpam-5687	459	1	[	[	X
ejpam-5687	459	2	27	27	NUM
ejpam-5687	459	3	]	]	PUNCT
ejpam-5687	459	4	badr	badr	PROPN
ejpam-5687	459	5	saad	saad	PROPN
ejpam-5687	459	6	t	t	PROPN
ejpam-5687	459	7	alkahtani	alkahtani	PROPN
ejpam-5687	459	8	and	and	CCONJ
ejpam-5687	459	9	sara	sara	PROPN
ejpam-5687	459	10	salem	salem	PROPN
ejpam-5687	459	11	alzaid	alzaid	PROPN
ejpam-5687	459	12	.	.	PUNCT
ejpam-5687	460	1	studying	study	VERB
ejpam-5687	460	2	the	the	DET
ejpam-5687	460	3	dynamics	dynamic	NOUN
ejpam-5687	460	4	of	of	ADP
ejpam-5687	460	5	the	the	DET
ejpam-5687	460	6	rumor	rumor	NOUN
ejpam-5687	460	7	spread	spread	NOUN
ejpam-5687	460	8	model	model	NOUN
ejpam-5687	460	9	with	with	ADP
ejpam-5687	460	10	fractional	fractional	ADJ
ejpam-5687	460	11	piecewise	piecewise	NOUN
ejpam-5687	460	12	derivative	derivative	NOUN
ejpam-5687	460	13	.	.	PUNCT
ejpam-5687	460	14	symmetry	symmetry	PROPN
ejpam-5687	460	15	,	,	PUNCT
ejpam-5687	460	16	15(8):1537	15(8):1537	NUM
ejpam-5687	460	17	,	,	PUNCT
ejpam-5687	460	18	2023	2023	NUM
ejpam-5687	460	19	.	.	PUNCT
ejpam-5687	461	1	[	[	X
ejpam-5687	461	2	28	28	NUM
ejpam-5687	461	3	]	]	X
ejpam-5687	461	4	rashid	rashid	PROPN
ejpam-5687	461	5	jan	jan	PROPN
ejpam-5687	461	6	,	,	PUNCT
ejpam-5687	461	7	muhammad	muhammad	PROPN
ejpam-5687	461	8	altaf	altaf	PROPN
ejpam-5687	461	9	khan	khan	PROPN
ejpam-5687	461	10	,	,	PUNCT
ejpam-5687	461	11	poom	poom	NOUN
ejpam-5687	461	12	kumam	kumam	NOUN
ejpam-5687	461	13	,	,	PUNCT
ejpam-5687	461	14	and	and	CCONJ
ejpam-5687	461	15	phatiphat	phatiphat	PRON
ejpam-5687	461	16	thounthong	thounthong	NOUN
ejpam-5687	461	17	.	.	PUNCT
ejpam-5687	462	1	modeling	model	VERB
ejpam-5687	462	2	the	the	DET
ejpam-5687	462	3	transmission	transmission	NOUN
ejpam-5687	462	4	of	of	ADP
ejpam-5687	462	5	dengue	dengue	NOUN
ejpam-5687	462	6	infection	infection	NOUN
ejpam-5687	462	7	through	through	ADP
ejpam-5687	462	8	fractional	fractional	ADJ
ejpam-5687	462	9	derivatives	derivative	NOUN
ejpam-5687	462	10	.	.	PUNCT
ejpam-5687	463	1	chaos	chaos	NOUN
ejpam-5687	463	2	,	,	PUNCT
ejpam-5687	463	3	solitons	soliton	NOUN
ejpam-5687	463	4	&	&	CCONJ
ejpam-5687	463	5	fractals	fractal	NOUN
ejpam-5687	463	6	,	,	PUNCT
ejpam-5687	463	7	127:189–216	127:189–216	NUM
ejpam-5687	463	8	,	,	PUNCT
ejpam-5687	463	9	2019	2019	NUM
ejpam-5687	463	10	.	.	PUNCT
ejpam-5687	464	1	[	[	X
ejpam-5687	464	2	29	29	NUM
ejpam-5687	464	3	]	]	X
ejpam-5687	464	4	nicolae	nicolae	PROPN
ejpam-5687	464	5	grigore	grigore	PROPN
ejpam-5687	464	6	,	,	PUNCT
ejpam-5687	464	7	maria	maria	PROPN
ejpam-5687	464	8	totan	totan	PROPN
ejpam-5687	464	9	,	,	PUNCT
ejpam-5687	464	10	valentin	valentin	PROPN
ejpam-5687	464	11	pirvut	pirvut	ADJ
ejpam-5687	464	12	,	,	PUNCT
ejpam-5687	464	13	sebastian	sebastian	PROPN
ejpam-5687	464	14	ioan	ioan	PROPN
ejpam-5687	464	15	cernusca	cernusca	PROPN
ejpam-5687	464	16	mitariu	mitariu	PROPN
ejpam-5687	464	17	,	,	PUNCT
ejpam-5687	464	18	radu	radu	PROPN
ejpam-5687	464	19	chicea	chicea	PROPN
ejpam-5687	464	20	,	,	PUNCT
ejpam-5687	464	21	mihai	mihai	PROPN
ejpam-5687	464	22	sava	sava	PROPN
ejpam-5687	464	23	,	,	PUNCT
ejpam-5687	464	24	and	and	CCONJ
ejpam-5687	464	25	adrian	adrian	PROPN
ejpam-5687	464	26	hasegan	hasegan	PROPN
ejpam-5687	464	27	.	.	PUNCT
ejpam-5687	465	1	a	a	DET
ejpam-5687	465	2	risk	risk	NOUN
ejpam-5687	465	3	assessment	assessment	NOUN
ejpam-5687	465	4	of	of	ADP
ejpam-5687	465	5	clostridium	clostridium	NOUN
ejpam-5687	465	6	difficile	difficile	ADJ
ejpam-5687	465	7	infection	infection	NOUN
ejpam-5687	465	8	after	after	ADP
ejpam-5687	465	9	antibiotherapy	antibiotherapy	NOUN
ejpam-5687	465	10	for	for	ADP
ejpam-5687	465	11	urinary	urinary	ADJ
ejpam-5687	465	12	tract	tract	NOUN
ejpam-5687	465	13	infections	infection	NOUN
ejpam-5687	465	14	in	in	ADP
ejpam-5687	465	15	the	the	DET
ejpam-5687	465	16	n.	n.	PROPN
ejpam-5687	465	17	ullah	ullah	PROPN
ejpam-5687	465	18	et	et	PROPN
ejpam-5687	465	19	al	al	PROPN
ejpam-5687	465	20	.	.	PUNCT
ejpam-5687	465	21	/	/	SYM
ejpam-5687	465	22	eur	eur	PROPN
ejpam-5687	465	23	.	.	PUNCT
ejpam-5687	466	1	j.	j.	PROPN
ejpam-5687	466	2	pure	pure	PROPN
ejpam-5687	466	3	appl	appl	PROPN
ejpam-5687	466	4	.	.	PROPN
ejpam-5687	466	5	math	math	PROPN
ejpam-5687	466	6	,	,	PUNCT
ejpam-5687	466	7	18	18	NUM
ejpam-5687	466	8	(	(	PUNCT
ejpam-5687	466	9	2	2	NUM
ejpam-5687	466	10	)	)	PUNCT
ejpam-5687	466	11	(	(	PUNCT
ejpam-5687	466	12	2025	2025	NUM
ejpam-5687	466	13	)	)	PUNCT
ejpam-5687	466	14	,	,	PUNCT
ejpam-5687	466	15	5687	5687	NUM
ejpam-5687	466	16	25	25	NUM
ejpam-5687	466	17	of	of	ADP
ejpam-5687	466	18	25	25	NUM
ejpam-5687	466	19	urology	urology	NOUN
ejpam-5687	466	20	department	department	NOUN
ejpam-5687	466	21	for	for	ADP
ejpam-5687	466	22	hospitalized	hospitalize	VERB
ejpam-5687	466	23	patients	patient	NOUN
ejpam-5687	466	24	.	.	PUNCT
ejpam-5687	467	1	rev	rev	PROPN
ejpam-5687	467	2	.	.	PUNCT
ejpam-5687	468	1	chim	chim	PROPN
ejpam-5687	468	2	,	,	PUNCT
ejpam-5687	468	3	68:1453–1456	68:1453–1456	PROPN
ejpam-5687	468	4	,	,	PUNCT
ejpam-5687	468	5	2017	2017	NUM
ejpam-5687	468	6	.	.	PUNCT
ejpam-5687	469	1	[	[	X
ejpam-5687	469	2	30	30	NUM
ejpam-5687	469	3	]	]	X
ejpam-5687	469	4	ionela	ionela	PROPN
ejpam-5687	469	5	mihai	mihai	PROPN
ejpam-5687	469	6	,	,	PUNCT
ejpam-5687	469	7	adrian	adrian	PROPN
ejpam-5687	469	8	boicean	boicean	PROPN
ejpam-5687	469	9	,	,	PUNCT
ejpam-5687	469	10	cosmin	cosmin	PROPN
ejpam-5687	469	11	adrian	adrian	PROPN
ejpam-5687	469	12	teodoru	teodoru	PROPN
ejpam-5687	469	13	,	,	PUNCT
ejpam-5687	469	14	nicolae	nicolae	PROPN
ejpam-5687	469	15	grigore	grigore	PROPN
ejpam-5687	469	16	,	,	PUNCT
ejpam-5687	469	17	gabriela	gabriela	PROPN
ejpam-5687	469	18	mariana	mariana	PROPN
ejpam-5687	469	19	iancu	iancu	PROPN
ejpam-5687	469	20	,	,	PUNCT
ejpam-5687	469	21	horatiu	horatiu	NOUN
ejpam-5687	469	22	dura	dura	PROPN
ejpam-5687	469	23	,	,	PUNCT
ejpam-5687	469	24	dan	dan	PROPN
ejpam-5687	469	25	georgian	georgian	PROPN
ejpam-5687	469	26	bratu	bratu	PROPN
ejpam-5687	469	27	,	,	PUNCT
ejpam-5687	469	28	mihai	mihai	PROPN
ejpam-5687	469	29	dan	dan	PROPN
ejpam-5687	469	30	roman	roman	PROPN
ejpam-5687	469	31	,	,	PUNCT
ejpam-5687	469	32	cosmin	cosmin	PROPN
ejpam-5687	469	33	ioan	ioan	PROPN
ejpam-5687	469	34	mohor	mohor	PROPN
ejpam-5687	469	35	,	,	PUNCT
ejpam-5687	469	36	samuel	samuel	PROPN
ejpam-5687	469	37	bogdan	bogdan	PROPN
ejpam-5687	469	38	todor	todor	PROPN
ejpam-5687	469	39	,	,	PUNCT
ejpam-5687	469	40	et	et	PROPN
ejpam-5687	469	41	al	al	PROPN
ejpam-5687	469	42	.	.	PROPN
ejpam-5687	469	43	laparoscopic	laparoscopic	PROPN
ejpam-5687	469	44	adrenalectomy	adrenalectomy	NOUN
ejpam-5687	469	45	:	:	PUNCT
ejpam-5687	469	46	tailoring	tailor	VERB
ejpam-5687	469	47	approaches	approach	NOUN
ejpam-5687	469	48	for	for	ADP
ejpam-5687	469	49	the	the	DET
ejpam-5687	469	50	optimal	optimal	ADJ
ejpam-5687	469	51	resection	resection	NOUN
ejpam-5687	469	52	of	of	ADP
ejpam-5687	469	53	adrenal	adrenal	ADJ
ejpam-5687	469	54	tumors	tumor	NOUN
ejpam-5687	469	55	.	.	PUNCT
ejpam-5687	470	1	diagnostics	diagnostic	NOUN
ejpam-5687	470	2	,	,	PUNCT
ejpam-5687	470	3	13(21):3351	13(21):3351	NUM
ejpam-5687	470	4	,	,	PUNCT
ejpam-5687	470	5	2023	2023	NUM
ejpam-5687	470	6	.	.	PUNCT
ejpam-5687	471	1	[	[	X
ejpam-5687	471	2	31	31	NUM
ejpam-5687	471	3	]	]	PUNCT
ejpam-5687	471	4	ionela	ionela	PROPN
ejpam-5687	471	5	mihai	mihai	PROPN
ejpam-5687	471	6	,	,	PUNCT
ejpam-5687	471	7	horatiu	horatiu	NOUN
ejpam-5687	471	8	dura	dura	NOUN
ejpam-5687	471	9	,	,	PUNCT
ejpam-5687	471	10	cosmin	cosmin	PROPN
ejpam-5687	471	11	adrian	adrian	PROPN
ejpam-5687	471	12	teodoru	teodoru	PROPN
ejpam-5687	471	13	,	,	PUNCT
ejpam-5687	471	14	samuel	samuel	PROPN
ejpam-5687	471	15	bogdan	bogdan	PROPN
ejpam-5687	471	16	todor	todor	PROPN
ejpam-5687	471	17	,	,	PUNCT
ejpam-5687	471	18	cristian	cristian	PROPN
ejpam-5687	471	19	ichim	ichim	PROPN
ejpam-5687	471	20	,	,	PUNCT
ejpam-5687	471	21	nicolae	nicolae	PROPN
ejpam-5687	471	22	grigore	grigore	PROPN
ejpam-5687	471	23	,	,	PUNCT
ejpam-5687	471	24	cosmin	cosmin	PROPN
ejpam-5687	471	25	ioan	ioan	PROPN
ejpam-5687	471	26	mohor	mohor	PROPN
ejpam-5687	471	27	,	,	PUNCT
ejpam-5687	471	28	alin	alin	PROPN
ejpam-5687	471	29	mihetiu	mihetiu	PROPN
ejpam-5687	471	30	,	,	PUNCT
ejpam-5687	471	31	george	george	PROPN
ejpam-5687	471	32	oprinca	oprinca	PROPN
ejpam-5687	471	33	,	,	PUNCT
ejpam-5687	471	34	nicolae	nicolae	PROPN
ejpam-5687	471	35	bacalbasa	bacalbasa	PROPN
ejpam-5687	471	36	,	,	PUNCT
ejpam-5687	471	37	et	et	PROPN
ejpam-5687	471	38	al	al	PROPN
ejpam-5687	471	39	.	.	PROPN
ejpam-5687	471	40	intraoperative	intraoperative	PROPN
ejpam-5687	471	41	ultrasound	ultrasound	PROPN
ejpam-5687	471	42	:	:	PUNCT
ejpam-5687	471	43	bridging	bridge	VERB
ejpam-5687	471	44	the	the	DET
ejpam-5687	471	45	gap	gap	NOUN
ejpam-5687	471	46	between	between	ADP
ejpam-5687	471	47	laparoscopy	laparoscopy	NOUN
ejpam-5687	471	48	and	and	CCONJ
ejpam-5687	471	49	surgical	surgical	ADJ
ejpam-5687	471	50	precision	precision	NOUN
ejpam-5687	471	51	during	during	ADP
ejpam-5687	471	52	3d	3d	NUM
ejpam-5687	471	53	laparoscopic	laparoscopic	ADJ
ejpam-5687	471	54	partial	partial	ADJ
ejpam-5687	471	55	nephrectomies	nephrectomy	NOUN
ejpam-5687	471	56	.	.	PUNCT
ejpam-5687	472	1	diagnostics	diagnostic	NOUN
ejpam-5687	472	2	,	,	PUNCT
ejpam-5687	472	3	14(9):942	14(9):942	NUM
ejpam-5687	472	4	,	,	PUNCT
ejpam-5687	472	5	2024	2024	NUM
ejpam-5687	472	6	.	.	PUNCT
ejpam-5687	473	1	[	[	X
ejpam-5687	473	2	32	32	NUM
ejpam-5687	473	3	]	]	X
ejpam-5687	473	4	adrian	adrian	PROPN
ejpam-5687	473	5	ha?egan	ha?egan	PROPN
ejpam-5687	473	6	,	,	PUNCT
ejpam-5687	473	7	ionela	ionela	PROPN
ejpam-5687	473	8	mihai	mihai	PROPN
ejpam-5687	473	9	,	,	PUNCT
ejpam-5687	473	10	cosmin	cosmin	PROPN
ejpam-5687	473	11	adrian	adrian	PROPN
ejpam-5687	473	12	teodoru	teodoru	PROPN
ejpam-5687	473	13	,	,	PUNCT
ejpam-5687	473	14	ioana	ioana	PROPN
ejpam-5687	473	15	bogdan	bogdan	PROPN
ejpam-5687	473	16	matacuta	matacuta	PROPN
ejpam-5687	473	17	,	,	PUNCT
ejpam-5687	473	18	hora?iu	hora?iu	X
ejpam-5687	473	19	dura	dura	PROPN
ejpam-5687	473	20	,	,	PUNCT
ejpam-5687	473	21	samuel	samuel	PROPN
ejpam-5687	473	22	bogdan	bogdan	PROPN
ejpam-5687	473	23	todor	todor	PROPN
ejpam-5687	473	24	,	,	PUNCT
ejpam-5687	473	25	cristian	cristian	PROPN
ejpam-5687	473	26	ichim	ichim	PROPN
ejpam-5687	473	27	,	,	PUNCT
ejpam-5687	473	28	denisa	denisa	NOUN
ejpam-5687	473	29	tanasescu	tanasescu	NOUN
ejpam-5687	473	30	,	,	PUNCT
ejpam-5687	473	31	nicolae	nicolae	PROPN
ejpam-5687	473	32	grigore	grigore	PROPN
ejpam-5687	473	33	,	,	PUNCT
ejpam-5687	473	34	ciprian	ciprian	PROPN
ejpam-5687	473	35	nicolae	nicolae	PROPN
ejpam-5687	473	36	bolca	bolca	PROPN
ejpam-5687	473	37	,	,	PUNCT
ejpam-5687	473	38	et	et	PROPN
ejpam-5687	473	39	al	al	PROPN
ejpam-5687	473	40	.	.	PUNCT
ejpam-5687	473	41	exploring	explore	VERB
ejpam-5687	473	42	the	the	DET
ejpam-5687	473	43	challenges	challenge	NOUN
ejpam-5687	473	44	of	of	ADP
ejpam-5687	473	45	using	use	VERB
ejpam-5687	473	46	minimal	minimal	ADJ
ejpam-5687	473	47	invasive	invasive	ADJ
ejpam-5687	473	48	surgery	surgery	NOUN
ejpam-5687	473	49	to	to	PART
ejpam-5687	473	50	treat	treat	VERB
ejpam-5687	473	51	stress	stress	ADJ
ejpam-5687	473	52	urinary	urinary	ADJ
ejpam-5687	473	53	incontinence	incontinence	NOUN
ejpam-5687	473	54	:	:	PUNCT
ejpam-5687	474	1	insights	insight	NOUN
ejpam-5687	474	2	from	from	ADP
ejpam-5687	474	3	a	a	DET
ejpam-5687	474	4	retrospective	retrospective	ADJ
ejpam-5687	474	5	case	case	NOUN
ejpam-5687	474	6	-	-	PUNCT
ejpam-5687	474	7	control	control	NOUN
ejpam-5687	474	8	study	study	NOUN
ejpam-5687	474	9	.	.	PUNCT
ejpam-5687	475	1	diagnostics	diagnostic	NOUN
ejpam-5687	475	2	,	,	PUNCT
ejpam-5687	475	3	14(3):323	14(3):323	NUM
ejpam-5687	475	4	,	,	PUNCT
ejpam-5687	475	5	2024	2024	NUM
ejpam-5687	475	6	.	.	PUNCT
ejpam-5687	476	1	[	[	X
ejpam-5687	476	2	33	33	NUM
ejpam-5687	476	3	]	]	X
ejpam-5687	476	4	tao	tao	PROPN
ejpam-5687	476	5	-	-	PUNCT
ejpam-5687	476	6	qian	qian	PROPN
ejpam-5687	476	7	tang	tang	PROPN
ejpam-5687	476	8	,	,	PUNCT
ejpam-5687	476	9	rashid	rashid	PROPN
ejpam-5687	476	10	jan	jan	PROPN
ejpam-5687	476	11	,	,	PUNCT
ejpam-5687	476	12	ziad	ziad	PROPN
ejpam-5687	476	13	ur	ur	PROPN
ejpam-5687	476	14	rehman	rehman	PROPN
ejpam-5687	476	15	,	,	PUNCT
ejpam-5687	476	16	zahir	zahir	ADJ
ejpam-5687	476	17	shah	shah	NOUN
ejpam-5687	476	18	,	,	PUNCT
ejpam-5687	476	19	narcisa	narcisa	NOUN
ejpam-5687	476	20	vrinceanu	vrinceanu	NOUN
ejpam-5687	476	21	,	,	PUNCT
ejpam-5687	476	22	and	and	CCONJ
ejpam-5687	476	23	mihaela	mihaela	PROPN
ejpam-5687	476	24	racheriu	racheriu	NOUN
ejpam-5687	476	25	.	.	PUNCT
ejpam-5687	477	1	modeling	model	VERB
ejpam-5687	477	2	the	the	DET
ejpam-5687	477	3	dynamics	dynamic	NOUN
ejpam-5687	477	4	of	of	ADP
ejpam-5687	477	5	chronic	chronic	ADJ
ejpam-5687	477	6	myelogenous	myelogenous	ADJ
ejpam-5687	477	7	leukemia	leukemia	NOUN
ejpam-5687	477	8	through	through	ADP
ejpam-5687	477	9	fractional	fractional	ADJ
ejpam-5687	477	10	-	-	PUNCT
ejpam-5687	477	11	calculus	calculus	NOUN
ejpam-5687	477	12	.	.	PUNCT
ejpam-5687	478	1	fractals	fractal	NOUN
ejpam-5687	478	2	,	,	PUNCT
ejpam-5687	478	3	30(10):2240262	30(10):2240262	NUM
ejpam-5687	478	4	,	,	PUNCT
ejpam-5687	478	5	2022	2022	NUM
ejpam-5687	478	6	.	.	PUNCT
ejpam-5687	479	1	[	[	X
ejpam-5687	479	2	34	34	NUM
ejpam-5687	479	3	]	]	X
ejpam-5687	479	4	sultan	sultan	PROPN
ejpam-5687	479	5	alyobi	alyobi	PROPN
ejpam-5687	479	6	and	and	CCONJ
ejpam-5687	479	7	rashid	rashid	PROPN
ejpam-5687	479	8	jan	jan	PROPN
ejpam-5687	479	9	.	.	PROPN
ejpam-5687	479	10	qualitative	qualitative	PROPN
ejpam-5687	479	11	and	and	CCONJ
ejpam-5687	479	12	quantitative	quantitative	ADJ
ejpam-5687	479	13	analysis	analysis	NOUN
ejpam-5687	479	14	of	of	ADP
ejpam-5687	479	15	fractional	fractional	ADJ
ejpam-5687	479	16	dynamics	dynamic	NOUN
ejpam-5687	479	17	of	of	ADP
ejpam-5687	479	18	infectious	infectious	ADJ
ejpam-5687	479	19	diseases	disease	NOUN
ejpam-5687	479	20	with	with	ADP
ejpam-5687	479	21	control	control	NOUN
ejpam-5687	479	22	measures	measure	NOUN
ejpam-5687	479	23	.	.	PUNCT
ejpam-5687	480	1	fractal	fractal	ADJ
ejpam-5687	480	2	and	and	CCONJ
ejpam-5687	480	3	fractional	fractional	ADJ
ejpam-5687	480	4	,	,	PUNCT
ejpam-5687	480	5	7(5):400	7(5):400	NUM
ejpam-5687	480	6	,	,	PUNCT
ejpam-5687	480	7	2023	2023	NUM
ejpam-5687	480	8	.	.	PUNCT
ejpam-5687	481	1	[	[	X
ejpam-5687	481	2	35	35	NUM
ejpam-5687	481	3	]	]	X
ejpam-5687	481	4	jennifer	jennifer	PROPN
ejpam-5687	481	5	bravo	bravo	PROPN
ejpam-5687	481	6	and	and	CCONJ
ejpam-5687	481	7	carlos	carlos	PROPN
ejpam-5687	481	8	lizama	lizama	PROPN
ejpam-5687	481	9	.	.	PUNCT
ejpam-5687	482	1	the	the	DET
ejpam-5687	482	2	abstract	abstract	ADJ
ejpam-5687	482	3	cauchy	cauchy	PROPN
ejpam-5687	482	4	problem	problem	NOUN
ejpam-5687	482	5	with	with	ADP
ejpam-5687	482	6	caputo	caputo	PROPN
ejpam-5687	482	7	–	–	PUNCT
ejpam-5687	482	8	fabrizio	fabrizio	PROPN
ejpam-5687	482	9	fractional	fractional	ADJ
ejpam-5687	482	10	derivative	derivative	NOUN
ejpam-5687	482	11	.	.	PUNCT
ejpam-5687	483	1	mathematics	mathematic	NOUN
ejpam-5687	483	2	,	,	PUNCT
ejpam-5687	483	3	10(19):3540	10(19):3540	NUM
ejpam-5687	483	4	,	,	PUNCT
ejpam-5687	483	5	2022	2022	NUM
ejpam-5687	483	6	.	.	PUNCT
ejpam-5687	484	1	[	[	X
ejpam-5687	484	2	36	36	NUM
ejpam-5687	484	3	]	]	X
ejpam-5687	484	4	muhammad	muhammad	PROPN
ejpam-5687	484	5	farhan	farhan	PROPN
ejpam-5687	484	6	,	,	PUNCT
ejpam-5687	484	7	zahir	zahir	ADJ
ejpam-5687	484	8	shah	shah	NOUN
ejpam-5687	484	9	,	,	PUNCT
ejpam-5687	484	10	rashid	rashid	PROPN
ejpam-5687	484	11	jan	jan	PROPN
ejpam-5687	484	12	,	,	PUNCT
ejpam-5687	484	13	and	and	CCONJ
ejpam-5687	484	14	saeed	saeed	PROPN
ejpam-5687	484	15	islam	islam	PROPN
ejpam-5687	484	16	.	.	PUNCT
ejpam-5687	485	1	a	a	DET
ejpam-5687	485	2	fractional	fractional	ADJ
ejpam-5687	485	3	modeling	modeling	NOUN
ejpam-5687	485	4	approach	approach	NOUN
ejpam-5687	485	5	of	of	ADP
ejpam-5687	485	6	buruli	buruli	ADJ
ejpam-5687	485	7	ulcer	ulcer	NOUN
ejpam-5687	485	8	in	in	ADP
ejpam-5687	485	9	possum	possum	NOUN
ejpam-5687	485	10	mammals	mammal	NOUN
ejpam-5687	485	11	.	.	PUNCT
ejpam-5687	486	1	physica	physica	PROPN
ejpam-5687	486	2	scripta	scripta	PROPN
ejpam-5687	486	3	,	,	PUNCT
ejpam-5687	486	4	98(6):065219	98(6):065219	NUM
ejpam-5687	486	5	,	,	PUNCT
ejpam-5687	486	6	2023	2023	NUM
ejpam-5687	486	7	.	.	PUNCT