id	sid	tid	token	lemma	pos
ejpam-6776	1	1	european	european	PROPN
ejpam-6776	1	2	journal	journal	PROPN
ejpam-6776	1	3	of	of	ADP
ejpam-6776	1	4	pure	pure	ADJ
ejpam-6776	1	5	and	and	CCONJ
ejpam-6776	1	6	applied	applied	ADJ
ejpam-6776	1	7	mathematics	mathematic	NOUN
ejpam-6776	1	8	2025	2025	NUM
ejpam-6776	1	9	,	,	PUNCT
ejpam-6776	1	10	vol	vol	NOUN
ejpam-6776	1	11	.	.	PROPN
ejpam-6776	1	12	18	18	NUM
ejpam-6776	1	13	,	,	PUNCT
ejpam-6776	1	14	issue	issue	NOUN
ejpam-6776	1	15	4	4	NUM
ejpam-6776	1	16	,	,	PUNCT
ejpam-6776	1	17	article	article	NOUN
ejpam-6776	1	18	number	number	NOUN
ejpam-6776	1	19	6776	6776	NUM
ejpam-6776	1	20	issn	issn	VERB
ejpam-6776	1	21	1307	1307	NUM
ejpam-6776	1	22	-	-	SYM
ejpam-6776	1	23	5543	5543	NUM
ejpam-6776	1	24	–	–	PUNCT
ejpam-6776	1	25	ejpam.com	ejpam.com	X
ejpam-6776	1	26	published	publish	VERB
ejpam-6776	1	27	by	by	ADP
ejpam-6776	1	28	new	new	PROPN
ejpam-6776	1	29	york	york	PROPN
ejpam-6776	1	30	business	business	PROPN
ejpam-6776	1	31	global	global	ADJ
ejpam-6776	1	32	stochastic	stochastic	ADJ
ejpam-6776	1	33	dynamics	dynamic	NOUN
ejpam-6776	1	34	of	of	ADP
ejpam-6776	1	35	epidemic	epidemic	NOUN
ejpam-6776	1	36	models	model	NOUN
ejpam-6776	1	37	with	with	ADP
ejpam-6776	1	38	resource	resource	NOUN
ejpam-6776	1	39	constraints	constraint	NOUN
ejpam-6776	1	40	:	:	PUNCT
ejpam-6776	1	41	extinction	extinction	NOUN
ejpam-6776	1	42	and	and	CCONJ
ejpam-6776	1	43	ergodicity	ergodicity	PROPN
ejpam-6776	1	44	j.	j.	PROPN
ejpam-6776	1	45	leo	leo	PROPN
ejpam-6776	1	46	amalraj1	amalraj1	PROPN
ejpam-6776	1	47	,	,	PUNCT
ejpam-6776	1	48	manivannan	manivannan	NOUN
ejpam-6776	1	49	balamurugan2	balamurugan2	PROPN
ejpam-6776	1	50	,	,	PUNCT
ejpam-6776	1	51	pankaj	pankaj	PROPN
ejpam-6776	1	52	shukla3	shukla3	PROPN
ejpam-6776	1	53	,	,	PUNCT
ejpam-6776	1	54	m.	m.	NOUN
ejpam-6776	1	55	v.	v.	ADP
ejpam-6776	1	56	rajesh4	rajesh4	NOUN
ejpam-6776	1	57	,	,	PUNCT
ejpam-6776	1	58	n.	n.	NOUN
ejpam-6776	1	59	avinash5	avinash5	PROPN
ejpam-6776	1	60	,	,	PUNCT
ejpam-6776	1	61	vediyappan	vediyappan	ADJ
ejpam-6776	1	62	govindan6	govindan6	PROPN
ejpam-6776	1	63	,	,	PUNCT
ejpam-6776	1	64	siriluk	siriluk	NOUN
ejpam-6776	1	65	donganont7,∗	donganont7,∗	ADJ
ejpam-6776	1	66	1	1	NUM
ejpam-6776	1	67	department	department	NOUN
ejpam-6776	1	68	of	of	ADP
ejpam-6776	1	69	mathematics	mathematic	NOUN
ejpam-6776	1	70	,	,	PUNCT
ejpam-6776	1	71	rmk	rmk	PROPN
ejpam-6776	1	72	college	college	PROPN
ejpam-6776	1	73	of	of	ADP
ejpam-6776	1	74	engineering	engineering	NOUN
ejpam-6776	1	75	and	and	CCONJ
ejpam-6776	1	76	technology	technology	NOUN
ejpam-6776	1	77	,	,	PUNCT
ejpam-6776	1	78	puduvoyal	puduvoyal	ADJ
ejpam-6776	1	79	,	,	PUNCT
ejpam-6776	1	80	thiruvallur	thiruvallur	NOUN
ejpam-6776	1	81	,	,	PUNCT
ejpam-6776	1	82	tamil	tamil	PROPN
ejpam-6776	1	83	nadu	nadu	PROPN
ejpam-6776	1	84	,	,	PUNCT
ejpam-6776	1	85	india	india	PROPN
ejpam-6776	1	86	2	2	NUM
ejpam-6776	1	87	department	department	NOUN
ejpam-6776	1	88	of	of	ADP
ejpam-6776	1	89	mathematics	mathematic	NOUN
ejpam-6776	1	90	,	,	PUNCT
ejpam-6776	1	91	vel	vel	PROPN
ejpam-6776	1	92	tech	tech	PROPN
ejpam-6776	1	93	rangarajan	rangarajan	PROPN
ejpam-6776	1	94	dr	dr	PROPN
ejpam-6776	1	95	.	.	PROPN
ejpam-6776	1	96	sagunthala	sagunthala	PROPN
ejpam-6776	1	97	r&d	r&d	PROPN
ejpam-6776	1	98	institute	institute	PROPN
ejpam-6776	1	99	of	of	ADP
ejpam-6776	1	100	science	science	NOUN
ejpam-6776	1	101	and	and	CCONJ
ejpam-6776	1	102	technology	technology	NOUN
ejpam-6776	1	103	,	,	PUNCT
ejpam-6776	1	104	chennai	chennai	VERB
ejpam-6776	1	105	600	600	NUM
ejpam-6776	1	106	062	062	NUM
ejpam-6776	1	107	,	,	PUNCT
ejpam-6776	1	108	tamil	tamil	PROPN
ejpam-6776	1	109	nadu	nadu	PROPN
ejpam-6776	1	110	,	,	PUNCT
ejpam-6776	1	111	india	india	PROPN
ejpam-6776	1	112	3	3	NUM
ejpam-6776	1	113	department	department	PROPN
ejpam-6776	1	114	of	of	ADP
ejpam-6776	1	115	mathematics	mathematic	NOUN
ejpam-6776	1	116	,	,	PUNCT
ejpam-6776	1	117	school	school	NOUN
ejpam-6776	1	118	of	of	ADP
ejpam-6776	1	119	advanced	advanced	ADJ
ejpam-6776	1	120	sciences	science	NOUN
ejpam-6776	1	121	,	,	PUNCT
ejpam-6776	1	122	vellore	vellore	PROPN
ejpam-6776	1	123	institute	institute	PROPN
ejpam-6776	1	124	of	of	ADP
ejpam-6776	1	125	technology	technology	PROPN
ejpam-6776	1	126	,	,	PUNCT
ejpam-6776	1	127	chennai	chennai	PROPN
ejpam-6776	1	128	,	,	PUNCT
ejpam-6776	1	129	tamil	tamil	PROPN
ejpam-6776	1	130	nadu	nadu	PROPN
ejpam-6776	1	131	,	,	PUNCT
ejpam-6776	1	132	india	india	PROPN
ejpam-6776	1	133	4	4	NUM
ejpam-6776	1	134	department	department	NOUN
ejpam-6776	1	135	of	of	ADP
ejpam-6776	1	136	information	information	NOUN
ejpam-6776	1	137	technology	technology	NOUN
ejpam-6776	1	138	,	,	PUNCT
ejpam-6776	1	139	aditya	aditya	PROPN
ejpam-6776	1	140	university	university	PROPN
ejpam-6776	1	141	,	,	PUNCT
ejpam-6776	1	142	surampalem	surampalem	NOUN
ejpam-6776	1	143	,	,	PUNCT
ejpam-6776	1	144	india	india	PROPN
ejpam-6776	1	145	5	5	NUM
ejpam-6776	1	146	department	department	NOUN
ejpam-6776	1	147	of	of	ADP
ejpam-6776	1	148	mathematics	mathematic	NOUN
ejpam-6776	1	149	,	,	PUNCT
ejpam-6776	1	150	sacred	sacred	ADJ
ejpam-6776	1	151	heart	heart	NOUN
ejpam-6776	1	152	college	college	NOUN
ejpam-6776	1	153	(	(	PUNCT
ejpam-6776	1	154	autonomous	autonomous	ADJ
ejpam-6776	1	155	)	)	PUNCT
ejpam-6776	1	156	,	,	PUNCT
ejpam-6776	1	157	tirupattur	tirupattur	VERB
ejpam-6776	1	158	635	635	NUM
ejpam-6776	1	159	601	601	NUM
ejpam-6776	1	160	,	,	PUNCT
ejpam-6776	1	161	tamil	tamil	PROPN
ejpam-6776	1	162	nadu	nadu	PROPN
ejpam-6776	1	163	,	,	PUNCT
ejpam-6776	1	164	india	india	PROPN
ejpam-6776	1	165	6	6	NUM
ejpam-6776	1	166	department	department	NOUN
ejpam-6776	1	167	of	of	ADP
ejpam-6776	1	168	mathematics	mathematic	NOUN
ejpam-6776	1	169	,	,	PUNCT
ejpam-6776	1	170	hindustan	hindustan	PROPN
ejpam-6776	1	171	institute	institute	PROPN
ejpam-6776	1	172	of	of	ADP
ejpam-6776	1	173	technology	technology	PROPN
ejpam-6776	1	174	and	and	CCONJ
ejpam-6776	1	175	science	science	NOUN
ejpam-6776	1	176	,	,	PUNCT
ejpam-6776	1	177	chennai	chennai	PROPN
ejpam-6776	1	178	,	,	PUNCT
ejpam-6776	1	179	tamil	tamil	PROPN
ejpam-6776	1	180	nadu	nadu	PROPN
ejpam-6776	1	181	,	,	PUNCT
ejpam-6776	1	182	india	india	PROPN
ejpam-6776	1	183	7	7	NUM
ejpam-6776	1	184	school	school	NOUN
ejpam-6776	1	185	of	of	ADP
ejpam-6776	1	186	science	science	NOUN
ejpam-6776	1	187	,	,	PUNCT
ejpam-6776	1	188	university	university	NOUN
ejpam-6776	1	189	of	of	ADP
ejpam-6776	1	190	phayao	phayao	NOUN
ejpam-6776	1	191	,	,	PUNCT
ejpam-6776	1	192	phayao	phayao	NOUN
ejpam-6776	1	193	56000	56000	NUM
ejpam-6776	1	194	,	,	PUNCT
ejpam-6776	1	195	thailand	thailand	PROPN
ejpam-6776	1	196	abstract	abstract	PROPN
ejpam-6776	1	197	.	.	PUNCT
ejpam-6776	2	1	recent	recent	ADJ
ejpam-6776	2	2	studies	study	NOUN
ejpam-6776	2	3	highlight	highlight	VERB
ejpam-6776	2	4	how	how	SCONJ
ejpam-6776	2	5	stochastic	stochastic	ADJ
ejpam-6776	2	6	effects	effect	NOUN
ejpam-6776	2	7	,	,	PUNCT
ejpam-6776	2	8	such	such	ADJ
ejpam-6776	2	9	as	as	ADP
ejpam-6776	2	10	environmental	environmental	ADJ
ejpam-6776	2	11	noise	noise	NOUN
ejpam-6776	2	12	and	and	CCONJ
ejpam-6776	2	13	resource	resource	NOUN
ejpam-6776	2	14	constraints	constraint	NOUN
ejpam-6776	2	15	,	,	PUNCT
ejpam-6776	2	16	alter	alter	VERB
ejpam-6776	2	17	epidemic	epidemic	NOUN
ejpam-6776	2	18	dynamics	dynamic	NOUN
ejpam-6776	2	19	,	,	PUNCT
ejpam-6776	2	20	diverging	diverge	VERB
ejpam-6776	2	21	from	from	ADP
ejpam-6776	2	22	deterministic	deterministic	ADJ
ejpam-6776	2	23	predictions	prediction	NOUN
ejpam-6776	2	24	.	.	PUNCT
ejpam-6776	3	1	unlike	unlike	ADP
ejpam-6776	3	2	classical	classical	ADJ
ejpam-6776	3	3	deterministic	deterministic	ADJ
ejpam-6776	3	4	models	model	NOUN
ejpam-6776	3	5	that	that	PRON
ejpam-6776	3	6	exhibit	exhibit	VERB
ejpam-6776	3	7	backward	backward	ADJ
ejpam-6776	3	8	and	and	CCONJ
ejpam-6776	3	9	hopf	hopf	ADJ
ejpam-6776	3	10	bifurcations	bifurcation	NOUN
ejpam-6776	3	11	,	,	PUNCT
ejpam-6776	3	12	stochastic	stochastic	ADJ
ejpam-6776	3	13	models	model	NOUN
ejpam-6776	3	14	incorporating	incorporate	VERB
ejpam-6776	3	15	white	white	ADJ
ejpam-6776	3	16	noise	noise	NOUN
ejpam-6776	3	17	perturbations	perturbation	NOUN
ejpam-6776	3	18	capture	capture	VERB
ejpam-6776	3	19	more	more	ADV
ejpam-6776	3	20	realistic	realistic	ADJ
ejpam-6776	3	21	outbreak	outbreak	NOUN
ejpam-6776	3	22	scenarios	scenario	NOUN
ejpam-6776	3	23	by	by	ADP
ejpam-6776	3	24	smoothing	smooth	VERB
ejpam-6776	3	25	transitions	transition	NOUN
ejpam-6776	3	26	and	and	CCONJ
ejpam-6776	3	27	expanding	expand	VERB
ejpam-6776	3	28	extinction	extinction	NOUN
ejpam-6776	3	29	regions	region	NOUN
ejpam-6776	3	30	.	.	PUNCT
ejpam-6776	4	1	this	this	DET
ejpam-6776	4	2	paper	paper	NOUN
ejpam-6776	4	3	analyzes	analyze	VERB
ejpam-6776	4	4	a	a	DET
ejpam-6776	4	5	stochastic	stochastic	ADJ
ejpam-6776	4	6	sir	sir	NOUN
ejpam-6776	4	7	model	model	NOUN
ejpam-6776	4	8	with	with	ADP
ejpam-6776	4	9	nonlinear	nonlinear	ADJ
ejpam-6776	4	10	incidence	incidence	NOUN
ejpam-6776	4	11	βsi	βsi	NOUN
ejpam-6776	4	12	1+ki	1+ki	NUM
ejpam-6776	4	13	,	,	PUNCT
ejpam-6776	4	14	limited	limited	ADJ
ejpam-6776	4	15	medical	medical	ADJ
ejpam-6776	4	16	resources	resource	NOUN
ejpam-6776	4	17	modeled	model	VERB
ejpam-6776	4	18	as	as	ADP
ejpam-6776	4	19	αi	αi	ADV
ejpam-6776	4	20	λ+i	λ+i	X
ejpam-6776	4	21	,	,	PUNCT
ejpam-6776	4	22	and	and	CCONJ
ejpam-6776	4	23	environmental	environmental	ADJ
ejpam-6776	4	24	noise	noise	NOUN
ejpam-6776	4	25	via	via	ADP
ejpam-6776	4	26	brownian	brownian	ADJ
ejpam-6776	4	27	motion	motion	NOUN
ejpam-6776	4	28	terms	term	NOUN
ejpam-6776	4	29	.	.	PUNCT
ejpam-6776	5	1	research	research	NOUN
ejpam-6776	5	2	suggests	suggest	VERB
ejpam-6776	5	3	that	that	SCONJ
ejpam-6776	5	4	limited	limited	ADJ
ejpam-6776	5	5	medical	medical	ADJ
ejpam-6776	5	6	resources	resource	NOUN
ejpam-6776	5	7	,	,	PUNCT
ejpam-6776	5	8	coupled	couple	VERB
ejpam-6776	5	9	with	with	ADP
ejpam-6776	5	10	stochastic	stochastic	ADJ
ejpam-6776	5	11	fluctuations	fluctuation	NOUN
ejpam-6776	5	12	,	,	PUNCT
ejpam-6776	5	13	significantly	significantly	ADV
ejpam-6776	5	14	influence	influence	NOUN
ejpam-6776	5	15	disease	disease	NOUN
ejpam-6776	5	16	spread	spread	VERB
ejpam-6776	5	17	,	,	PUNCT
ejpam-6776	5	18	persistence	persistence	NOUN
ejpam-6776	5	19	,	,	PUNCT
ejpam-6776	5	20	and	and	CCONJ
ejpam-6776	5	21	extinction	extinction	NOUN
ejpam-6776	5	22	conditions	condition	NOUN
ejpam-6776	5	23	,	,	PUNCT
ejpam-6776	5	24	as	as	SCONJ
ejpam-6776	5	25	governed	govern	VERB
ejpam-6776	5	26	by	by	ADP
ejpam-6776	5	27	a	a	DET
ejpam-6776	5	28	stochastic	stochastic	ADJ
ejpam-6776	5	29	threshold	threshold	NOUN
ejpam-6776	5	30	η	η	PROPN
ejpam-6776	5	31	.	.	PROPN
ejpam-6776	5	32	numerical	numerical	PROPN
ejpam-6776	5	33	simulations	simulation	NOUN
ejpam-6776	5	34	,	,	PUNCT
ejpam-6776	5	35	including	include	VERB
ejpam-6776	5	36	bifurcation	bifurcation	NOUN
ejpam-6776	5	37	surfaces	surface	NOUN
ejpam-6776	5	38	and	and	CCONJ
ejpam-6776	5	39	trajectory	trajectory	NOUN
ejpam-6776	5	40	comparisons	comparison	NOUN
ejpam-6776	5	41	,	,	PUNCT
ejpam-6776	5	42	support	support	VERB
ejpam-6776	5	43	these	these	DET
ejpam-6776	5	44	findings	finding	NOUN
ejpam-6776	5	45	,	,	PUNCT
ejpam-6776	5	46	demonstrating	demonstrate	VERB
ejpam-6776	5	47	how	how	SCONJ
ejpam-6776	5	48	noise	noise	NOUN
ejpam-6776	5	49	eliminates	eliminate	VERB
ejpam-6776	5	50	bifurcations	bifurcation	NOUN
ejpam-6776	5	51	and	and	CCONJ
ejpam-6776	5	52	promotes	promote	VERB
ejpam-6776	5	53	disease	disease	NOUN
ejpam-6776	5	54	control	control	NOUN
ejpam-6776	5	55	.	.	PUNCT
ejpam-6776	6	1	these	these	DET
ejpam-6776	6	2	insights	insight	NOUN
ejpam-6776	6	3	emphasize	emphasize	VERB
ejpam-6776	6	4	the	the	DET
ejpam-6776	6	5	need	need	NOUN
ejpam-6776	6	6	for	for	ADP
ejpam-6776	6	7	randomness	randomness	NOUN
ejpam-6776	6	8	in	in	ADP
ejpam-6776	6	9	epidemic	epidemic	NOUN
ejpam-6776	6	10	modeling	modeling	NOUN
ejpam-6776	6	11	to	to	PART
ejpam-6776	6	12	improve	improve	VERB
ejpam-6776	6	13	predictive	predictive	ADJ
ejpam-6776	6	14	accuracy	accuracy	NOUN
ejpam-6776	6	15	and	and	CCONJ
ejpam-6776	6	16	inform	inform	VERB
ejpam-6776	6	17	public	public	ADJ
ejpam-6776	6	18	health	health	NOUN
ejpam-6776	6	19	interventions	intervention	NOUN
ejpam-6776	6	20	.	.	PUNCT
ejpam-6776	7	1	understanding	understand	VERB
ejpam-6776	7	2	these	these	DET
ejpam-6776	7	3	stochastic	stochastic	ADJ
ejpam-6776	7	4	influences	influence	NOUN
ejpam-6776	7	5	can	can	AUX
ejpam-6776	7	6	aid	aid	VERB
ejpam-6776	7	7	in	in	ADP
ejpam-6776	7	8	developing	develop	VERB
ejpam-6776	7	9	more	more	ADJ
ejpam-6776	7	10	adaptive	adaptive	ADJ
ejpam-6776	7	11	policies	policy	NOUN
ejpam-6776	7	12	for	for	ADP
ejpam-6776	7	13	epidemic	epidemic	NOUN
ejpam-6776	7	14	mitigation	mitigation	NOUN
ejpam-6776	7	15	,	,	PUNCT
ejpam-6776	7	16	particularly	particularly	ADV
ejpam-6776	7	17	in	in	ADP
ejpam-6776	7	18	resource	resource	NOUN
ejpam-6776	7	19	-	-	PUNCT
ejpam-6776	7	20	limited	limit	VERB
ejpam-6776	7	21	settings	setting	NOUN
ejpam-6776	7	22	.	.	PUNCT
ejpam-6776	8	1	future	future	ADJ
ejpam-6776	8	2	research	research	NOUN
ejpam-6776	8	3	aims	aim	VERB
ejpam-6776	8	4	to	to	PART
ejpam-6776	8	5	refine	refine	VERB
ejpam-6776	8	6	these	these	DET
ejpam-6776	8	7	models	model	NOUN
ejpam-6776	8	8	by	by	ADP
ejpam-6776	8	9	incorporating	incorporate	VERB
ejpam-6776	8	10	spatial	spatial	ADJ
ejpam-6776	8	11	heterogeneity	heterogeneity	NOUN
ejpam-6776	8	12	,	,	PUNCT
ejpam-6776	8	13	population	population	NOUN
ejpam-6776	8	14	diversity	diversity	NOUN
ejpam-6776	8	15	,	,	PUNCT
ejpam-6776	8	16	time	time	NOUN
ejpam-6776	8	17	delays	delay	NOUN
ejpam-6776	8	18	,	,	PUNCT
ejpam-6776	8	19	and	and	CCONJ
ejpam-6776	8	20	pathogen	pathogen	VERB
ejpam-6776	8	21	evolution	evolution	NOUN
ejpam-6776	8	22	for	for	ADP
ejpam-6776	8	23	better	well	ADJ
ejpam-6776	8	24	epidemic	epidemic	NOUN
ejpam-6776	8	25	control	control	NOUN
ejpam-6776	8	26	.	.	PUNCT
ejpam-6776	9	1	2020	2020	NUM
ejpam-6776	9	2	mathematics	mathematic	NOUN
ejpam-6776	9	3	subject	subject	NOUN
ejpam-6776	9	4	classifications	classification	NOUN
ejpam-6776	9	5	:	:	PUNCT
ejpam-6776	9	6	92d30	92d30	NUM
ejpam-6776	9	7	,	,	PUNCT
ejpam-6776	9	8	60j28	60j28	NUM
ejpam-6776	9	9	,	,	PUNCT
ejpam-6776	9	10	34f10	34f10	NUM
ejpam-6776	9	11	,	,	PUNCT
ejpam-6776	9	12	92c60	92c60	NUM
ejpam-6776	9	13	,	,	PUNCT
ejpam-6776	9	14	37n25	37n25	NUM
ejpam-6776	9	15	key	key	ADJ
ejpam-6776	9	16	words	word	NOUN
ejpam-6776	9	17	and	and	CCONJ
ejpam-6776	9	18	phrases	phrase	NOUN
ejpam-6776	9	19	:	:	PUNCT
ejpam-6776	9	20	stochastic	stochastic	ADJ
ejpam-6776	9	21	modeling	modeling	NOUN
ejpam-6776	9	22	,	,	PUNCT
ejpam-6776	9	23	sir	sir	NOUN
ejpam-6776	9	24	model	model	NOUN
ejpam-6776	9	25	,	,	PUNCT
ejpam-6776	9	26	backward	backward	ADJ
ejpam-6776	9	27	bifurcation	bifurcation	NOUN
ejpam-6776	9	28	,	,	PUNCT
ejpam-6776	9	29	medical	medical	ADJ
ejpam-6776	9	30	resources	resource	NOUN
ejpam-6776	9	31	,	,	PUNCT
ejpam-6776	9	32	disease	disease	NOUN
ejpam-6776	9	33	dynamics	dynamic	NOUN
ejpam-6776	9	34	∗corresponding	∗corresponde	VERB
ejpam-6776	9	35	author	author	NOUN
ejpam-6776	9	36	.	.	PUNCT
ejpam-6776	10	1	doi	doi	NOUN
ejpam-6776	10	2	:	:	PUNCT
ejpam-6776	10	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6776	https://doi.org/10.29020/nybg.ejpam.v18i4.6776	NOUN
ejpam-6776	10	4	email	email	NOUN
ejpam-6776	10	5	addresses	address	NOUN
ejpam-6776	10	6	:	:	PUNCT
ejpam-6776	10	7	leoamalraj@rmkcet.ac.in	leoamalraj@rmkcet.ac.in	PROPN
ejpam-6776	10	8	(	(	PUNCT
ejpam-6776	10	9	j.	j.	PROPN
ejpam-6776	10	10	leo	leo	PROPN
ejpam-6776	10	11	amalraj	amalraj	PROPN
ejpam-6776	10	12	)	)	PUNCT
ejpam-6776	10	13	,	,	PUNCT
ejpam-6776	10	14	balamurugansvm@gmail.com	balamurugansvm@gmail.com	X
ejpam-6776	11	1	(	(	PUNCT
ejpam-6776	11	2	m.	m.	NOUN
ejpam-6776	11	3	balamurugan	balamurugan	PROPN
ejpam-6776	11	4	)	)	PUNCT
ejpam-6776	11	5	,	,	PUNCT
ejpam-6776	11	6	pankaj.shukla@vit.ac.in	pankaj.shukla@vit.ac.in	PRON
ejpam-6776	11	7	(	(	PUNCT
ejpam-6776	11	8	p.	p.	NOUN
ejpam-6776	11	9	shukla	shukla	NOUN
ejpam-6776	11	10	)	)	PUNCT
ejpam-6776	11	11	,	,	PUNCT
ejpam-6776	11	12	rajesh.masina@adityauniversity.in	rajesh.masina@adityauniversity.in	X
ejpam-6776	11	13	(	(	PUNCT
ejpam-6776	11	14	m.	m.	NOUN
ejpam-6776	11	15	v.	v.	ADP
ejpam-6776	11	16	rajesh	rajesh	PROPN
ejpam-6776	11	17	)	)	PUNCT
ejpam-6776	11	18	,	,	PUNCT
ejpam-6776	11	19	avinashprofess@gmail.com	avinashprofess@gmail.com	X
ejpam-6776	12	1	(	(	PUNCT
ejpam-6776	12	2	n.	n.	NOUN
ejpam-6776	12	3	avinash	avinash	PROPN
ejpam-6776	12	4	)	)	PUNCT
ejpam-6776	12	5	,	,	PUNCT
ejpam-6776	12	6	vgovindandr@gmail.com	vgovindandr@gmail.com	X
ejpam-6776	13	1	(	(	PUNCT
ejpam-6776	13	2	v.	v.	ADP
ejpam-6776	13	3	govindan	govindan	PROPN
ejpam-6776	13	4	)	)	PUNCT
ejpam-6776	13	5	,	,	PUNCT
ejpam-6776	13	6	siriluk.pa@up.ac.th	siriluk.pa@up.ac.th	PROPN
ejpam-6776	13	7	(	(	PUNCT
ejpam-6776	13	8	s.	s.	PROPN
ejpam-6776	13	9	donganont	donganont	PROPN
ejpam-6776	13	10	)	)	PUNCT
ejpam-6776	13	11	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6776	14	1	1	1	NUM
ejpam-6776	14	2	copyright	copyright	NOUN
ejpam-6776	14	3	:	:	PUNCT
ejpam-6776	14	4	©	©	PROPN
ejpam-6776	14	5	2025	2025	NUM
ejpam-6776	14	6	the	the	DET
ejpam-6776	14	7	author(s	author(s	NOUN
ejpam-6776	14	8	)	)	PUNCT
ejpam-6776	14	9	.	.	PUNCT
ejpam-6776	15	1	(	(	PUNCT
ejpam-6776	15	2	cc	cc	NOUN
ejpam-6776	15	3	by	by	ADP
ejpam-6776	15	4	-	-	PUNCT
ejpam-6776	15	5	nc	nc	PROPN
ejpam-6776	15	6	4.0	4.0	NUM
ejpam-6776	15	7	)	)	PUNCT
ejpam-6776	15	8	j.	j.	PROPN
ejpam-6776	15	9	leo	leo	PROPN
ejpam-6776	15	10	amalraj	amalraj	PROPN
ejpam-6776	15	11	et	et	PROPN
ejpam-6776	15	12	al	al	PROPN
ejpam-6776	15	13	.	.	PUNCT
ejpam-6776	15	14	/	/	SYM
ejpam-6776	15	15	eur	eur	PROPN
ejpam-6776	15	16	.	.	PUNCT
ejpam-6776	16	1	j.	j.	PROPN
ejpam-6776	16	2	pure	pure	PROPN
ejpam-6776	16	3	appl	appl	PROPN
ejpam-6776	16	4	.	.	PROPN
ejpam-6776	16	5	math	math	PROPN
ejpam-6776	16	6	,	,	PUNCT
ejpam-6776	16	7	18	18	NUM
ejpam-6776	16	8	(	(	PUNCT
ejpam-6776	16	9	4	4	NUM
ejpam-6776	16	10	)	)	PUNCT
ejpam-6776	16	11	(	(	PUNCT
ejpam-6776	16	12	2025	2025	NUM
ejpam-6776	16	13	)	)	PUNCT
ejpam-6776	16	14	,	,	PUNCT
ejpam-6776	16	15	6776	6776	NUM
ejpam-6776	16	16	2	2	NUM
ejpam-6776	16	17	of	of	ADP
ejpam-6776	16	18	22	22	NUM
ejpam-6776	16	19	1	1	NUM
ejpam-6776	16	20	.	.	PUNCT
ejpam-6776	17	1	introduction	introduction	NOUN
ejpam-6776	17	2	infectious	infectious	ADJ
ejpam-6776	17	3	diseases	disease	NOUN
ejpam-6776	17	4	,	,	PUNCT
ejpam-6776	17	5	such	such	ADJ
ejpam-6776	17	6	as	as	ADP
ejpam-6776	17	7	tuberculosis	tuberculosis	NOUN
ejpam-6776	17	8	(	(	PUNCT
ejpam-6776	17	9	tb	tb	NOUN
ejpam-6776	17	10	)	)	PUNCT
ejpam-6776	17	11	,	,	PUNCT
ejpam-6776	17	12	hiv	hiv	PROPN
ejpam-6776	17	13	,	,	PUNCT
ejpam-6776	17	14	and	and	CCONJ
ejpam-6776	17	15	emerging	emerge	VERB
ejpam-6776	17	16	threats	threat	NOUN
ejpam-6776	17	17	like	like	ADP
ejpam-6776	17	18	covid19	covid19	NOUN
ejpam-6776	17	19	,	,	PUNCT
ejpam-6776	17	20	continue	continue	VERB
ejpam-6776	17	21	to	to	PART
ejpam-6776	17	22	impose	impose	VERB
ejpam-6776	17	23	a	a	DET
ejpam-6776	17	24	substantial	substantial	ADJ
ejpam-6776	17	25	global	global	ADJ
ejpam-6776	17	26	health	health	NOUN
ejpam-6776	17	27	burden	burden	NOUN
ejpam-6776	17	28	.	.	PUNCT
ejpam-6776	18	1	rapid	rapid	ADJ
ejpam-6776	18	2	urbanization	urbanization	NOUN
ejpam-6776	18	3	,	,	PUNCT
ejpam-6776	18	4	climate	climate	NOUN
ejpam-6776	18	5	change	change	NOUN
ejpam-6776	18	6	,	,	PUNCT
ejpam-6776	18	7	and	and	CCONJ
ejpam-6776	18	8	increasing	increase	VERB
ejpam-6776	18	9	human	human	ADJ
ejpam-6776	18	10	aggregation	aggregation	NOUN
ejpam-6776	18	11	exacerbate	exacerbate	VERB
ejpam-6776	18	12	the	the	DET
ejpam-6776	18	13	spread	spread	NOUN
ejpam-6776	18	14	of	of	ADP
ejpam-6776	18	15	these	these	DET
ejpam-6776	18	16	diseases	disease	NOUN
ejpam-6776	18	17	,	,	PUNCT
ejpam-6776	18	18	necessitating	necessitate	VERB
ejpam-6776	18	19	advanced	advanced	ADJ
ejpam-6776	18	20	tools	tool	NOUN
ejpam-6776	18	21	for	for	ADP
ejpam-6776	18	22	prediction	prediction	NOUN
ejpam-6776	18	23	and	and	CCONJ
ejpam-6776	18	24	control	control	NOUN
ejpam-6776	18	25	.	.	PUNCT
ejpam-6776	19	1	tuberculosis	tuberculosis	NOUN
ejpam-6776	19	2	,	,	PUNCT
ejpam-6776	19	3	caused	cause	VERB
ejpam-6776	19	4	by	by	ADP
ejpam-6776	19	5	mycobacterium	mycobacterium	NOUN
ejpam-6776	19	6	tuberculosis	tuberculosis	NOUN
ejpam-6776	19	7	,	,	PUNCT
ejpam-6776	19	8	remains	remain	VERB
ejpam-6776	19	9	a	a	DET
ejpam-6776	19	10	leading	lead	VERB
ejpam-6776	19	11	cause	cause	NOUN
ejpam-6776	19	12	of	of	ADP
ejpam-6776	19	13	mortality	mortality	NOUN
ejpam-6776	19	14	,	,	PUNCT
ejpam-6776	19	15	claiming	claim	VERB
ejpam-6776	19	16	1.18	1.18	NUM
ejpam-6776	19	17	million	million	NUM
ejpam-6776	19	18	lives	life	NOUN
ejpam-6776	19	19	in	in	ADP
ejpam-6776	19	20	2017	2017	NUM
ejpam-6776	19	21	,	,	PUNCT
ejpam-6776	19	22	while	while	SCONJ
ejpam-6776	19	23	hiv	hiv	NOUN
ejpam-6776	19	24	-	-	PUNCT
ejpam-6776	19	25	related	relate	VERB
ejpam-6776	19	26	illnesses	illness	NOUN
ejpam-6776	19	27	accounted	account	VERB
ejpam-6776	19	28	for	for	ADP
ejpam-6776	19	29	940,000	940,000	NUM
ejpam-6776	19	30	deaths	death	NOUN
ejpam-6776	19	31	in	in	ADP
ejpam-6776	19	32	the	the	DET
ejpam-6776	19	33	same	same	ADJ
ejpam-6776	19	34	year	year	NOUN
ejpam-6776	19	35	[	[	X
ejpam-6776	19	36	1	1	NUM
ejpam-6776	19	37	]	]	PUNCT
ejpam-6776	19	38	.	.	PUNCT
ejpam-6776	20	1	the	the	DET
ejpam-6776	20	2	covid-19	covid-19	PROPN
ejpam-6776	20	3	pandemic	pandemic	NOUN
ejpam-6776	20	4	,	,	PUNCT
ejpam-6776	20	5	with	with	ADP
ejpam-6776	20	6	over	over	ADP
ejpam-6776	20	7	21	21	NUM
ejpam-6776	20	8	million	million	NUM
ejpam-6776	20	9	cases	case	NOUN
ejpam-6776	20	10	by	by	ADP
ejpam-6776	20	11	august	august	PROPN
ejpam-6776	20	12	2020	2020	NUM
ejpam-6776	20	13	,	,	PUNCT
ejpam-6776	20	14	underscores	underscore	VERB
ejpam-6776	20	15	the	the	DET
ejpam-6776	20	16	urgency	urgency	NOUN
ejpam-6776	20	17	of	of	ADP
ejpam-6776	20	18	addressing	address	VERB
ejpam-6776	20	19	these	these	DET
ejpam-6776	20	20	challenges	challenge	NOUN
ejpam-6776	20	21	[	[	X
ejpam-6776	20	22	1	1	NUM
ejpam-6776	20	23	]	]	PUNCT
ejpam-6776	20	24	.	.	PUNCT
ejpam-6776	21	1	cutting	cut	VERB
ejpam-6776	21	2	-	-	PUNCT
ejpam-6776	21	3	edge	edge	NOUN
ejpam-6776	21	4	epidemic	epidemic	NOUN
ejpam-6776	21	5	modeling	modeling	NOUN
ejpam-6776	21	6	,	,	PUNCT
ejpam-6776	21	7	particularly	particularly	ADV
ejpam-6776	21	8	approaches	approach	VERB
ejpam-6776	21	9	incorporating	incorporate	VERB
ejpam-6776	21	10	stochasticity	stochasticity	NOUN
ejpam-6776	21	11	and	and	CCONJ
ejpam-6776	21	12	resource	resource	NOUN
ejpam-6776	21	13	constraints	constraint	NOUN
ejpam-6776	21	14	,	,	PUNCT
ejpam-6776	21	15	offers	offer	VERB
ejpam-6776	21	16	critical	critical	ADJ
ejpam-6776	21	17	insights	insight	NOUN
ejpam-6776	21	18	into	into	ADP
ejpam-6776	21	19	disease	disease	NOUN
ejpam-6776	21	20	dynamics	dynamic	NOUN
ejpam-6776	21	21	,	,	PUNCT
ejpam-6776	21	22	enabling	enable	VERB
ejpam-6776	21	23	more	more	ADV
ejpam-6776	21	24	effective	effective	ADJ
ejpam-6776	21	25	public	public	ADJ
ejpam-6776	21	26	health	health	NOUN
ejpam-6776	21	27	strategies	strategy	NOUN
ejpam-6776	21	28	[	[	X
ejpam-6776	21	29	2	2	NUM
ejpam-6776	21	30	]	]	PUNCT
ejpam-6776	21	31	.	.	PUNCT
ejpam-6776	22	1	stochastic	stochastic	ADJ
ejpam-6776	22	2	modeling	modeling	NOUN
ejpam-6776	22	3	is	be	AUX
ejpam-6776	22	4	a	a	DET
ejpam-6776	22	5	cornerstone	cornerstone	NOUN
ejpam-6776	22	6	for	for	ADP
ejpam-6776	22	7	analyzing	analyze	VERB
ejpam-6776	22	8	complex	complex	ADJ
ejpam-6776	22	9	systems	system	NOUN
ejpam-6776	22	10	influenced	influence	VERB
ejpam-6776	22	11	by	by	ADP
ejpam-6776	22	12	randomness	randomness	NOUN
ejpam-6776	22	13	,	,	PUNCT
ejpam-6776	22	14	with	with	ADP
ejpam-6776	22	15	applications	application	NOUN
ejpam-6776	22	16	spanning	span	VERB
ejpam-6776	22	17	biology	biology	NOUN
ejpam-6776	22	18	,	,	PUNCT
ejpam-6776	22	19	finance	finance	NOUN
ejpam-6776	22	20	,	,	PUNCT
ejpam-6776	22	21	engineering	engineering	NOUN
ejpam-6776	22	22	,	,	PUNCT
ejpam-6776	22	23	and	and	CCONJ
ejpam-6776	22	24	physics	physics	NOUN
ejpam-6776	22	25	[	[	X
ejpam-6776	22	26	3	3	NUM
ejpam-6776	22	27	]	]	PUNCT
ejpam-6776	22	28	.	.	PUNCT
ejpam-6776	23	1	by	by	ADP
ejpam-6776	23	2	leveraging	leverage	VERB
ejpam-6776	23	3	probability	probability	NOUN
ejpam-6776	23	4	theory	theory	NOUN
ejpam-6776	23	5	,	,	PUNCT
ejpam-6776	23	6	statistical	statistical	ADJ
ejpam-6776	23	7	inference	inference	NOUN
ejpam-6776	23	8	,	,	PUNCT
ejpam-6776	23	9	and	and	CCONJ
ejpam-6776	23	10	techniques	technique	NOUN
ejpam-6776	23	11	like	like	ADP
ejpam-6776	23	12	markov	markov	NOUN
ejpam-6776	23	13	chains	chain	NOUN
ejpam-6776	23	14	,	,	PUNCT
ejpam-6776	23	15	brownian	brownian	ADJ
ejpam-6776	23	16	motion	motion	NOUN
ejpam-6776	23	17	,	,	PUNCT
ejpam-6776	23	18	and	and	CCONJ
ejpam-6776	23	19	monte	monte	PROPN
ejpam-6776	23	20	carlo	carlo	PROPN
ejpam-6776	23	21	simulations	simulation	NOUN
ejpam-6776	23	22	,	,	PUNCT
ejpam-6776	23	23	these	these	DET
ejpam-6776	23	24	models	model	NOUN
ejpam-6776	23	25	quantify	quantify	VERB
ejpam-6776	23	26	uncertainty	uncertainty	NOUN
ejpam-6776	23	27	and	and	CCONJ
ejpam-6776	23	28	identify	identify	VERB
ejpam-6776	23	29	key	key	ADJ
ejpam-6776	23	30	drivers	driver	NOUN
ejpam-6776	23	31	in	in	ADP
ejpam-6776	23	32	dynamic	dynamic	ADJ
ejpam-6776	23	33	systems	system	NOUN
ejpam-6776	23	34	.	.	PUNCT
ejpam-6776	24	1	in	in	ADP
ejpam-6776	24	2	epidemiology	epidemiology	NOUN
ejpam-6776	24	3	,	,	PUNCT
ejpam-6776	24	4	stochastic	stochastic	NOUN
ejpam-6776	24	5	models	model	NOUN
ejpam-6776	24	6	enhance	enhance	VERB
ejpam-6776	24	7	the	the	DET
ejpam-6776	24	8	understanding	understanding	NOUN
ejpam-6776	24	9	of	of	ADP
ejpam-6776	24	10	irregular	irregular	ADJ
ejpam-6776	24	11	epidemic	epidemic	NOUN
ejpam-6776	24	12	patterns	pattern	NOUN
ejpam-6776	24	13	,	,	PUNCT
ejpam-6776	24	14	such	such	ADJ
ejpam-6776	24	15	as	as	ADP
ejpam-6776	24	16	those	those	PRON
ejpam-6776	24	17	observed	observe	VERB
ejpam-6776	24	18	in	in	ADP
ejpam-6776	24	19	covid-19	covid-19	PROPN
ejpam-6776	24	20	,	,	PUNCT
ejpam-6776	24	21	by	by	ADP
ejpam-6776	24	22	accounting	account	VERB
ejpam-6776	24	23	for	for	ADP
ejpam-6776	24	24	demographic	demographic	ADJ
ejpam-6776	24	25	noise	noise	NOUN
ejpam-6776	24	26	and	and	CCONJ
ejpam-6776	24	27	environmental	environmental	ADJ
ejpam-6776	24	28	disturbances	disturbance	NOUN
ejpam-6776	24	29	[	[	X
ejpam-6776	24	30	4	4	NUM
ejpam-6776	24	31	]	]	PUNCT
ejpam-6776	24	32	.	.	PUNCT
ejpam-6776	25	1	for	for	ADP
ejpam-6776	25	2	instance	instance	NOUN
ejpam-6776	25	3	,	,	PUNCT
ejpam-6776	25	4	research	research	NOUN
ejpam-6776	25	5	on	on	ADP
ejpam-6776	25	6	susceptible	susceptible	ADJ
ejpam-6776	25	7	–	–	PUNCT
ejpam-6776	25	8	infected	infected	ADJ
ejpam-6776	25	9	–	–	PUNCT
ejpam-6776	25	10	recovered	recovered	ADJ
ejpam-6776	25	11	(	(	PUNCT
ejpam-6776	25	12	sir	sir	NOUN
ejpam-6776	25	13	)	)	PUNCT
ejpam-6776	25	14	models	model	NOUN
ejpam-6776	25	15	reveals	reveal	VERB
ejpam-6776	25	16	that	that	SCONJ
ejpam-6776	25	17	stochastic	stochastic	ADJ
ejpam-6776	25	18	noise	noise	NOUN
ejpam-6776	25	19	expands	expand	VERB
ejpam-6776	25	20	turing	ture	VERB
ejpam-6776	25	21	instability	instability	NOUN
ejpam-6776	25	22	regions	region	NOUN
ejpam-6776	25	23	,	,	PUNCT
ejpam-6776	25	24	leading	lead	VERB
ejpam-6776	25	25	to	to	ADP
ejpam-6776	25	26	unpredictable	unpredictable	ADJ
ejpam-6776	25	27	disease	disease	NOUN
ejpam-6776	25	28	spread	spread	VERB
ejpam-6776	25	29	[	[	X
ejpam-6776	25	30	4	4	NUM
ejpam-6776	25	31	]	]	PUNCT
ejpam-6776	25	32	.	.	PUNCT
ejpam-6776	26	1	similarly	similarly	ADV
ejpam-6776	26	2	,	,	PUNCT
ejpam-6776	26	3	susceptible	susceptible	ADJ
ejpam-6776	26	4	–	–	PUNCT
ejpam-6776	26	5	vaccinated	vaccinated	ADJ
ejpam-6776	26	6	–	–	PUNCT
ejpam-6776	26	7	infected	infected	ADJ
ejpam-6776	26	8	–	–	PUNCT
ejpam-6776	26	9	recovered	recovered	ADJ
ejpam-6776	26	10	(	(	PUNCT
ejpam-6776	26	11	svir	svir	NOUN
ejpam-6776	26	12	)	)	PUNCT
ejpam-6776	26	13	models	model	NOUN
ejpam-6776	26	14	explore	explore	VERB
ejpam-6776	26	15	dual	dual	ADJ
ejpam-6776	26	16	-	-	PUNCT
ejpam-6776	26	17	disease	disease	NOUN
ejpam-6776	26	18	dynamics	dynamic	NOUN
ejpam-6776	26	19	and	and	CCONJ
ejpam-6776	26	20	vaccination	vaccination	NOUN
ejpam-6776	26	21	strategies	strategy	NOUN
ejpam-6776	26	22	,	,	PUNCT
ejpam-6776	26	23	using	use	VERB
ejpam-6776	26	24	lyapunov	lyapunov	NOUN
ejpam-6776	26	25	functions	function	NOUN
ejpam-6776	26	26	and	and	CCONJ
ejpam-6776	26	27	numerical	numerical	ADJ
ejpam-6776	26	28	methods	method	NOUN
ejpam-6776	26	29	like	like	ADP
ejpam-6776	26	30	the	the	DET
ejpam-6776	26	31	milstein	milstein	ADJ
ejpam-6776	26	32	scheme	scheme	NOUN
ejpam-6776	26	33	to	to	PART
ejpam-6776	26	34	assess	assess	VERB
ejpam-6776	26	35	disease	disease	NOUN
ejpam-6776	26	36	extinction	extinction	NOUN
ejpam-6776	26	37	conditions	condition	NOUN
ejpam-6776	26	38	[	[	X
ejpam-6776	26	39	5	5	NUM
ejpam-6776	26	40	]	]	PUNCT
ejpam-6776	26	41	.	.	PUNCT
ejpam-6776	27	1	unlike	unlike	ADP
ejpam-6776	27	2	deterministic	deterministic	ADJ
ejpam-6776	27	3	models	model	NOUN
ejpam-6776	27	4	,	,	PUNCT
ejpam-6776	27	5	which	which	PRON
ejpam-6776	27	6	assume	assume	VERB
ejpam-6776	27	7	constant	constant	ADJ
ejpam-6776	27	8	parameters	parameter	NOUN
ejpam-6776	27	9	,	,	PUNCT
ejpam-6776	27	10	stochastic	stochastic	ADJ
ejpam-6776	27	11	approaches	approach	NOUN
ejpam-6776	27	12	capture	capture	VERB
ejpam-6776	27	13	real	real	ADJ
ejpam-6776	27	14	-	-	PUNCT
ejpam-6776	27	15	world	world	NOUN
ejpam-6776	27	16	variability	variability	NOUN
ejpam-6776	27	17	,	,	PUNCT
ejpam-6776	27	18	making	make	VERB
ejpam-6776	27	19	them	they	PRON
ejpam-6776	27	20	indispensable	indispensable	ADJ
ejpam-6776	27	21	for	for	ADP
ejpam-6776	27	22	realistic	realistic	ADJ
ejpam-6776	27	23	epidemic	epidemic	NOUN
ejpam-6776	27	24	predictions	prediction	NOUN
ejpam-6776	27	25	[	[	X
ejpam-6776	27	26	6–10	6–10	NOUN
ejpam-6776	27	27	]	]	X
ejpam-6776	27	28	.	.	PUNCT
ejpam-6776	28	1	recent	recent	ADJ
ejpam-6776	28	2	advancements	advancement	NOUN
ejpam-6776	28	3	in	in	ADP
ejpam-6776	28	4	stochastic	stochastic	ADJ
ejpam-6776	28	5	epidemic	epidemic	NOUN
ejpam-6776	28	6	modeling	modeling	NOUN
ejpam-6776	28	7	include	include	VERB
ejpam-6776	28	8	multiphasic	multiphasic	NOUN
ejpam-6776	28	9	models	model	NOUN
ejpam-6776	28	10	for	for	ADP
ejpam-6776	28	11	phased	phased	ADJ
ejpam-6776	28	12	outbreaks	outbreak	NOUN
ejpam-6776	28	13	[	[	X
ejpam-6776	28	14	11	11	NUM
ejpam-6776	28	15	]	]	PUNCT
ejpam-6776	28	16	,	,	PUNCT
ejpam-6776	28	17	seiqr	seiqr	ADJ
ejpam-6776	28	18	models	model	NOUN
ejpam-6776	28	19	with	with	ADP
ejpam-6776	28	20	generalized	generalized	ADJ
ejpam-6776	28	21	incidence	incidence	NOUN
ejpam-6776	28	22	and	and	CCONJ
ejpam-6776	28	23	environmental	environmental	ADJ
ejpam-6776	28	24	noise	noise	NOUN
ejpam-6776	28	25	[	[	X
ejpam-6776	28	26	12	12	NUM
ejpam-6776	28	27	]	]	PUNCT
ejpam-6776	28	28	,	,	PUNCT
ejpam-6776	28	29	and	and	CCONJ
ejpam-6776	28	30	sir	sir	NOUN
ejpam-6776	28	31	variants	variant	NOUN
ejpam-6776	28	32	incorporating	incorporate	VERB
ejpam-6776	28	33	ornstein	ornstein	PROPN
ejpam-6776	28	34	-	-	PUNCT
ejpam-6776	28	35	uhlenbeck	uhlenbeck	PROPN
ejpam-6776	28	36	processes	process	NOUN
ejpam-6776	28	37	for	for	ADP
ejpam-6776	28	38	individual	individual	ADJ
ejpam-6776	28	39	heterogeneity	heterogeneity	NOUN
ejpam-6776	28	40	[	[	X
ejpam-6776	28	41	13	13	NUM
ejpam-6776	28	42	]	]	PUNCT
ejpam-6776	28	43	,	,	PUNCT
ejpam-6776	28	44	as	as	ADV
ejpam-6776	28	45	well	well	ADV
ejpam-6776	28	46	as	as	ADP
ejpam-6776	28	47	models	model	NOUN
ejpam-6776	28	48	with	with	ADP
ejpam-6776	28	49	telegraph	telegraph	NOUN
ejpam-6776	28	50	and	and	CCONJ
ejpam-6776	28	51	lévy	lévy	NOUN
ejpam-6776	28	52	noise	noise	NOUN
ejpam-6776	28	53	for	for	ADP
ejpam-6776	28	54	abrupt	abrupt	ADJ
ejpam-6776	28	55	environmental	environmental	ADJ
ejpam-6776	28	56	changes	change	NOUN
ejpam-6776	28	57	[	[	X
ejpam-6776	28	58	14	14	NUM
ejpam-6776	28	59	]	]	PUNCT
ejpam-6776	28	60	.	.	PUNCT
ejpam-6776	29	1	industrial	industrial	ADJ
ejpam-6776	29	2	progress	progress	NOUN
ejpam-6776	29	3	has	have	AUX
ejpam-6776	29	4	improved	improve	VERB
ejpam-6776	29	5	living	living	NOUN
ejpam-6776	29	6	standards	standard	NOUN
ejpam-6776	29	7	but	but	CCONJ
ejpam-6776	29	8	introduced	introduce	VERB
ejpam-6776	29	9	significant	significant	ADJ
ejpam-6776	29	10	environmental	environmental	ADJ
ejpam-6776	29	11	challenges	challenge	NOUN
ejpam-6776	29	12	,	,	PUNCT
ejpam-6776	29	13	notably	notably	ADV
ejpam-6776	29	14	air	air	NOUN
ejpam-6776	29	15	pollution	pollution	NOUN
ejpam-6776	29	16	from	from	ADP
ejpam-6776	29	17	coal	coal	NOUN
ejpam-6776	29	18	-	-	PUNCT
ejpam-6776	29	19	based	base	VERB
ejpam-6776	29	20	energy	energy	NOUN
ejpam-6776	29	21	sources	source	NOUN
ejpam-6776	29	22	emitting	emit	VERB
ejpam-6776	29	23	pollutants	pollutant	NOUN
ejpam-6776	29	24	like	like	ADP
ejpam-6776	29	25	so2	so2	PROPN
ejpam-6776	29	26	,	,	PUNCT
ejpam-6776	29	27	no	no	INTJ
ejpam-6776	29	28	,	,	PUNCT
ejpam-6776	29	29	o3	o3	PROPN
ejpam-6776	29	30	,	,	PUNCT
ejpam-6776	29	31	co	co	NOUN
ejpam-6776	29	32	,	,	PUNCT
ejpam-6776	29	33	and	and	CCONJ
ejpam-6776	29	34	particulate	particulate	NOUN
ejpam-6776	29	35	matter	matter	NOUN
ejpam-6776	29	36	(	(	PUNCT
ejpam-6776	29	37	pm	pm	NOUN
ejpam-6776	29	38	)	)	PUNCT
ejpam-6776	30	1	[	[	X
ejpam-6776	30	2	15	15	NUM
ejpam-6776	30	3	]	]	PUNCT
ejpam-6776	30	4	.	.	PUNCT
ejpam-6776	31	1	fine	fine	ADJ
ejpam-6776	31	2	particles	particle	NOUN
ejpam-6776	31	3	(	(	PUNCT
ejpam-6776	31	4	pm2.5	pm2.5	X
ejpam-6776	31	5	)	)	PUNCT
ejpam-6776	31	6	pose	pose	VERB
ejpam-6776	31	7	severe	severe	ADJ
ejpam-6776	31	8	risks	risk	NOUN
ejpam-6776	31	9	,	,	PUNCT
ejpam-6776	31	10	penetrating	penetrate	VERB
ejpam-6776	31	11	deep	deep	ADV
ejpam-6776	31	12	into	into	ADP
ejpam-6776	31	13	the	the	DET
ejpam-6776	31	14	lungs	lung	NOUN
ejpam-6776	31	15	and	and	CCONJ
ejpam-6776	31	16	bloodstream	bloodstream	NOUN
ejpam-6776	31	17	,	,	PUNCT
ejpam-6776	31	18	contributing	contribute	VERB
ejpam-6776	31	19	to	to	ADP
ejpam-6776	31	20	respiratory	respiratory	ADJ
ejpam-6776	31	21	and	and	CCONJ
ejpam-6776	31	22	cardiovascular	cardiovascular	ADJ
ejpam-6776	31	23	diseases	disease	NOUN
ejpam-6776	31	24	such	such	ADJ
ejpam-6776	31	25	as	as	ADP
ejpam-6776	31	26	asthma	asthma	NOUN
ejpam-6776	31	27	,	,	PUNCT
ejpam-6776	31	28	chronic	chronic	ADJ
ejpam-6776	31	29	obstructive	obstructive	ADJ
ejpam-6776	31	30	pulmonary	pulmonary	ADJ
ejpam-6776	31	31	disease	disease	NOUN
ejpam-6776	31	32	(	(	PUNCT
ejpam-6776	31	33	copd	copd	PROPN
ejpam-6776	31	34	)	)	PUNCT
ejpam-6776	31	35	,	,	PUNCT
ejpam-6776	31	36	and	and	CCONJ
ejpam-6776	31	37	heart	heart	NOUN
ejpam-6776	31	38	disease	disease	NOUN
ejpam-6776	31	39	[	[	X
ejpam-6776	31	40	16	16	NUM
ejpam-6776	31	41	]	]	PUNCT
ejpam-6776	31	42	.	.	PUNCT
ejpam-6776	32	1	the	the	DET
ejpam-6776	32	2	air	air	NOUN
ejpam-6776	32	3	quality	quality	PROPN
ejpam-6776	32	4	index	index	NOUN
ejpam-6776	32	5	(	(	PUNCT
ejpam-6776	32	6	aqi	aqi	PROPN
ejpam-6776	32	7	)	)	PUNCT
ejpam-6776	32	8	,	,	PUNCT
ejpam-6776	32	9	a	a	DET
ejpam-6776	32	10	standardized	standardized	ADJ
ejpam-6776	32	11	tool	tool	NOUN
ejpam-6776	32	12	,	,	PUNCT
ejpam-6776	32	13	communicates	communicate	VERB
ejpam-6776	32	14	pollution	pollution	NOUN
ejpam-6776	32	15	severity	severity	NOUN
ejpam-6776	32	16	and	and	CCONJ
ejpam-6776	32	17	health	health	NOUN
ejpam-6776	32	18	risks	risk	NOUN
ejpam-6776	32	19	,	,	PUNCT
ejpam-6776	32	20	guiding	guide	VERB
ejpam-6776	32	21	public	public	ADJ
ejpam-6776	32	22	health	health	NOUN
ejpam-6776	32	23	responses	response	NOUN
ejpam-6776	32	24	[	[	X
ejpam-6776	32	25	15	15	NUM
ejpam-6776	32	26	]	]	PUNCT
ejpam-6776	32	27	.	.	PUNCT
ejpam-6776	33	1	however	however	ADV
ejpam-6776	33	2	,	,	PUNCT
ejpam-6776	33	3	research	research	NOUN
ejpam-6776	33	4	on	on	ADP
ejpam-6776	33	5	ultrafine	ultrafine	ADJ
ejpam-6776	33	6	particles	particle	NOUN
ejpam-6776	33	7	(	(	PUNCT
ejpam-6776	33	8	ufp	ufp	NOUN
ejpam-6776	33	9	)	)	PUNCT
ejpam-6776	33	10	remains	remain	VERB
ejpam-6776	33	11	limited	limited	ADJ
ejpam-6776	33	12	,	,	PUNCT
ejpam-6776	33	13	with	with	ADP
ejpam-6776	33	14	only	only	ADV
ejpam-6776	33	15	one	one	NUM
ejpam-6776	33	16	large	large	ADJ
ejpam-6776	33	17	-	-	PUNCT
ejpam-6776	33	18	scale	scale	NOUN
ejpam-6776	33	19	study	study	NOUN
ejpam-6776	33	20	examining	examine	VERB
ejpam-6776	33	21	long	long	ADJ
ejpam-6776	33	22	-	-	PUNCT
ejpam-6776	33	23	term	term	NOUN
ejpam-6776	33	24	exposure	exposure	NOUN
ejpam-6776	33	25	[	[	X
ejpam-6776	33	26	17–19	17–19	NUM
ejpam-6776	33	27	]	]	PUNCT
ejpam-6776	33	28	.	.	PUNCT
ejpam-6776	34	1	standardized	standardized	ADJ
ejpam-6776	34	2	monitoring	monitoring	NOUN
ejpam-6776	34	3	for	for	ADP
ejpam-6776	34	4	ufps	ufps	NOUN
ejpam-6776	34	5	could	could	AUX
ejpam-6776	34	6	unlock	unlock	VERB
ejpam-6776	34	7	new	new	ADJ
ejpam-6776	34	8	insights	insight	NOUN
ejpam-6776	34	9	into	into	ADP
ejpam-6776	34	10	their	their	PRON
ejpam-6776	34	11	health	health	NOUN
ejpam-6776	34	12	impacts	impact	NOUN
ejpam-6776	34	13	,	,	PUNCT
ejpam-6776	34	14	addressing	address	VERB
ejpam-6776	34	15	a	a	DET
ejpam-6776	34	16	critical	critical	ADJ
ejpam-6776	34	17	gap	gap	NOUN
ejpam-6776	34	18	in	in	ADP
ejpam-6776	34	19	environmental	environmental	ADJ
ejpam-6776	34	20	health	health	NOUN
ejpam-6776	34	21	research	research	NOUN
ejpam-6776	34	22	.	.	PUNCT
ejpam-6776	35	1	epidemic	epidemic	NOUN
ejpam-6776	35	2	models	model	NOUN
ejpam-6776	35	3	are	be	AUX
ejpam-6776	35	4	vital	vital	ADJ
ejpam-6776	35	5	for	for	ADP
ejpam-6776	35	6	informing	inform	VERB
ejpam-6776	35	7	public	public	ADJ
ejpam-6776	35	8	health	health	NOUN
ejpam-6776	35	9	strategies	strategy	NOUN
ejpam-6776	35	10	,	,	PUNCT
ejpam-6776	35	11	yet	yet	CCONJ
ejpam-6776	35	12	traditional	traditional	ADJ
ejpam-6776	35	13	approaches	approach	NOUN
ejpam-6776	35	14	often	often	ADV
ejpam-6776	35	15	overlook	overlook	VERB
ejpam-6776	35	16	stochastic	stochastic	ADJ
ejpam-6776	35	17	factors	factor	NOUN
ejpam-6776	35	18	like	like	ADP
ejpam-6776	35	19	white	white	ADJ
ejpam-6776	35	20	noise	noise	NOUN
ejpam-6776	35	21	,	,	PUNCT
ejpam-6776	35	22	telegraph	telegraph	NOUN
ejpam-6776	35	23	noise	noise	NOUN
ejpam-6776	35	24	,	,	PUNCT
ejpam-6776	35	25	and	and	CCONJ
ejpam-6776	35	26	lévy	lévy	NUM
ejpam-6776	35	27	noise	noise	NOUN
ejpam-6776	35	28	,	,	PUNCT
ejpam-6776	35	29	j.	j.	PROPN
ejpam-6776	35	30	leo	leo	PROPN
ejpam-6776	35	31	amalraj	amalraj	PROPN
ejpam-6776	35	32	et	et	PROPN
ejpam-6776	35	33	al	al	PROPN
ejpam-6776	35	34	.	.	PUNCT
ejpam-6776	35	35	/	/	SYM
ejpam-6776	35	36	eur	eur	PROPN
ejpam-6776	35	37	.	.	PUNCT
ejpam-6776	36	1	j.	j.	PROPN
ejpam-6776	36	2	pure	pure	PROPN
ejpam-6776	36	3	appl	appl	PROPN
ejpam-6776	36	4	.	.	PROPN
ejpam-6776	36	5	math	math	PROPN
ejpam-6776	36	6	,	,	PUNCT
ejpam-6776	36	7	18	18	NUM
ejpam-6776	36	8	(	(	PUNCT
ejpam-6776	36	9	4	4	NUM
ejpam-6776	36	10	)	)	PUNCT
ejpam-6776	36	11	(	(	PUNCT
ejpam-6776	36	12	2025	2025	NUM
ejpam-6776	36	13	)	)	PUNCT
ejpam-6776	36	14	,	,	PUNCT
ejpam-6776	36	15	6776	6776	NUM
ejpam-6776	36	16	3	3	NUM
ejpam-6776	36	17	of	of	ADP
ejpam-6776	36	18	22	22	NUM
ejpam-6776	36	19	which	which	PRON
ejpam-6776	36	20	significantly	significantly	ADV
ejpam-6776	36	21	influence	influence	VERB
ejpam-6776	36	22	disease	disease	NOUN
ejpam-6776	36	23	persistence	persistence	NOUN
ejpam-6776	36	24	and	and	CCONJ
ejpam-6776	36	25	extinction	extinction	NOUN
ejpam-6776	36	26	[	[	X
ejpam-6776	36	27	6	6	NUM
ejpam-6776	36	28	]	]	PUNCT
ejpam-6776	36	29	.	.	PUNCT
ejpam-6776	37	1	recent	recent	ADJ
ejpam-6776	37	2	studies	study	NOUN
ejpam-6776	37	3	integrating	integrate	VERB
ejpam-6776	37	4	these	these	DET
ejpam-6776	37	5	elements	element	NOUN
ejpam-6776	37	6	have	have	AUX
ejpam-6776	37	7	improved	improve	VERB
ejpam-6776	37	8	prediction	prediction	NOUN
ejpam-6776	37	9	accuracy	accuracy	NOUN
ejpam-6776	37	10	,	,	PUNCT
ejpam-6776	37	11	particularly	particularly	ADV
ejpam-6776	37	12	for	for	ADP
ejpam-6776	37	13	abrupt	abrupt	ADJ
ejpam-6776	37	14	environmental	environmental	ADJ
ejpam-6776	37	15	changes	change	NOUN
ejpam-6776	37	16	[	[	X
ejpam-6776	37	17	6	6	NUM
ejpam-6776	37	18	]	]	PUNCT
ejpam-6776	37	19	.	.	PUNCT
ejpam-6776	38	1	markov	markov	NOUN
ejpam-6776	38	2	chain	chain	NOUN
ejpam-6776	38	3	processes	process	NOUN
ejpam-6776	38	4	and	and	CCONJ
ejpam-6776	38	5	regime	regime	NOUN
ejpam-6776	38	6	-	-	PUNCT
ejpam-6776	38	7	switching	switch	VERB
ejpam-6776	38	8	models	model	NOUN
ejpam-6776	38	9	,	,	PUNCT
ejpam-6776	38	10	such	such	ADJ
ejpam-6776	38	11	as	as	ADP
ejpam-6776	38	12	stochastic	stochastic	ADJ
ejpam-6776	38	13	sis	sis	NOUN
ejpam-6776	38	14	models	model	NOUN
ejpam-6776	38	15	,	,	PUNCT
ejpam-6776	38	16	further	far	ADV
ejpam-6776	38	17	enhance	enhance	VERB
ejpam-6776	38	18	realism	realism	NOUN
ejpam-6776	38	19	by	by	ADP
ejpam-6776	38	20	accounting	account	VERB
ejpam-6776	38	21	for	for	ADP
ejpam-6776	38	22	environmental	environmental	ADJ
ejpam-6776	38	23	fluctuations	fluctuation	NOUN
ejpam-6776	38	24	like	like	ADP
ejpam-6776	38	25	weather	weather	NOUN
ejpam-6776	38	26	or	or	CCONJ
ejpam-6776	38	27	food	food	NOUN
ejpam-6776	38	28	supply	supply	NOUN
ejpam-6776	38	29	changes	change	NOUN
ejpam-6776	38	30	[	[	X
ejpam-6776	38	31	7–10	7–10	X
ejpam-6776	38	32	]	]	X
ejpam-6776	38	33	.	.	PUNCT
ejpam-6776	39	1	the	the	DET
ejpam-6776	39	2	covid-19	covid-19	PROPN
ejpam-6776	39	3	pandemic	pandemic	NOUN
ejpam-6776	39	4	highlighted	highlight	VERB
ejpam-6776	39	5	the	the	DET
ejpam-6776	39	6	importance	importance	NOUN
ejpam-6776	39	7	of	of	ADP
ejpam-6776	39	8	such	such	ADJ
ejpam-6776	39	9	models	model	NOUN
ejpam-6776	39	10	,	,	PUNCT
ejpam-6776	39	11	with	with	ADP
ejpam-6776	39	12	adaptations	adaptation	NOUN
ejpam-6776	39	13	incorporating	incorporate	VERB
ejpam-6776	39	14	fractional	fractional	ADJ
ejpam-6776	39	15	-	-	PUNCT
ejpam-6776	39	16	order	order	NOUN
ejpam-6776	39	17	equations	equation	NOUN
ejpam-6776	39	18	and	and	CCONJ
ejpam-6776	39	19	fuzzy	fuzzy	ADJ
ejpam-6776	39	20	caputo	caputo	PROPN
ejpam-6776	39	21	methods	method	NOUN
ejpam-6776	39	22	to	to	PART
ejpam-6776	39	23	capture	capture	VERB
ejpam-6776	39	24	complex	complex	ADJ
ejpam-6776	39	25	dynamics	dynamic	NOUN
ejpam-6776	39	26	[	[	X
ejpam-6776	39	27	7–10	7–10	X
ejpam-6776	39	28	]	]	PUNCT
ejpam-6776	39	29	.	.	PUNCT
ejpam-6776	40	1	intervention	intervention	NOUN
ejpam-6776	40	2	strategies	strategy	NOUN
ejpam-6776	40	3	,	,	PUNCT
ejpam-6776	40	4	both	both	PRON
ejpam-6776	40	5	pharmaceutical	pharmaceutical	NOUN
ejpam-6776	40	6	(	(	PUNCT
ejpam-6776	40	7	e.g.	e.g.	ADV
ejpam-6776	40	8	,	,	PUNCT
ejpam-6776	40	9	vaccination	vaccination	NOUN
ejpam-6776	40	10	)	)	PUNCT
ejpam-6776	40	11	and	and	CCONJ
ejpam-6776	40	12	non	non	ADJ
ejpam-6776	40	13	-	-	ADJ
ejpam-6776	40	14	pharmaceutical	pharmaceutical	ADJ
ejpam-6776	40	15	(	(	PUNCT
ejpam-6776	40	16	e.g.	e.g.	ADV
ejpam-6776	40	17	,	,	PUNCT
ejpam-6776	40	18	social	social	ADJ
ejpam-6776	40	19	distancing	distancing	NOUN
ejpam-6776	40	20	,	,	PUNCT
ejpam-6776	40	21	mask	mask	NOUN
ejpam-6776	40	22	-	-	PUNCT
ejpam-6776	40	23	wearing	wear	VERB
ejpam-6776	40	24	)	)	PUNCT
ejpam-6776	40	25	,	,	PUNCT
ejpam-6776	40	26	are	be	AUX
ejpam-6776	40	27	critical	critical	ADJ
ejpam-6776	40	28	for	for	ADP
ejpam-6776	40	29	controlling	control	VERB
ejpam-6776	40	30	disease	disease	NOUN
ejpam-6776	40	31	spread	spread	VERB
ejpam-6776	40	32	[	[	X
ejpam-6776	40	33	20	20	NUM
ejpam-6776	40	34	,	,	PUNCT
ejpam-6776	40	35	21	21	NUM
ejpam-6776	40	36	]	]	PUNCT
ejpam-6776	40	37	.	.	PUNCT
ejpam-6776	41	1	behavioral	behavioral	ADJ
ejpam-6776	41	2	responses	response	NOUN
ejpam-6776	41	3	,	,	PUNCT
ejpam-6776	41	4	such	such	ADJ
ejpam-6776	41	5	as	as	ADP
ejpam-6776	41	6	condom	condom	NOUN
ejpam-6776	41	7	use	use	NOUN
ejpam-6776	41	8	for	for	ADP
ejpam-6776	41	9	sti	sti	PROPN
ejpam-6776	41	10	prevention	prevention	PROPN
ejpam-6776	41	11	or	or	CCONJ
ejpam-6776	41	12	mask	mask	NOUN
ejpam-6776	41	13	adherence	adherence	NOUN
ejpam-6776	41	14	during	during	ADP
ejpam-6776	41	15	covid-19	covid-19	PROPN
ejpam-6776	41	16	,	,	PUNCT
ejpam-6776	41	17	shape	shape	NOUN
ejpam-6776	41	18	epidemic	epidemic	NOUN
ejpam-6776	41	19	trajectories	trajectory	NOUN
ejpam-6776	41	20	and	and	CCONJ
ejpam-6776	41	21	must	must	AUX
ejpam-6776	41	22	be	be	AUX
ejpam-6776	41	23	integrated	integrate	VERB
ejpam-6776	41	24	into	into	ADP
ejpam-6776	41	25	models	model	NOUN
ejpam-6776	41	26	for	for	ADP
ejpam-6776	41	27	effective	effective	ADJ
ejpam-6776	41	28	control	control	NOUN
ejpam-6776	42	1	[	[	X
ejpam-6776	42	2	20	20	NUM
ejpam-6776	42	3	,	,	PUNCT
ejpam-6776	42	4	21	21	NUM
ejpam-6776	42	5	]	]	PUNCT
ejpam-6776	42	6	.	.	PUNCT
ejpam-6776	43	1	zoonotic	zoonotic	ADJ
ejpam-6776	43	2	diseases	disease	NOUN
ejpam-6776	43	3	like	like	ADP
ejpam-6776	43	4	sars	sar	NOUN
ejpam-6776	43	5	-	-	PUNCT
ejpam-6776	43	6	cov-2	cov-2	NOUN
ejpam-6776	43	7	,	,	PUNCT
ejpam-6776	43	8	which	which	PRON
ejpam-6776	43	9	lack	lack	VERB
ejpam-6776	43	10	preexisting	preexist	VERB
ejpam-6776	43	11	immunity	immunity	NOUN
ejpam-6776	43	12	,	,	PUNCT
ejpam-6776	43	13	underscore	underscore	VERB
ejpam-6776	43	14	the	the	DET
ejpam-6776	43	15	reliance	reliance	NOUN
ejpam-6776	43	16	on	on	ADP
ejpam-6776	43	17	early	early	ADJ
ejpam-6776	43	18	non	non	ADJ
ejpam-6776	43	19	-	-	ADJ
ejpam-6776	43	20	pharmaceutical	pharmaceutical	ADJ
ejpam-6776	43	21	interventions	intervention	NOUN
ejpam-6776	43	22	,	,	PUNCT
ejpam-6776	43	23	despite	despite	SCONJ
ejpam-6776	43	24	their	their	PRON
ejpam-6776	43	25	social	social	ADJ
ejpam-6776	43	26	and	and	CCONJ
ejpam-6776	43	27	economic	economic	ADJ
ejpam-6776	43	28	costs	cost	NOUN
ejpam-6776	43	29	[	[	X
ejpam-6776	43	30	22–24	22–24	NUM
ejpam-6776	43	31	]	]	PUNCT
ejpam-6776	43	32	.	.	PUNCT
ejpam-6776	44	1	policymakers	policymaker	NOUN
ejpam-6776	44	2	have	have	AUX
ejpam-6776	44	3	leaned	lean	VERB
ejpam-6776	44	4	on	on	ADP
ejpam-6776	44	5	epidemic	epidemic	NOUN
ejpam-6776	44	6	models	model	NOUN
ejpam-6776	44	7	to	to	PART
ejpam-6776	44	8	navigate	navigate	VERB
ejpam-6776	44	9	these	these	DET
ejpam-6776	44	10	trade	trade	NOUN
ejpam-6776	44	11	-	-	PUNCT
ejpam-6776	44	12	offs	off	NOUN
ejpam-6776	44	13	,	,	PUNCT
ejpam-6776	44	14	though	though	SCONJ
ejpam-6776	44	15	comparing	compare	VERB
ejpam-6776	44	16	predictions	prediction	NOUN
ejpam-6776	44	17	remains	remains	AUX
ejpam-6776	44	18	challenging	challenge	VERB
ejpam-6776	44	19	without	without	ADP
ejpam-6776	44	20	robust	robust	ADJ
ejpam-6776	44	21	numerical	numerical	ADJ
ejpam-6776	44	22	and	and	CCONJ
ejpam-6776	44	23	theoretical	theoretical	ADJ
ejpam-6776	44	24	frameworks	framework	NOUN
ejpam-6776	44	25	[	[	X
ejpam-6776	44	26	22–24	22–24	NUM
ejpam-6776	44	27	]	]	PUNCT
ejpam-6776	44	28	.	.	PUNCT
ejpam-6776	45	1	the	the	DET
ejpam-6776	45	2	rise	rise	NOUN
ejpam-6776	45	3	of	of	ADP
ejpam-6776	45	4	emerging	emerge	VERB
ejpam-6776	45	5	infectious	infectious	ADJ
ejpam-6776	45	6	diseases	disease	NOUN
ejpam-6776	45	7	(	(	PUNCT
ejpam-6776	45	8	eids	eid	NOUN
ejpam-6776	45	9	)	)	PUNCT
ejpam-6776	45	10	like	like	ADP
ejpam-6776	45	11	covid-19	covid-19	PROPN
ejpam-6776	45	12	emphasizes	emphasize	VERB
ejpam-6776	45	13	the	the	DET
ejpam-6776	45	14	need	need	NOUN
ejpam-6776	45	15	to	to	PART
ejpam-6776	45	16	understand	understand	VERB
ejpam-6776	45	17	immune	immune	ADJ
ejpam-6776	45	18	responses	response	NOUN
ejpam-6776	45	19	and	and	CCONJ
ejpam-6776	45	20	transmission	transmission	NOUN
ejpam-6776	45	21	dynamics	dynamic	NOUN
ejpam-6776	45	22	[	[	X
ejpam-6776	45	23	25	25	NUM
ejpam-6776	45	24	]	]	PUNCT
ejpam-6776	45	25	.	.	PUNCT
ejpam-6776	46	1	research	research	NOUN
ejpam-6776	46	2	on	on	ADP
ejpam-6776	46	3	backward	backward	ADJ
ejpam-6776	46	4	bifurcation	bifurcation	NOUN
ejpam-6776	46	5	and	and	CCONJ
ejpam-6776	46	6	immunity	immunity	NOUN
ejpam-6776	46	7	decline	decline	NOUN
ejpam-6776	46	8	reveals	reveal	VERB
ejpam-6776	46	9	complex	complex	ADJ
ejpam-6776	46	10	patterns	pattern	NOUN
ejpam-6776	46	11	,	,	PUNCT
ejpam-6776	46	12	highlighting	highlight	VERB
ejpam-6776	46	13	the	the	DET
ejpam-6776	46	14	role	role	NOUN
ejpam-6776	46	15	of	of	ADP
ejpam-6776	46	16	mathematical	mathematical	ADJ
ejpam-6776	46	17	modeling	modeling	NOUN
ejpam-6776	46	18	in	in	ADP
ejpam-6776	46	19	crafting	craft	VERB
ejpam-6776	46	20	control	control	NOUN
ejpam-6776	46	21	strategies	strategy	NOUN
ejpam-6776	46	22	[	[	X
ejpam-6776	46	23	25	25	NUM
ejpam-6776	46	24	]	]	PUNCT
ejpam-6776	46	25	.	.	PUNCT
ejpam-6776	47	1	by	by	ADP
ejpam-6776	47	2	may	may	PROPN
ejpam-6776	47	3	2020	2020	NUM
ejpam-6776	47	4	,	,	PUNCT
ejpam-6776	47	5	covid-19	covid-19	PROPN
ejpam-6776	47	6	had	have	AUX
ejpam-6776	47	7	caused	cause	VERB
ejpam-6776	47	8	over	over	ADP
ejpam-6776	47	9	6.2	6.2	NUM
ejpam-6776	47	10	million	million	NUM
ejpam-6776	47	11	cases	case	NOUN
ejpam-6776	47	12	and	and	CCONJ
ejpam-6776	47	13	372,344	372,344	NUM
ejpam-6776	47	14	deaths	death	NOUN
ejpam-6776	47	15	globally	globally	ADV
ejpam-6776	47	16	,	,	PUNCT
ejpam-6776	47	17	yet	yet	CCONJ
ejpam-6776	47	18	national	national	ADJ
ejpam-6776	47	19	response	response	NOUN
ejpam-6776	47	20	strategies	strategy	NOUN
ejpam-6776	47	21	prevented	prevent	VERB
ejpam-6776	47	22	hundreds	hundred	NOUN
ejpam-6776	47	23	of	of	ADP
ejpam-6776	47	24	thousands	thousand	NOUN
ejpam-6776	47	25	of	of	ADP
ejpam-6776	47	26	cases	case	NOUN
ejpam-6776	47	27	in	in	ADP
ejpam-6776	47	28	several	several	ADJ
ejpam-6776	47	29	countries	country	NOUN
ejpam-6776	48	1	[	[	X
ejpam-6776	48	2	26	26	NUM
ejpam-6776	48	3	,	,	PUNCT
ejpam-6776	48	4	27	27	NUM
ejpam-6776	48	5	]	]	PUNCT
ejpam-6776	48	6	.	.	PUNCT
ejpam-6776	49	1	the	the	DET
ejpam-6776	49	2	world	world	PROPN
ejpam-6776	49	3	health	health	PROPN
ejpam-6776	49	4	organization	organization	NOUN
ejpam-6776	49	5	’s	’s	PART
ejpam-6776	49	6	six	six	NUM
ejpam-6776	49	7	criteria	criterion	NOUN
ejpam-6776	49	8	for	for	ADP
ejpam-6776	49	9	lifting	lift	VERB
ejpam-6776	49	10	lockdowns	lockdown	NOUN
ejpam-6776	49	11	—	—	PUNCT
ejpam-6776	49	12	controlled	control	VERB
ejpam-6776	49	13	transmission	transmission	NOUN
ejpam-6776	49	14	,	,	PUNCT
ejpam-6776	49	15	healthcare	healthcare	NOUN
ejpam-6776	49	16	readiness	readiness	NOUN
ejpam-6776	49	17	,	,	PUNCT
ejpam-6776	49	18	and	and	CCONJ
ejpam-6776	49	19	community	community	NOUN
ejpam-6776	49	20	engagement	engagement	NOUN
ejpam-6776	49	21	—	—	PUNCT
ejpam-6776	49	22	underscore	underscore	VERB
ejpam-6776	49	23	the	the	DET
ejpam-6776	49	24	need	need	NOUN
ejpam-6776	49	25	for	for	ADP
ejpam-6776	49	26	strategic	strategic	ADJ
ejpam-6776	49	27	planning	planning	NOUN
ejpam-6776	49	28	to	to	PART
ejpam-6776	49	29	prevent	prevent	VERB
ejpam-6776	49	30	resurgence	resurgence	NOUN
ejpam-6776	49	31	[	[	X
ejpam-6776	49	32	28	28	NUM
ejpam-6776	49	33	,	,	PUNCT
ejpam-6776	49	34	29	29	NUM
ejpam-6776	49	35	]	]	PUNCT
ejpam-6776	49	36	.	.	PUNCT
ejpam-6776	50	1	tools	tool	NOUN
ejpam-6776	50	2	like	like	ADP
ejpam-6776	50	3	swot	swot	NOUN
ejpam-6776	50	4	analysis	analysis	NOUN
ejpam-6776	50	5	have	have	AUX
ejpam-6776	50	6	further	far	ADV
ejpam-6776	50	7	supported	support	VERB
ejpam-6776	50	8	pandemic	pandemic	ADJ
ejpam-6776	50	9	control	control	NOUN
ejpam-6776	50	10	by	by	ADP
ejpam-6776	50	11	fostering	foster	VERB
ejpam-6776	50	12	resource	resource	NOUN
ejpam-6776	50	13	integration	integration	NOUN
ejpam-6776	50	14	across	across	ADP
ejpam-6776	50	15	sectors	sector	NOUN
ejpam-6776	50	16	[	[	X
ejpam-6776	50	17	26	26	NUM
ejpam-6776	50	18	,	,	PUNCT
ejpam-6776	50	19	27	27	NUM
ejpam-6776	50	20	]	]	PUNCT
ejpam-6776	50	21	.	.	PUNCT
ejpam-6776	51	1	tuberculosis	tuberculosis	NOUN
ejpam-6776	51	2	remains	remain	VERB
ejpam-6776	51	3	a	a	DET
ejpam-6776	51	4	global	global	ADJ
ejpam-6776	51	5	health	health	NOUN
ejpam-6776	51	6	priority	priority	NOUN
ejpam-6776	51	7	,	,	PUNCT
ejpam-6776	51	8	primarily	primarily	ADV
ejpam-6776	51	9	transmitted	transmit	VERB
ejpam-6776	51	10	through	through	ADP
ejpam-6776	51	11	airborne	airborne	ADJ
ejpam-6776	51	12	droplets	droplet	NOUN
ejpam-6776	51	13	and	and	CCONJ
ejpam-6776	51	14	influenced	influence	VERB
ejpam-6776	51	15	by	by	ADP
ejpam-6776	51	16	factors	factor	NOUN
ejpam-6776	51	17	like	like	ADP
ejpam-6776	51	18	exposure	exposure	NOUN
ejpam-6776	51	19	duration	duration	NOUN
ejpam-6776	51	20	and	and	CCONJ
ejpam-6776	51	21	environmental	environmental	ADJ
ejpam-6776	51	22	conditions	condition	NOUN
ejpam-6776	51	23	[	[	X
ejpam-6776	51	24	30	30	NUM
ejpam-6776	51	25	,	,	PUNCT
ejpam-6776	51	26	31	31	NUM
ejpam-6776	51	27	]	]	PUNCT
ejpam-6776	51	28	.	.	PUNCT
ejpam-6776	52	1	while	while	SCONJ
ejpam-6776	52	2	the	the	DET
ejpam-6776	52	3	immune	immune	ADJ
ejpam-6776	52	4	system	system	NOUN
ejpam-6776	52	5	often	often	ADV
ejpam-6776	52	6	controls	control	VERB
ejpam-6776	52	7	tb	tb	ADP
ejpam-6776	52	8	bacteria	bacteria	NOUN
ejpam-6776	52	9	,	,	PUNCT
ejpam-6776	52	10	unchecked	unchecked	ADJ
ejpam-6776	52	11	proliferation	proliferation	NOUN
ejpam-6776	52	12	leads	lead	VERB
ejpam-6776	52	13	to	to	ADP
ejpam-6776	52	14	active	active	ADJ
ejpam-6776	52	15	disease	disease	NOUN
ejpam-6776	52	16	,	,	PUNCT
ejpam-6776	52	17	posing	pose	VERB
ejpam-6776	52	18	significant	significant	ADJ
ejpam-6776	52	19	public	public	ADJ
ejpam-6776	52	20	health	health	NOUN
ejpam-6776	52	21	risks	risk	NOUN
ejpam-6776	52	22	in	in	ADP
ejpam-6776	52	23	high	high	ADJ
ejpam-6776	52	24	-	-	PUNCT
ejpam-6776	52	25	prevalence	prevalence	NOUN
ejpam-6776	52	26	regions	region	NOUN
ejpam-6776	52	27	[	[	X
ejpam-6776	52	28	31	31	NUM
ejpam-6776	52	29	,	,	PUNCT
ejpam-6776	52	30	32	32	NUM
ejpam-6776	52	31	]	]	PUNCT
ejpam-6776	52	32	.	.	PUNCT
ejpam-6776	53	1	similarly	similarly	ADV
ejpam-6776	53	2	,	,	PUNCT
ejpam-6776	53	3	pneumonia	pneumonia	NOUN
ejpam-6776	53	4	,	,	PUNCT
ejpam-6776	53	5	driven	drive	VERB
ejpam-6776	53	6	by	by	ADP
ejpam-6776	53	7	pathogens	pathogen	NOUN
ejpam-6776	53	8	like	like	ADP
ejpam-6776	53	9	streptococcus	streptococcus	VERB
ejpam-6776	53	10	pneumoniae	pneumoniae	NOUN
ejpam-6776	53	11	,	,	PUNCT
ejpam-6776	53	12	is	be	AUX
ejpam-6776	53	13	a	a	DET
ejpam-6776	53	14	leading	lead	VERB
ejpam-6776	53	15	cause	cause	NOUN
ejpam-6776	53	16	of	of	ADP
ejpam-6776	53	17	morbidity	morbidity	NOUN
ejpam-6776	53	18	and	and	CCONJ
ejpam-6776	53	19	mortality	mortality	NOUN
ejpam-6776	53	20	,	,	PUNCT
ejpam-6776	53	21	particularly	particularly	ADV
ejpam-6776	53	22	among	among	ADP
ejpam-6776	53	23	vulnerable	vulnerable	ADJ
ejpam-6776	53	24	populations	population	NOUN
ejpam-6776	53	25	[	[	X
ejpam-6776	53	26	33	33	NUM
ejpam-6776	53	27	]	]	PUNCT
ejpam-6776	53	28	.	.	PUNCT
ejpam-6776	54	1	vaccines	vaccine	NOUN
ejpam-6776	54	2	like	like	ADP
ejpam-6776	54	3	pcv	pcv	NOUN
ejpam-6776	54	4	and	and	CCONJ
ejpam-6776	54	5	ppv	ppv	NOUN
ejpam-6776	54	6	offer	offer	VERB
ejpam-6776	54	7	preventive	preventive	ADJ
ejpam-6776	54	8	benefits	benefit	NOUN
ejpam-6776	54	9	,	,	PUNCT
ejpam-6776	54	10	but	but	CCONJ
ejpam-6776	54	11	comprehensive	comprehensive	ADJ
ejpam-6776	54	12	strategies	strategy	NOUN
ejpam-6776	54	13	combining	combine	VERB
ejpam-6776	54	14	immunization	immunization	NOUN
ejpam-6776	54	15	,	,	PUNCT
ejpam-6776	54	16	treatment	treatment	NOUN
ejpam-6776	54	17	,	,	PUNCT
ejpam-6776	54	18	and	and	CCONJ
ejpam-6776	54	19	environmental	environmental	ADJ
ejpam-6776	54	20	controls	control	NOUN
ejpam-6776	54	21	are	be	AUX
ejpam-6776	54	22	essential	essential	ADJ
ejpam-6776	54	23	for	for	ADP
ejpam-6776	54	24	eradication	eradication	NOUN
ejpam-6776	54	25	[	[	X
ejpam-6776	54	26	33	33	NUM
ejpam-6776	54	27	]	]	PUNCT
ejpam-6776	54	28	.	.	PUNCT
ejpam-6776	55	1	beyond	beyond	ADP
ejpam-6776	55	2	modeling	modeling	NOUN
ejpam-6776	55	3	and	and	CCONJ
ejpam-6776	55	4	interventions	intervention	NOUN
ejpam-6776	55	5	,	,	PUNCT
ejpam-6776	55	6	systemic	systemic	ADJ
ejpam-6776	55	7	improvements	improvement	NOUN
ejpam-6776	55	8	in	in	ADP
ejpam-6776	55	9	healthcare	healthcare	NOUN
ejpam-6776	55	10	are	be	AUX
ejpam-6776	55	11	crucial	crucial	ADJ
ejpam-6776	55	12	for	for	ADP
ejpam-6776	55	13	addressing	address	VERB
ejpam-6776	55	14	infectious	infectious	ADJ
ejpam-6776	55	15	diseases	disease	NOUN
ejpam-6776	55	16	.	.	PUNCT
ejpam-6776	56	1	while	while	SCONJ
ejpam-6776	56	2	simulation	simulation	NOUN
ejpam-6776	56	3	-	-	PUNCT
ejpam-6776	56	4	based	base	VERB
ejpam-6776	56	5	training	training	NOUN
ejpam-6776	56	6	enhances	enhance	VERB
ejpam-6776	56	7	patient	patient	ADJ
ejpam-6776	56	8	safety	safety	NOUN
ejpam-6776	56	9	,	,	PUNCT
ejpam-6776	56	10	it	it	PRON
ejpam-6776	56	11	must	must	AUX
ejpam-6776	56	12	be	be	AUX
ejpam-6776	56	13	paired	pair	VERB
ejpam-6776	56	14	with	with	ADP
ejpam-6776	56	15	structural	structural	ADJ
ejpam-6776	56	16	changes	change	NOUN
ejpam-6776	56	17	,	,	PUNCT
ejpam-6776	56	18	cultural	cultural	ADJ
ejpam-6776	56	19	shifts	shift	NOUN
ejpam-6776	56	20	,	,	PUNCT
ejpam-6776	56	21	and	and	CCONJ
ejpam-6776	56	22	process	process	NOUN
ejpam-6776	56	23	improvements	improvement	NOUN
ejpam-6776	56	24	to	to	PART
ejpam-6776	56	25	ensure	ensure	VERB
ejpam-6776	56	26	lasting	lasting	ADJ
ejpam-6776	56	27	impact	impact	NOUN
ejpam-6776	57	1	[	[	X
ejpam-6776	57	2	34	34	NUM
ejpam-6776	57	3	]	]	PUNCT
ejpam-6776	57	4	.	.	PUNCT
ejpam-6776	58	1	these	these	DET
ejpam-6776	58	2	efforts	effort	NOUN
ejpam-6776	58	3	,	,	PUNCT
ejpam-6776	58	4	combined	combine	VERB
ejpam-6776	58	5	with	with	ADP
ejpam-6776	58	6	advanced	advanced	ADJ
ejpam-6776	58	7	modeling	modeling	NOUN
ejpam-6776	58	8	and	and	CCONJ
ejpam-6776	58	9	environmental	environmental	ADJ
ejpam-6776	58	10	monitoring	monitoring	NOUN
ejpam-6776	58	11	,	,	PUNCT
ejpam-6776	58	12	form	form	VERB
ejpam-6776	58	13	a	a	DET
ejpam-6776	58	14	holistic	holistic	ADJ
ejpam-6776	58	15	approach	approach	NOUN
ejpam-6776	58	16	to	to	ADP
ejpam-6776	58	17	tackling	tackle	VERB
ejpam-6776	58	18	global	global	ADJ
ejpam-6776	58	19	health	health	NOUN
ejpam-6776	58	20	challenges	challenge	NOUN
ejpam-6776	58	21	.	.	PUNCT
ejpam-6776	59	1	the	the	DET
ejpam-6776	59	2	interplay	interplay	NOUN
ejpam-6776	59	3	of	of	ADP
ejpam-6776	59	4	infectious	infectious	ADJ
ejpam-6776	59	5	diseases	disease	NOUN
ejpam-6776	59	6	,	,	PUNCT
ejpam-6776	59	7	environmental	environmental	ADJ
ejpam-6776	59	8	factors	factor	NOUN
ejpam-6776	59	9	,	,	PUNCT
ejpam-6776	59	10	and	and	CCONJ
ejpam-6776	59	11	stochastic	stochastic	ADJ
ejpam-6776	59	12	dynamics	dynamic	NOUN
ejpam-6776	59	13	demands	demand	VERB
ejpam-6776	59	14	innovative	innovative	ADJ
ejpam-6776	59	15	solutions	solution	NOUN
ejpam-6776	59	16	.	.	PUNCT
ejpam-6776	60	1	stochastic	stochastic	ADJ
ejpam-6776	60	2	modeling	modeling	NOUN
ejpam-6776	60	3	,	,	PUNCT
ejpam-6776	60	4	with	with	ADP
ejpam-6776	60	5	its	its	PRON
ejpam-6776	60	6	ability	ability	NOUN
ejpam-6776	60	7	to	to	PART
ejpam-6776	60	8	capture	capture	VERB
ejpam-6776	60	9	uncertainty	uncertainty	NOUN
ejpam-6776	60	10	and	and	CCONJ
ejpam-6776	60	11	variability	variability	NOUN
ejpam-6776	60	12	,	,	PUNCT
ejpam-6776	60	13	offers	offer	VERB
ejpam-6776	60	14	a	a	DET
ejpam-6776	60	15	powerful	powerful	ADJ
ejpam-6776	60	16	tool	tool	NOUN
ejpam-6776	60	17	for	for	ADP
ejpam-6776	60	18	predicting	predict	VERB
ejpam-6776	60	19	and	and	CCONJ
ejpam-6776	60	20	controlling	control	VERB
ejpam-6776	60	21	epidemics	epidemic	NOUN
ejpam-6776	60	22	.	.	PUNCT
ejpam-6776	61	1	j.	j.	PROPN
ejpam-6776	61	2	leo	leo	PROPN
ejpam-6776	61	3	amalraj	amalraj	PROPN
ejpam-6776	61	4	et	et	PROPN
ejpam-6776	61	5	al	al	PROPN
ejpam-6776	61	6	.	.	PUNCT
ejpam-6776	61	7	/	/	SYM
ejpam-6776	61	8	eur	eur	PROPN
ejpam-6776	61	9	.	.	PUNCT
ejpam-6776	62	1	j.	j.	PROPN
ejpam-6776	62	2	pure	pure	PROPN
ejpam-6776	62	3	appl	appl	PROPN
ejpam-6776	62	4	.	.	PROPN
ejpam-6776	62	5	math	math	PROPN
ejpam-6776	62	6	,	,	PUNCT
ejpam-6776	62	7	18	18	NUM
ejpam-6776	62	8	(	(	PUNCT
ejpam-6776	62	9	4	4	NUM
ejpam-6776	62	10	)	)	PUNCT
ejpam-6776	62	11	(	(	PUNCT
ejpam-6776	62	12	2025	2025	NUM
ejpam-6776	62	13	)	)	PUNCT
ejpam-6776	62	14	,	,	PUNCT
ejpam-6776	62	15	6776	6776	NUM
ejpam-6776	62	16	4	4	NUM
ejpam-6776	62	17	of	of	ADP
ejpam-6776	62	18	22	22	NUM
ejpam-6776	62	19	coupled	couple	VERB
ejpam-6776	62	20	with	with	ADP
ejpam-6776	62	21	robust	robust	ADJ
ejpam-6776	62	22	intervention	intervention	NOUN
ejpam-6776	62	23	strategies	strategy	NOUN
ejpam-6776	62	24	and	and	CCONJ
ejpam-6776	62	25	systemic	systemic	ADJ
ejpam-6776	62	26	healthcare	healthcare	NOUN
ejpam-6776	62	27	improvements	improvement	NOUN
ejpam-6776	62	28	,	,	PUNCT
ejpam-6776	62	29	these	these	DET
ejpam-6776	62	30	approaches	approach	NOUN
ejpam-6776	62	31	can	can	AUX
ejpam-6776	62	32	mitigate	mitigate	VERB
ejpam-6776	62	33	the	the	DET
ejpam-6776	62	34	global	global	ADJ
ejpam-6776	62	35	burden	burden	NOUN
ejpam-6776	62	36	of	of	ADP
ejpam-6776	62	37	diseases	disease	NOUN
ejpam-6776	62	38	like	like	ADP
ejpam-6776	62	39	tb	tb	NOUN
ejpam-6776	62	40	,	,	PUNCT
ejpam-6776	62	41	hiv	hiv	PROPN
ejpam-6776	62	42	,	,	PUNCT
ejpam-6776	62	43	and	and	CCONJ
ejpam-6776	62	44	covid-19	covid-19	PROPN
ejpam-6776	62	45	.	.	PROPN
ejpam-6776	63	1	continued	continue	VERB
ejpam-6776	63	2	research	research	NOUN
ejpam-6776	63	3	into	into	ADP
ejpam-6776	63	4	environmental	environmental	ADJ
ejpam-6776	63	5	health	health	NOUN
ejpam-6776	63	6	,	,	PUNCT
ejpam-6776	63	7	particularly	particularly	ADV
ejpam-6776	63	8	air	air	NOUN
ejpam-6776	63	9	pollution	pollution	NOUN
ejpam-6776	63	10	and	and	CCONJ
ejpam-6776	63	11	ufps	ufps	NOUN
ejpam-6776	63	12	,	,	PUNCT
ejpam-6776	63	13	will	will	AUX
ejpam-6776	63	14	further	far	ADV
ejpam-6776	63	15	strengthen	strengthen	VERB
ejpam-6776	63	16	public	public	ADJ
ejpam-6776	63	17	health	health	NOUN
ejpam-6776	63	18	responses	response	NOUN
ejpam-6776	63	19	,	,	PUNCT
ejpam-6776	63	20	paving	pave	VERB
ejpam-6776	63	21	the	the	DET
ejpam-6776	63	22	way	way	NOUN
ejpam-6776	63	23	for	for	ADP
ejpam-6776	63	24	a	a	DET
ejpam-6776	63	25	more	more	ADV
ejpam-6776	63	26	resilient	resilient	ADJ
ejpam-6776	63	27	future	future	NOUN
ejpam-6776	63	28	.	.	PUNCT
ejpam-6776	64	1	2	2	X
ejpam-6776	64	2	.	.	X
ejpam-6776	64	3	long	long	ADJ
ejpam-6776	64	4	-	-	PUNCT
ejpam-6776	64	5	term	term	NOUN
ejpam-6776	64	6	behavior	behavior	NOUN
ejpam-6776	64	7	of	of	ADP
ejpam-6776	64	8	the	the	DET
ejpam-6776	64	9	epidemic	epidemic	NOUN
ejpam-6776	64	10	we	we	PRON
ejpam-6776	64	11	investigate	investigate	VERB
ejpam-6776	64	12	the	the	DET
ejpam-6776	64	13	persistence	persistence	NOUN
ejpam-6776	64	14	of	of	ADP
ejpam-6776	64	15	an	an	DET
ejpam-6776	64	16	infectious	infectious	ADJ
ejpam-6776	64	17	disease	disease	NOUN
ejpam-6776	64	18	using	use	VERB
ejpam-6776	64	19	a	a	DET
ejpam-6776	64	20	stochastic	stochastic	ADJ
ejpam-6776	64	21	model	model	NOUN
ejpam-6776	64	22	,	,	PUNCT
ejpam-6776	64	23	focusing	focus	VERB
ejpam-6776	64	24	on	on	ADP
ejpam-6776	64	25	the	the	DET
ejpam-6776	64	26	susceptible	susceptible	ADJ
ejpam-6776	64	27	(	(	PUNCT
ejpam-6776	64	28	s(t	s(t	PROPN
ejpam-6776	64	29	)	)	PUNCT
ejpam-6776	64	30	)	)	PUNCT
ejpam-6776	64	31	and	and	CCONJ
ejpam-6776	64	32	infected	infect	VERB
ejpam-6776	64	33	(	(	PUNCT
ejpam-6776	64	34	i(t	i(t	PROPN
ejpam-6776	64	35	)	)	PUNCT
ejpam-6776	64	36	)	)	PUNCT
ejpam-6776	64	37	populations	population	NOUN
ejpam-6776	64	38	.	.	PUNCT
ejpam-6776	65	1	define	define	VERB
ejpam-6776	65	2	the	the	DET
ejpam-6776	65	3	positive	positive	ADJ
ejpam-6776	65	4	cone	cone	NOUN
ejpam-6776	65	5	:	:	PUNCT
ejpam-6776	65	6	r2	r2	NOUN
ejpam-6776	65	7	+	+	CCONJ
ejpam-6776	65	8	=	=	SYM
ejpam-6776	65	9	{	{	PUNCT
ejpam-6776	65	10	(	(	PUNCT
ejpam-6776	65	11	x	x	NOUN
ejpam-6776	65	12	,	,	PUNCT
ejpam-6776	65	13	y	y	NOUN
ejpam-6776	65	14	)	)	PUNCT
ejpam-6776	65	15	∈	∈	PROPN
ejpam-6776	65	16	r2	r2	NOUN
ejpam-6776	65	17	:	:	PUNCT
ejpam-6776	65	18	x	x	SYM
ejpam-6776	65	19	>	>	X
ejpam-6776	65	20	0	0	PROPN
ejpam-6776	65	21	,	,	PUNCT
ejpam-6776	65	22	y	y	PROPN
ejpam-6776	65	23	>	>	X
ejpam-6776	65	24	0	0	NUM
ejpam-6776	65	25	}	}	PUNCT
ejpam-6776	65	26	,	,	PUNCT
ejpam-6776	65	27	representing	represent	VERB
ejpam-6776	65	28	biologically	biologically	ADV
ejpam-6776	65	29	relevant	relevant	ADJ
ejpam-6776	65	30	states	state	NOUN
ejpam-6776	65	31	.	.	PUNCT
ejpam-6776	66	1	here	here	ADV
ejpam-6776	66	2	,	,	PUNCT
ejpam-6776	66	3	s(t	s(t	PROPN
ejpam-6776	66	4	)	)	PUNCT
ejpam-6776	66	5	(	(	PUNCT
ejpam-6776	66	6	or	or	CCONJ
ejpam-6776	66	7	simply	simply	ADV
ejpam-6776	66	8	s(t	s(t	PROPN
ejpam-6776	66	9	)	)	PUNCT
ejpam-6776	66	10	)	)	PUNCT
ejpam-6776	66	11	represents	represent	VERB
ejpam-6776	66	12	the	the	DET
ejpam-6776	66	13	number	number	NOUN
ejpam-6776	66	14	of	of	ADP
ejpam-6776	66	15	susceptible	susceptible	ADJ
ejpam-6776	66	16	individuals	individual	NOUN
ejpam-6776	66	17	in	in	ADP
ejpam-6776	66	18	the	the	DET
ejpam-6776	66	19	population	population	NOUN
ejpam-6776	66	20	at	at	ADP
ejpam-6776	66	21	time	time	NOUN
ejpam-6776	66	22	t.	t.	PROPN
ejpam-6776	66	23	lemma	lemma	PROPN
ejpam-6776	66	24	1	1	NUM
ejpam-6776	66	25	.	.	PUNCT
ejpam-6776	67	1	for	for	ADP
ejpam-6776	67	2	any	any	DET
ejpam-6776	67	3	initial	initial	ADJ
ejpam-6776	67	4	condition	condition	NOUN
ejpam-6776	67	5	(	(	PUNCT
ejpam-6776	67	6	s(0	s(0	PROPN
ejpam-6776	67	7	)	)	PUNCT
ejpam-6776	67	8	,	,	PUNCT
ejpam-6776	67	9	i(0	i(0	PROPN
ejpam-6776	67	10	)	)	PUNCT
ejpam-6776	67	11	)	)	PUNCT
ejpam-6776	68	1	∈	∈	PROPN
ejpam-6776	68	2	r2	r2	NOUN
ejpam-6776	68	3	+	+	ADV
ejpam-6776	68	4	,	,	PUNCT
ejpam-6776	68	5	the	the	DET
ejpam-6776	68	6	solution	solution	NOUN
ejpam-6776	68	7	to	to	ADP
ejpam-6776	68	8	the	the	DET
ejpam-6776	68	9	stochastic	stochastic	ADJ
ejpam-6776	68	10	system	system	NOUN
ejpam-6776	68	11	:	:	PUNCT
ejpam-6776	68	12	ds(t	ds(t	X
ejpam-6776	68	13	)	)	PUNCT
ejpam-6776	68	14	=	=	SYM
ejpam-6776	68	15	(	(	PUNCT
ejpam-6776	68	16	λ−	λ−	PROPN
ejpam-6776	68	17	βs(t)i(t	βs(t)i(t	ADV
ejpam-6776	68	18	)	)	PUNCT
ejpam-6776	68	19	1+ki(t	1+ki(t	NUM
ejpam-6776	68	20	)	)	PUNCT
ejpam-6776	68	21	−	−	NOUN
ejpam-6776	68	22	δs(t	δs(t	NUM
ejpam-6776	68	23	)	)	PUNCT
ejpam-6776	68	24	)	)	PUNCT
ejpam-6776	69	1	dt−	dt−	PUNCT
ejpam-6776	69	2	σs(t)i(t	σs(t)i(t	ADJ
ejpam-6776	69	3	)	)	PUNCT
ejpam-6776	69	4	1+ki(t	1+ki(t	NUM
ejpam-6776	69	5	)	)	PUNCT
ejpam-6776	69	6	db(t	db(t	NOUN
ejpam-6776	69	7	)	)	PUNCT
ejpam-6776	69	8	,	,	PUNCT
ejpam-6776	69	9	di(t	di(t	NOUN
ejpam-6776	69	10	)	)	PUNCT
ejpam-6776	70	1	=	=	NOUN
ejpam-6776	70	2	(	(	PUNCT
ejpam-6776	70	3	βs(t)i(t	βs(t)i(t	ADP
ejpam-6776	70	4	)	)	PUNCT
ejpam-6776	70	5	1+ki(t	1+ki(t	NUM
ejpam-6776	70	6	)	)	PUNCT
ejpam-6776	70	7	−	−	PROPN
ejpam-6776	71	1	(	(	PUNCT
ejpam-6776	71	2	δ	δ	PROPN
ejpam-6776	71	3	+	+	CCONJ
ejpam-6776	71	4	γ	γ	PROPN
ejpam-6776	71	5	+	+	X
ejpam-6776	71	6	ϵ)i(t)−	ϵ)i(t)−	PROPN
ejpam-6776	71	7	αi(t	αi(t	NOUN
ejpam-6776	71	8	)	)	PUNCT
ejpam-6776	71	9	λ+i(t	λ+i(t	NOUN
ejpam-6776	71	10	)	)	PUNCT
ejpam-6776	71	11	)	)	PUNCT
ejpam-6776	72	1	dt+	dt+	NOUN
ejpam-6776	72	2	σs(t)i(t	σs(t)i(t	NOUN
ejpam-6776	72	3	)	)	PUNCT
ejpam-6776	72	4	1+ki(t	1+ki(t	NUM
ejpam-6776	72	5	)	)	PUNCT
ejpam-6776	72	6	db(t	db(t	NOUN
ejpam-6776	72	7	)	)	PUNCT
ejpam-6776	72	8	,	,	PUNCT
ejpam-6776	72	9	(	(	PUNCT
ejpam-6776	72	10	1	1	X
ejpam-6776	72	11	)	)	PUNCT
ejpam-6776	72	12	remains	remain	VERB
ejpam-6776	72	13	in	in	ADP
ejpam-6776	72	14	r2	r2	PROPN
ejpam-6776	72	15	+	+	CCONJ
ejpam-6776	72	16	for	for	ADP
ejpam-6776	72	17	all	all	DET
ejpam-6776	72	18	t	t	NOUN
ejpam-6776	72	19	≥	≥	NOUN
ejpam-6776	72	20	0	0	NUM
ejpam-6776	72	21	almost	almost	ADV
ejpam-6776	72	22	surely	surely	ADV
ejpam-6776	72	23	,	,	PUNCT
ejpam-6776	72	24	i.e.	i.e.	X
ejpam-6776	72	25	,	,	PUNCT
ejpam-6776	72	26	p((s(t	p((s(t	NOUN
ejpam-6776	72	27	)	)	PUNCT
ejpam-6776	72	28	,	,	PUNCT
ejpam-6776	72	29	i(t	i(t	PROPN
ejpam-6776	72	30	)	)	PUNCT
ejpam-6776	72	31	)	)	PUNCT
ejpam-6776	73	1	∈	∈	NOUN
ejpam-6776	73	2	r2	r2	NOUN
ejpam-6776	73	3	+	+	CCONJ
ejpam-6776	73	4	∀t	∀t	PROPN
ejpam-6776	73	5	≥	≥	NOUN
ejpam-6776	73	6	0	0	NUM
ejpam-6776	73	7	)	)	PUNCT
ejpam-6776	73	8	=	=	SYM
ejpam-6776	73	9	1	1	X
ejpam-6776	73	10	.	.	PUNCT
ejpam-6776	74	1	proof	proof	NOUN
ejpam-6776	74	2	.	.	PUNCT
ejpam-6776	75	1	the	the	DET
ejpam-6776	75	2	system	system	NOUN
ejpam-6776	75	3	(	(	PUNCT
ejpam-6776	75	4	1	1	X
ejpam-6776	75	5	)	)	PUNCT
ejpam-6776	75	6	has	have	AUX
ejpam-6776	75	7	locally	locally	ADV
ejpam-6776	75	8	lipschitz	lipschitz	NOUN
ejpam-6776	75	9	coefficients	coefficient	NOUN
ejpam-6776	75	10	,	,	PUNCT
ejpam-6776	75	11	ensuring	ensure	VERB
ejpam-6776	75	12	a	a	DET
ejpam-6776	75	13	unique	unique	ADJ
ejpam-6776	75	14	solution	solution	NOUN
ejpam-6776	75	15	up	up	ADP
ejpam-6776	75	16	to	to	ADP
ejpam-6776	75	17	an	an	DET
ejpam-6776	75	18	explosion	explosion	NOUN
ejpam-6776	75	19	time	time	NOUN
ejpam-6776	75	20	τ∗	τ∗	X
ejpam-6776	75	21	∈	∈	PROPN
ejpam-6776	75	22	(	(	PUNCT
ejpam-6776	75	23	0,∞	0,∞	NOUN
ejpam-6776	75	24	]	]	PUNCT
ejpam-6776	75	25	.	.	PUNCT
ejpam-6776	76	1	solving	solve	VERB
ejpam-6776	76	2	explicitly	explicitly	ADV
ejpam-6776	76	3	,	,	PUNCT
ejpam-6776	76	4	we	we	PRON
ejpam-6776	76	5	obtain	obtain	VERB
ejpam-6776	76	6	:	:	PUNCT
ejpam-6776	76	7	s(t	s(t	NUM
ejpam-6776	76	8	)	)	PUNCT
ejpam-6776	76	9	=	=	SYM
ejpam-6776	76	10	s(0	s(0	PROPN
ejpam-6776	76	11	)	)	PUNCT
ejpam-6776	76	12	exp	exp	NOUN
ejpam-6776	76	13	(	(	PUNCT
ejpam-6776	76	14	∫	∫	PROPN
ejpam-6776	76	15	t	t	PROPN
ejpam-6776	76	16	0	0	NUM
ejpam-6776	77	1	(	(	PUNCT
ejpam-6776	77	2	−	−	PROPN
ejpam-6776	77	3	βi(u	βi(u	NUM
ejpam-6776	77	4	)	)	PUNCT
ejpam-6776	77	5	1	1	NUM
ejpam-6776	78	1	+	+	NUM
ejpam-6776	78	2	ki(u	ki(u	NOUN
ejpam-6776	78	3	)	)	PUNCT
ejpam-6776	79	1	−	−	PROPN
ejpam-6776	79	2	δ	δ	PROPN
ejpam-6776	79	3	−	−	PROPN
ejpam-6776	79	4	σ2i2(u	σ2i2(u	NOUN
ejpam-6776	79	5	)	)	PUNCT
ejpam-6776	79	6	2(1	2(1	NUM
ejpam-6776	80	1	+	+	CCONJ
ejpam-6776	80	2	ki(u))2	ki(u))2	PROPN
ejpam-6776	80	3	)	)	PUNCT
ejpam-6776	80	4	du−	du−	PROPN
ejpam-6776	80	5	∫	∫	PROPN
ejpam-6776	80	6	t	t	PROPN
ejpam-6776	80	7	0	0	NUM
ejpam-6776	80	8	σi(u	σi(u	NOUN
ejpam-6776	80	9	)	)	PUNCT
ejpam-6776	80	10	1	1	NUM
ejpam-6776	80	11	+	+	CCONJ
ejpam-6776	80	12	ki(u	ki(u	NOUN
ejpam-6776	80	13	)	)	PUNCT
ejpam-6776	80	14	db(u	db(u	X
ejpam-6776	80	15	)	)	PUNCT
ejpam-6776	80	16	)	)	PUNCT
ejpam-6776	80	17	,	,	PUNCT
ejpam-6776	80	18	i(t	i(t	PROPN
ejpam-6776	80	19	)	)	PUNCT
ejpam-6776	81	1	=	=	SYM
ejpam-6776	81	2	i(0	i(0	PROPN
ejpam-6776	81	3	)	)	PUNCT
ejpam-6776	81	4	exp	exp	NOUN
ejpam-6776	81	5	(	(	PUNCT
ejpam-6776	81	6	∫	∫	PROPN
ejpam-6776	81	7	t	t	PROPN
ejpam-6776	81	8	0	0	NUM
ejpam-6776	81	9	(	(	PUNCT
ejpam-6776	81	10	βs(u	βs(u	SYM
ejpam-6776	81	11	)	)	PUNCT
ejpam-6776	81	12	1	1	NUM
ejpam-6776	81	13	+	+	NUM
ejpam-6776	81	14	ki(u	ki(u	NOUN
ejpam-6776	81	15	)	)	PUNCT
ejpam-6776	81	16	−	−	PROPN
ejpam-6776	82	1	(	(	PUNCT
ejpam-6776	82	2	δ	δ	PROPN
ejpam-6776	82	3	+	+	CCONJ
ejpam-6776	82	4	γ	γ	PROPN
ejpam-6776	82	5	+	+	X
ejpam-6776	82	6	ϵ)−	ϵ)−	ADJ
ejpam-6776	82	7	α	α	NOUN
ejpam-6776	82	8	λ+	λ+	PUNCT
ejpam-6776	82	9	i(u	i(u	PROPN
ejpam-6776	82	10	)	)	PUNCT
ejpam-6776	83	1	−	−	PROPN
ejpam-6776	83	2	σ2s2(u	σ2s2(u	NOUN
ejpam-6776	83	3	)	)	PUNCT
ejpam-6776	83	4	2(1	2(1	NUM
ejpam-6776	84	1	+	+	CCONJ
ejpam-6776	84	2	ki(u))2	ki(u))2	PROPN
ejpam-6776	84	3	)	)	PUNCT
ejpam-6776	84	4	du+	du+	NOUN
ejpam-6776	84	5	∫	∫	PROPN
ejpam-6776	84	6	t	t	PROPN
ejpam-6776	84	7	0	0	NUM
ejpam-6776	84	8	σs(u	σs(u	PROPN
ejpam-6776	84	9	)	)	PUNCT
ejpam-6776	84	10	1	1	NUM
ejpam-6776	84	11	+	+	NUM
ejpam-6776	84	12	ki(u	ki(u	NOUN
ejpam-6776	84	13	)	)	PUNCT
ejpam-6776	84	14	db(u	db(u	X
ejpam-6776	84	15	)	)	PUNCT
ejpam-6776	84	16	)	)	PUNCT
ejpam-6776	84	17	.	.	PUNCT
ejpam-6776	85	1	since	since	SCONJ
ejpam-6776	85	2	s(0	s(0	PROPN
ejpam-6776	85	3	)	)	PUNCT
ejpam-6776	85	4	,	,	PUNCT
ejpam-6776	85	5	i(0	i(0	PROPN
ejpam-6776	85	6	)	)	PUNCT
ejpam-6776	85	7	>	>	X
ejpam-6776	85	8	0	0	NUM
ejpam-6776	85	9	,	,	PUNCT
ejpam-6776	85	10	the	the	DET
ejpam-6776	85	11	exponential	exponential	ADJ
ejpam-6776	85	12	terms	term	NOUN
ejpam-6776	85	13	guarantee	guarantee	VERB
ejpam-6776	85	14	positivity	positivity	NOUN
ejpam-6776	85	15	for	for	ADP
ejpam-6776	85	16	t	t	PROPN
ejpam-6776	85	17	<	<	X
ejpam-6776	85	18	τ∗.	τ∗.	PUNCT
ejpam-6776	85	19	to	to	PART
ejpam-6776	85	20	prove	prove	VERB
ejpam-6776	85	21	τ∗	τ∗	NOUN
ejpam-6776	85	22	=	=	SYM
ejpam-6776	85	23	∞	∞	NOUN
ejpam-6776	85	24	almost	almost	ADV
ejpam-6776	85	25	surely	surely	ADV
ejpam-6776	85	26	,	,	PUNCT
ejpam-6776	85	27	suppose	suppose	VERB
ejpam-6776	85	28	p(τ∗	p(τ∗	X
ejpam-6776	85	29	<	<	X
ejpam-6776	85	30	∞	∞	PROPN
ejpam-6776	85	31	)	)	PUNCT
ejpam-6776	85	32	>	>	X
ejpam-6776	86	1	0	0	X
ejpam-6776	86	2	.	.	PUNCT
ejpam-6776	87	1	then	then	ADV
ejpam-6776	87	2	,	,	PUNCT
ejpam-6776	87	3	there	there	PRON
ejpam-6776	87	4	exist	exist	VERB
ejpam-6776	87	5	t	t	PROPN
ejpam-6776	87	6	,	,	PUNCT
ejpam-6776	87	7	κ	κ	X
ejpam-6776	87	8	>	>	X
ejpam-6776	87	9	0	0	NUM
ejpam-6776	87	10	such	such	ADJ
ejpam-6776	87	11	that	that	DET
ejpam-6776	87	12	p(τ∗	p(τ∗	NOUN
ejpam-6776	87	13	<	<	X
ejpam-6776	87	14	t	t	PROPN
ejpam-6776	87	15	)	)	PUNCT
ejpam-6776	87	16	>	>	X
ejpam-6776	88	1	κ	κ	X
ejpam-6776	88	2	.	.	PUNCT
ejpam-6776	88	3	define	define	VERB
ejpam-6776	88	4	the	the	DET
ejpam-6776	88	5	stopping	stopping	NOUN
ejpam-6776	88	6	time	time	NOUN
ejpam-6776	88	7	:	:	PUNCT
ejpam-6776	88	8	τn	τn	NOUN
ejpam-6776	88	9	=	=	PUNCT
ejpam-6776	88	10	inf{t	inf{t	PROPN
ejpam-6776	88	11	∈	∈	PROPN
ejpam-6776	88	12	(	(	PUNCT
ejpam-6776	88	13	0	0	NUM
ejpam-6776	88	14	,	,	PUNCT
ejpam-6776	88	15	τ∗	τ∗	NOUN
ejpam-6776	88	16	)	)	PUNCT
ejpam-6776	88	17	:	:	PUNCT
ejpam-6776	88	18	s(t	s(t	NUM
ejpam-6776	88	19	)	)	PUNCT
ejpam-6776	88	20	+	+	CCONJ
ejpam-6776	88	21	i(t	i(t	PROPN
ejpam-6776	88	22	)	)	PUNCT
ejpam-6776	88	23	≥	≥	NOUN
ejpam-6776	88	24	n	n	CCONJ
ejpam-6776	88	25	}	}	PUNCT
ejpam-6776	88	26	.	.	PUNCT
ejpam-6776	89	1	for	for	ADP
ejpam-6776	89	2	large	large	ADJ
ejpam-6776	89	3	n	n	CCONJ
ejpam-6776	89	4	,	,	PUNCT
ejpam-6776	89	5	p(τn	p(τn	PROPN
ejpam-6776	89	6	<	<	X
ejpam-6776	89	7	t	t	PROPN
ejpam-6776	89	8	)	)	PUNCT
ejpam-6776	89	9	>	>	X
ejpam-6776	89	10	κ	κ	X
ejpam-6776	89	11	.	.	PUNCT
ejpam-6776	89	12	summing	sum	VERB
ejpam-6776	89	13	(	(	PUNCT
ejpam-6776	89	14	1	1	NUM
ejpam-6776	89	15	):	):	PUNCT
ejpam-6776	89	16	d(s	d(s	PROPN
ejpam-6776	89	17	+	+	PROPN
ejpam-6776	89	18	i	i	NOUN
ejpam-6776	89	19	)	)	PUNCT
ejpam-6776	89	20	≤	≤	NOUN
ejpam-6776	89	21	(	(	PUNCT
ejpam-6776	89	22	λ−	λ−	PROPN
ejpam-6776	89	23	δ(s	δ(s	PROPN
ejpam-6776	89	24	+	+	CCONJ
ejpam-6776	89	25	i	i	NOUN
ejpam-6776	89	26	)	)	PUNCT
ejpam-6776	89	27	)	)	PUNCT
ejpam-6776	90	1	dt	dt	X
ejpam-6776	90	2	,	,	PUNCT
ejpam-6776	90	3	since	since	SCONJ
ejpam-6776	90	4	(	(	PUNCT
ejpam-6776	90	5	γ	γ	X
ejpam-6776	90	6	+	+	NUM
ejpam-6776	90	7	ϵ)i	ϵ)i	PUNCT
ejpam-6776	90	8	+	+	CCONJ
ejpam-6776	90	9	αi	αi	X
ejpam-6776	90	10	λ+i	λ+i	PUNCT
ejpam-6776	90	11	≥	≥	NOUN
ejpam-6776	90	12	0	0	NUM
ejpam-6776	90	13	.	.	PUNCT
ejpam-6776	90	14	integrating	integrate	VERB
ejpam-6776	90	15	over	over	ADP
ejpam-6776	90	16	[	[	X
ejpam-6776	90	17	0	0	NUM
ejpam-6776	90	18	,	,	PUNCT
ejpam-6776	90	19	t	t	NOUN
ejpam-6776	90	20	∧	∧	PROPN
ejpam-6776	90	21	τn	τn	PROPN
ejpam-6776	90	22	]	]	PUNCT
ejpam-6776	90	23	:	:	PUNCT
ejpam-6776	90	24	s(t	s(t	PROPN
ejpam-6776	90	25	∧	∧	PROPN
ejpam-6776	90	26	τn	τn	PROPN
ejpam-6776	90	27	)	)	PUNCT
ejpam-6776	90	28	+	+	NUM
ejpam-6776	90	29	i(t	i(t	NOUN
ejpam-6776	90	30	∧	∧	PROPN
ejpam-6776	90	31	τn	τn	NOUN
ejpam-6776	90	32	)	)	PUNCT
ejpam-6776	90	33	≤	≤	NOUN
ejpam-6776	90	34	s(0	s(0	PROPN
ejpam-6776	90	35	)	)	PUNCT
ejpam-6776	90	36	+	+	PUNCT
ejpam-6776	90	37	i(0	i(0	PROPN
ejpam-6776	90	38	)	)	PUNCT
ejpam-6776	91	1	+	+	CCONJ
ejpam-6776	91	2	λ(t	λ(t	NOUN
ejpam-6776	91	3	∧	∧	PROPN
ejpam-6776	91	4	τn	τn	NOUN
ejpam-6776	91	5	)	)	PUNCT
ejpam-6776	91	6	.	.	PUNCT
ejpam-6776	92	1	j.	j.	PROPN
ejpam-6776	92	2	leo	leo	PROPN
ejpam-6776	92	3	amalraj	amalraj	PROPN
ejpam-6776	92	4	et	et	PROPN
ejpam-6776	92	5	al	al	PROPN
ejpam-6776	92	6	.	.	PUNCT
ejpam-6776	92	7	/	/	SYM
ejpam-6776	92	8	eur	eur	PROPN
ejpam-6776	92	9	.	.	PUNCT
ejpam-6776	93	1	j.	j.	PROPN
ejpam-6776	93	2	pure	pure	PROPN
ejpam-6776	93	3	appl	appl	PROPN
ejpam-6776	93	4	.	.	PROPN
ejpam-6776	93	5	math	math	PROPN
ejpam-6776	93	6	,	,	PUNCT
ejpam-6776	93	7	18	18	NUM
ejpam-6776	93	8	(	(	PUNCT
ejpam-6776	93	9	4	4	NUM
ejpam-6776	93	10	)	)	PUNCT
ejpam-6776	93	11	(	(	PUNCT
ejpam-6776	93	12	2025	2025	NUM
ejpam-6776	93	13	)	)	PUNCT
ejpam-6776	93	14	,	,	PUNCT
ejpam-6776	93	15	6776	6776	NUM
ejpam-6776	93	16	5	5	NUM
ejpam-6776	93	17	of	of	ADP
ejpam-6776	93	18	22	22	NUM
ejpam-6776	93	19	taking	take	VERB
ejpam-6776	93	20	expectations	expectation	NOUN
ejpam-6776	93	21	:	:	PUNCT
ejpam-6776	93	22	e[s(τn	e[s(τn	PROPN
ejpam-6776	93	23	)	)	PUNCT
ejpam-6776	94	1	+	+	CCONJ
ejpam-6776	95	1	i(τn	i(τn	PROPN
ejpam-6776	95	2	)	)	PUNCT
ejpam-6776	95	3	]	]	PUNCT
ejpam-6776	96	1	≤	≤	NUM
ejpam-6776	96	2	s(0	s(0	PROPN
ejpam-6776	96	3	)	)	PUNCT
ejpam-6776	96	4	+	+	PUNCT
ejpam-6776	96	5	i(0	i(0	PROPN
ejpam-6776	96	6	)	)	PUNCT
ejpam-6776	96	7	+	+	CCONJ
ejpam-6776	97	1	λt	λt	AUX
ejpam-6776	97	2	.	.	NOUN
ejpam-6776	97	3	since	since	SCONJ
ejpam-6776	97	4	s(τn	s(τn	PROPN
ejpam-6776	97	5	)	)	PUNCT
ejpam-6776	97	6	+	+	NUM
ejpam-6776	97	7	i(τn	i(τn	PROPN
ejpam-6776	97	8	)	)	PUNCT
ejpam-6776	97	9	≥	≥	NOUN
ejpam-6776	97	10	n	n	CCONJ
ejpam-6776	97	11	on	on	ADV
ejpam-6776	97	12	{	{	PUNCT
ejpam-6776	97	13	τn	τn	ADP
ejpam-6776	97	14	<	<	X
ejpam-6776	97	15	t	t	PROPN
ejpam-6776	97	16	}	}	PUNCT
ejpam-6776	97	17	,	,	PUNCT
ejpam-6776	97	18	we	we	PRON
ejpam-6776	97	19	get	get	VERB
ejpam-6776	97	20	nκ	nκ	DET
ejpam-6776	97	21	≤	≤	ADJ
ejpam-6776	97	22	s(0	s(0	PROPN
ejpam-6776	97	23	)	)	PUNCT
ejpam-6776	97	24	+	+	PUNCT
ejpam-6776	98	1	i(0	i(0	PROPN
ejpam-6776	98	2	)	)	PUNCT
ejpam-6776	99	1	+	+	CCONJ
ejpam-6776	99	2	λt	λt	ADP
ejpam-6776	99	3	,	,	PUNCT
ejpam-6776	99	4	a	a	DET
ejpam-6776	99	5	contradiction	contradiction	NOUN
ejpam-6776	99	6	as	as	ADP
ejpam-6776	99	7	n→	n→	PUNCT
ejpam-6776	99	8	∞.	∞.	PROPN
ejpam-6776	99	9	thus	thus	ADV
ejpam-6776	99	10	,	,	PUNCT
ejpam-6776	99	11	p(τ∗	p(τ∗	X
ejpam-6776	99	12	<	<	X
ejpam-6776	99	13	∞	∞	NOUN
ejpam-6776	99	14	)	)	PUNCT
ejpam-6776	99	15	=	=	SYM
ejpam-6776	99	16	0	0	NUM
ejpam-6776	99	17	,	,	PUNCT
ejpam-6776	99	18	ensuring	ensure	VERB
ejpam-6776	99	19	positivity	positivity	NOUN
ejpam-6776	99	20	.	.	PUNCT
ejpam-6776	100	1	to	to	PART
ejpam-6776	100	2	ensure	ensure	VERB
ejpam-6776	100	3	the	the	DET
ejpam-6776	100	4	model	model	NOUN
ejpam-6776	100	5	’s	’s	PART
ejpam-6776	100	6	biological	biological	ADJ
ejpam-6776	100	7	realism	realism	NOUN
ejpam-6776	100	8	,	,	PUNCT
ejpam-6776	100	9	we	we	PRON
ejpam-6776	100	10	confirm	confirm	VERB
ejpam-6776	100	11	that	that	SCONJ
ejpam-6776	100	12	solutions	solution	NOUN
ejpam-6776	100	13	remain	remain	VERB
ejpam-6776	100	14	bounded	bounded	ADJ
ejpam-6776	100	15	within	within	ADP
ejpam-6776	100	16	an	an	DET
ejpam-6776	100	17	invariant	invariant	ADJ
ejpam-6776	100	18	region	region	NOUN
ejpam-6776	100	19	.	.	PUNCT
ejpam-6776	101	1	lemma	lemma	PROPN
ejpam-6776	101	2	2	2	X
ejpam-6776	101	3	.	.	PUNCT
ejpam-6776	101	4	define	define	VERB
ejpam-6776	101	5	the	the	DET
ejpam-6776	101	6	region	region	NOUN
ejpam-6776	101	7	:	:	PUNCT
ejpam-6776	102	1	d	d	X
ejpam-6776	102	2	=	=	PRON
ejpam-6776	102	3	{	{	PUNCT
ejpam-6776	102	4	(	(	PUNCT
ejpam-6776	102	5	x	x	NOUN
ejpam-6776	102	6	,	,	PUNCT
ejpam-6776	102	7	y	y	NOUN
ejpam-6776	102	8	)	)	PUNCT
ejpam-6776	102	9	∈	∈	NOUN
ejpam-6776	102	10	r2	r2	NOUN
ejpam-6776	102	11	+	+	CCONJ
ejpam-6776	102	12	:	:	PUNCT
ejpam-6776	102	13	z∗	z∗	X
ejpam-6776	102	14	<	<	X
ejpam-6776	102	15	x+	x+	X
ejpam-6776	102	16	y	y	PROPN
ejpam-6776	102	17	<	<	X
ejpam-6776	102	18	λ	λ	X
ejpam-6776	102	19	δ	δ	PROPN
ejpam-6776	102	20	}	}	PUNCT
ejpam-6776	102	21	,	,	PUNCT
ejpam-6776	102	22	where	where	SCONJ
ejpam-6776	102	23	z∗	z∗	NOUN
ejpam-6776	102	24	is	be	AUX
ejpam-6776	102	25	the	the	DET
ejpam-6776	102	26	unique	unique	ADJ
ejpam-6776	102	27	root	root	NOUN
ejpam-6776	102	28	of	of	ADP
ejpam-6776	102	29	:	:	PUNCT
ejpam-6776	102	30	ψ(z	ψ(z	PROPN
ejpam-6776	102	31	)	)	PUNCT
ejpam-6776	102	32	=	=	SYM
ejpam-6776	102	33	λ−	λ−	PROPN
ejpam-6776	102	34	(	(	PUNCT
ejpam-6776	102	35	δ	δ	PROPN
ejpam-6776	102	36	+	+	CCONJ
ejpam-6776	102	37	γ	γ	X
ejpam-6776	102	38	+	+	CCONJ
ejpam-6776	102	39	ϵ)z	ϵ)z	NOUN
ejpam-6776	102	40	−	−	X
ejpam-6776	102	41	αz	αz	NOUN
ejpam-6776	102	42	λ+	λ+	PUNCT
ejpam-6776	102	43	z	z	X
ejpam-6776	102	44	.	.	PUNCT
ejpam-6776	103	1	(	(	PUNCT
ejpam-6776	103	2	2	2	NUM
ejpam-6776	103	3	)	)	PUNCT
ejpam-6776	103	4	then	then	ADV
ejpam-6776	103	5	,	,	PUNCT
ejpam-6776	103	6	d	d	PRON
ejpam-6776	103	7	is	be	AUX
ejpam-6776	103	8	positively	positively	ADV
ejpam-6776	103	9	invariant	invariant	ADJ
ejpam-6776	103	10	and	and	CCONJ
ejpam-6776	103	11	attractive	attractive	ADJ
ejpam-6776	103	12	for	for	ADP
ejpam-6776	103	13	(	(	PUNCT
ejpam-6776	103	14	1	1	NUM
ejpam-6776	103	15	)	)	PUNCT
ejpam-6776	103	16	.	.	PUNCT
ejpam-6776	104	1	proof	proof	NOUN
ejpam-6776	104	2	.	.	PUNCT
ejpam-6776	105	1	let	let	VERB
ejpam-6776	105	2	z(t	z(t	NOUN
ejpam-6776	105	3	)	)	PUNCT
ejpam-6776	105	4	=	=	SYM
ejpam-6776	105	5	s(t	s(t	PROPN
ejpam-6776	105	6	)	)	PUNCT
ejpam-6776	105	7	+	+	NUM
ejpam-6776	105	8	i(t	i(t	NOUN
ejpam-6776	105	9	)	)	PUNCT
ejpam-6776	105	10	.	.	PUNCT
ejpam-6776	106	1	from	from	ADP
ejpam-6776	106	2	(	(	PUNCT
ejpam-6776	106	3	1	1	NUM
ejpam-6776	106	4	):	):	PUNCT
ejpam-6776	106	5	dz	dz	ADJ
ejpam-6776	106	6	dt	dt	NOUN
ejpam-6776	106	7	=	=	SYM
ejpam-6776	106	8	λ−	λ−	PROPN
ejpam-6776	106	9	δz	δz	X
ejpam-6776	106	10	−	−	PROPN
ejpam-6776	106	11	(	(	PUNCT
ejpam-6776	106	12	γ	γ	X
ejpam-6776	106	13	+	+	X
ejpam-6776	106	14	ϵ)i	ϵ)i	NOUN
ejpam-6776	106	15	−	−	PROPN
ejpam-6776	106	16	αi	αi	VERB
ejpam-6776	106	17	λ+	λ+	PUNCT
ejpam-6776	106	18	i	i	PRON
ejpam-6776	106	19	.	.	PUNCT
ejpam-6776	107	1	since	since	SCONJ
ejpam-6776	107	2	i	i	PRON
ejpam-6776	107	3	≤	≤	X
ejpam-6776	108	1	z	z	NOUN
ejpam-6776	108	2	:	:	PUNCT
ejpam-6776	108	3	dz	dz	PROPN
ejpam-6776	108	4	dt	dt	X
ejpam-6776	108	5	≤	≤	PROPN
ejpam-6776	108	6	λ−	λ−	PROPN
ejpam-6776	108	7	δz	δz	NOUN
ejpam-6776	108	8	.	.	PUNCT
ejpam-6776	109	1	consider	consider	VERB
ejpam-6776	109	2	the	the	DET
ejpam-6776	109	3	comparison	comparison	NOUN
ejpam-6776	109	4	equation	equation	NOUN
ejpam-6776	109	5	:	:	PUNCT
ejpam-6776	109	6	dz̄	dz̄	NOUN
ejpam-6776	109	7	dt	dt	NOUN
ejpam-6776	109	8	=	=	SYM
ejpam-6776	109	9	λ−	λ−	PROPN
ejpam-6776	109	10	δz̄	δz̄	NOUN
ejpam-6776	109	11	,	,	PUNCT
ejpam-6776	109	12	z̄(0	z̄(0	NUM
ejpam-6776	109	13	)	)	PUNCT
ejpam-6776	109	14	=	=	PUNCT
ejpam-6776	109	15	z(0	z(0	X
ejpam-6776	109	16	)	)	PUNCT
ejpam-6776	109	17	.	.	PUNCT
ejpam-6776	110	1	solving	solve	VERB
ejpam-6776	110	2	:	:	PUNCT
ejpam-6776	110	3	z̄(t	z̄(t	X
ejpam-6776	110	4	)	)	PUNCT
ejpam-6776	111	1	=	=	PUNCT
ejpam-6776	111	2	λ	λ	X
ejpam-6776	111	3	δ	δ	PROPN
ejpam-6776	111	4	+	+	X
ejpam-6776	111	5	(	(	PUNCT
ejpam-6776	111	6	z(0)−	z(0)−	PROPN
ejpam-6776	111	7	λ	λ	PROPN
ejpam-6776	111	8	δ	δ	PROPN
ejpam-6776	111	9	)	)	PUNCT
ejpam-6776	111	10	e−δt	e−δt	PROPN
ejpam-6776	111	11	.	.	PUNCT
ejpam-6776	112	1	thus	thus	ADV
ejpam-6776	112	2	,	,	PUNCT
ejpam-6776	112	3	limt→∞	limt→∞	PROPN
ejpam-6776	112	4	z̄(t	z̄(t	ADJ
ejpam-6776	112	5	)	)	PUNCT
ejpam-6776	112	6	=	=	PUNCT
ejpam-6776	112	7	λ	λ	PROPN
ejpam-6776	112	8	δ	δ	PROPN
ejpam-6776	112	9	,	,	PUNCT
ejpam-6776	112	10	and	and	CCONJ
ejpam-6776	112	11	z(t	z(t	NOUN
ejpam-6776	112	12	)	)	PUNCT
ejpam-6776	112	13	≤	≤	NOUN
ejpam-6776	112	14	z̄(t	z̄(t	NUM
ejpam-6776	112	15	)	)	PUNCT
ejpam-6776	112	16	.	.	PUNCT
ejpam-6776	113	1	now	now	ADV
ejpam-6776	113	2	:	:	PUNCT
ejpam-6776	113	3	dz	dz	PROPN
ejpam-6776	113	4	dt	dt	X
ejpam-6776	113	5	≥	≥	PROPN
ejpam-6776	113	6	ψ(z	ψ(z	PROPN
ejpam-6776	113	7	)	)	PUNCT
ejpam-6776	113	8	,	,	PUNCT
ejpam-6776	113	9	where	where	SCONJ
ejpam-6776	113	10	ψ(z	ψ(z	PROPN
ejpam-6776	113	11	)	)	PUNCT
ejpam-6776	113	12	is	be	AUX
ejpam-6776	113	13	decreasing	decrease	VERB
ejpam-6776	113	14	,	,	PUNCT
ejpam-6776	113	15	with	with	ADP
ejpam-6776	113	16	ψ(0	ψ(0	NOUN
ejpam-6776	113	17	)	)	PUNCT
ejpam-6776	113	18	=	=	PUNCT
ejpam-6776	114	1	λ	λ	X
ejpam-6776	114	2	>	>	X
ejpam-6776	114	3	0	0	NUM
ejpam-6776	114	4	,	,	PUNCT
ejpam-6776	114	5	ψ(λ	ψ(λ	ADJ
ejpam-6776	114	6	/	/	SYM
ejpam-6776	114	7	δ	δ	NOUN
ejpam-6776	114	8	)	)	PUNCT
ejpam-6776	115	1	<	<	X
ejpam-6776	115	2	0	0	X
ejpam-6776	115	3	.	.	PUNCT
ejpam-6776	116	1	hence	hence	ADV
ejpam-6776	116	2	,	,	PUNCT
ejpam-6776	116	3	ψ(z∗	ψ(z∗	NOUN
ejpam-6776	116	4	)	)	PUNCT
ejpam-6776	116	5	=	=	SYM
ejpam-6776	116	6	0	0	NUM
ejpam-6776	116	7	for	for	ADP
ejpam-6776	116	8	a	a	DET
ejpam-6776	116	9	unique	unique	ADJ
ejpam-6776	116	10	z∗	z∗	NOUN
ejpam-6776	116	11	∈	∈	NOUN
ejpam-6776	116	12	(	(	PUNCT
ejpam-6776	116	13	0,λ	0,λ	NOUN
ejpam-6776	116	14	/	/	SYM
ejpam-6776	116	15	δ	δ	PROPN
ejpam-6776	116	16	)	)	PUNCT
ejpam-6776	116	17	.	.	PUNCT
ejpam-6776	117	1	by	by	ADP
ejpam-6776	117	2	comparison	comparison	NOUN
ejpam-6776	117	3	,	,	PUNCT
ejpam-6776	117	4	if	if	SCONJ
ejpam-6776	117	5	z(0	z(0	NOUN
ejpam-6776	117	6	)	)	PUNCT
ejpam-6776	117	7	>	>	X
ejpam-6776	117	8	z∗	z∗	PROPN
ejpam-6776	117	9	,	,	PUNCT
ejpam-6776	117	10	then	then	ADV
ejpam-6776	117	11	z(t	z(t	NOUN
ejpam-6776	117	12	)	)	PUNCT
ejpam-6776	117	13	≥	≥	NOUN
ejpam-6776	117	14	z∗.	z∗.	PROPN
ejpam-6776	117	15	for	for	ADP
ejpam-6776	117	16	attractivity	attractivity	NOUN
ejpam-6776	117	17	,	,	PUNCT
ejpam-6776	117	18	if	if	SCONJ
ejpam-6776	117	19	z(0	z(0	NOUN
ejpam-6776	117	20	)	)	PUNCT
ejpam-6776	117	21	>	>	PUNCT
ejpam-6776	117	22	λ	λ	PROPN
ejpam-6776	117	23	/	/	SYM
ejpam-6776	117	24	δ	δ	PROPN
ejpam-6776	117	25	:	:	PUNCT
ejpam-6776	117	26	dz	dz	X
ejpam-6776	117	27	dt	dt	X
ejpam-6776	117	28	∣∣	∣∣	X
ejpam-6776	117	29	z	z	PROPN
ejpam-6776	117	30	=	=	SYM
ejpam-6776	117	31	λ	λ	VERB
ejpam-6776	117	32	/	/	SYM
ejpam-6776	117	33	δ+a	δ+a	X
ejpam-6776	117	34	<	<	X
ejpam-6776	117	35	−δa	−δa	PROPN
ejpam-6776	117	36	,	,	PUNCT
ejpam-6776	117	37	so	so	ADV
ejpam-6776	117	38	z(t	z(t	NOUN
ejpam-6776	117	39	)	)	PUNCT
ejpam-6776	117	40	decreases	decrease	VERB
ejpam-6776	117	41	toward	toward	ADP
ejpam-6776	117	42	λ	λ	PROPN
ejpam-6776	117	43	/	/	SYM
ejpam-6776	117	44	δ	δ	PROPN
ejpam-6776	117	45	.	.	PUNCT
ejpam-6776	118	1	if	if	SCONJ
ejpam-6776	118	2	z(0	z(0	NOUN
ejpam-6776	118	3	)	)	PUNCT
ejpam-6776	119	1	<	<	X
ejpam-6776	119	2	z∗	z∗	PROPN
ejpam-6776	119	3	,	,	PUNCT
ejpam-6776	119	4	then	then	ADV
ejpam-6776	119	5	ψ(z	ψ(z	PROPN
ejpam-6776	119	6	)	)	PUNCT
ejpam-6776	119	7	>	>	X
ejpam-6776	119	8	0	0	NUM
ejpam-6776	119	9	,	,	PUNCT
ejpam-6776	119	10	so	so	ADV
ejpam-6776	119	11	z(t	z(t	NOUN
ejpam-6776	119	12	)	)	PUNCT
ejpam-6776	119	13	increases	increase	NOUN
ejpam-6776	119	14	toward	toward	ADP
ejpam-6776	119	15	z∗.	z∗.	NOUN
ejpam-6776	119	16	thus	thus	ADV
ejpam-6776	119	17	,	,	PUNCT
ejpam-6776	119	18	d	d	PROPN
ejpam-6776	119	19	is	be	AUX
ejpam-6776	119	20	invariant	invariant	ADJ
ejpam-6776	119	21	and	and	CCONJ
ejpam-6776	119	22	attractive	attractive	ADJ
ejpam-6776	119	23	.	.	PUNCT
ejpam-6776	120	1	we	we	PRON
ejpam-6776	120	2	now	now	ADV
ejpam-6776	120	3	analyze	analyze	VERB
ejpam-6776	120	4	the	the	DET
ejpam-6776	120	5	persistence	persistence	NOUN
ejpam-6776	120	6	of	of	ADP
ejpam-6776	120	7	the	the	DET
ejpam-6776	120	8	infected	infected	ADJ
ejpam-6776	120	9	population	population	NOUN
ejpam-6776	120	10	within	within	ADP
ejpam-6776	120	11	d.	d.	PROPN
ejpam-6776	120	12	j.	j.	PROPN
ejpam-6776	120	13	leo	leo	PROPN
ejpam-6776	120	14	amalraj	amalraj	PROPN
ejpam-6776	120	15	et	et	PROPN
ejpam-6776	120	16	al	al	PROPN
ejpam-6776	120	17	.	.	PUNCT
ejpam-6776	120	18	/	/	SYM
ejpam-6776	120	19	eur	eur	PROPN
ejpam-6776	120	20	.	.	PUNCT
ejpam-6776	121	1	j.	j.	PROPN
ejpam-6776	121	2	pure	pure	PROPN
ejpam-6776	121	3	appl	appl	PROPN
ejpam-6776	121	4	.	.	PROPN
ejpam-6776	121	5	math	math	PROPN
ejpam-6776	121	6	,	,	PUNCT
ejpam-6776	121	7	18	18	NUM
ejpam-6776	121	8	(	(	PUNCT
ejpam-6776	121	9	4	4	NUM
ejpam-6776	121	10	)	)	PUNCT
ejpam-6776	121	11	(	(	PUNCT
ejpam-6776	121	12	2025	2025	NUM
ejpam-6776	121	13	)	)	PUNCT
ejpam-6776	121	14	,	,	PUNCT
ejpam-6776	121	15	6776	6776	NUM
ejpam-6776	121	16	6	6	NUM
ejpam-6776	121	17	of	of	ADP
ejpam-6776	121	18	22	22	NUM
ejpam-6776	121	19	theorem	theorem	NOUN
ejpam-6776	121	20	1	1	NUM
ejpam-6776	121	21	.	.	PUNCT
ejpam-6776	122	1	for	for	ADP
ejpam-6776	122	2	(	(	PUNCT
ejpam-6776	122	3	s(0	s(0	PROPN
ejpam-6776	122	4	)	)	PUNCT
ejpam-6776	122	5	,	,	PUNCT
ejpam-6776	122	6	i(0	i(0	PROPN
ejpam-6776	122	7	)	)	PUNCT
ejpam-6776	122	8	)	)	PUNCT
ejpam-6776	123	1	∈	∈	PROPN
ejpam-6776	123	2	d	d	NOUN
ejpam-6776	123	3	,	,	PUNCT
ejpam-6776	123	4	the	the	DET
ejpam-6776	123	5	disease	disease	NOUN
ejpam-6776	123	6	goes	go	VERB
ejpam-6776	123	7	extinct	extinct	ADJ
ejpam-6776	123	8	if	if	SCONJ
ejpam-6776	123	9	:	:	PUNCT
ejpam-6776	123	10	η	η	PROPN
ejpam-6776	123	11	=	=	PROPN
ejpam-6776	123	12	βλ	βλ	PROPN
ejpam-6776	123	13	δ	δ	PROPN
ejpam-6776	123	14	−	−	PROPN
ejpam-6776	123	15	(	(	PUNCT
ejpam-6776	123	16	δ	δ	PROPN
ejpam-6776	123	17	+	+	CCONJ
ejpam-6776	123	18	γ	γ	PROPN
ejpam-6776	123	19	+	+	X
ejpam-6776	123	20	ϵ)−	ϵ)−	ADJ
ejpam-6776	123	21	α	α	NOUN
ejpam-6776	123	22	λ	λ	NOUN
ejpam-6776	123	23	−	−	NOUN
ejpam-6776	123	24	1	1	NUM
ejpam-6776	123	25	2	2	NUM
ejpam-6776	123	26	σ2	σ2	NOUN
ejpam-6776	123	27	(	(	PUNCT
ejpam-6776	123	28	λ	λ	X
ejpam-6776	123	29	δ	δ	PROPN
ejpam-6776	123	30	)	)	PUNCT
ejpam-6776	123	31	2	2	NUM
ejpam-6776	123	32	<	<	X
ejpam-6776	123	33	0	0	NUM
ejpam-6776	123	34	.	.	PUNCT
ejpam-6776	124	1	(	(	PUNCT
ejpam-6776	124	2	3	3	NUM
ejpam-6776	124	3	)	)	PUNCT
ejpam-6776	124	4	then	then	ADV
ejpam-6776	124	5	:	:	PUNCT
ejpam-6776	124	6	lim	lim	PROPN
ejpam-6776	124	7	inf	inf	PROPN
ejpam-6776	124	8	t→∞	t→∞	X
ejpam-6776	124	9	e[i(t	e[i(t	PROPN
ejpam-6776	124	10	)	)	PUNCT
ejpam-6776	124	11	]	]	PUNCT
ejpam-6776	125	1	≥	≥	PROPN
ejpam-6776	125	2	mi	mi	PROPN
ejpam-6776	125	3	,	,	PUNCT
ejpam-6776	125	4	where	where	SCONJ
ejpam-6776	125	5	mi	mi	PROPN
ejpam-6776	125	6	>	>	X
ejpam-6776	125	7	0	0	PROPN
ejpam-6776	125	8	is	be	AUX
ejpam-6776	125	9	a	a	DET
ejpam-6776	125	10	constant	constant	ADJ
ejpam-6776	125	11	.	.	PUNCT
ejpam-6776	126	1	proof	proof	NOUN
ejpam-6776	126	2	.	.	PUNCT
ejpam-6776	127	1	define	define	VERB
ejpam-6776	127	2	:	:	PUNCT
ejpam-6776	127	3	ξ	ξ	X
ejpam-6776	127	4	=	=	PUNCT
ejpam-6776	127	5	βλ	βλ	PROPN
ejpam-6776	127	6	δ	δ	PROPN
ejpam-6776	127	7	−	−	PROPN
ejpam-6776	128	1	(	(	PUNCT
ejpam-6776	128	2	δ	δ	PROPN
ejpam-6776	128	3	+	+	CCONJ
ejpam-6776	128	4	γ	γ	X
ejpam-6776	128	5	+	+	X
ejpam-6776	128	6	ϵ+	ϵ+	PUNCT
ejpam-6776	128	7	α	α	X
ejpam-6776	128	8	λ	λ	X
ejpam-6776	128	9	+	+	CCONJ
ejpam-6776	128	10	σ2λ2	σ2λ2	X
ejpam-6776	128	11	2δ2	2δ2	NUM
ejpam-6776	128	12	)	)	PUNCT
ejpam-6776	128	13	.	.	PUNCT
ejpam-6776	129	1	by	by	SCONJ
ejpam-6776	129	2	(	(	PUNCT
ejpam-6776	129	3	3	3	NUM
ejpam-6776	129	4	)	)	PUNCT
ejpam-6776	129	5	,	,	PUNCT
ejpam-6776	129	6	ξ	ξ	X
ejpam-6776	129	7	>	>	X
ejpam-6776	129	8	0	0	X
ejpam-6776	129	9	.	.	PUNCT
ejpam-6776	129	10	consider	consider	VERB
ejpam-6776	129	11	the	the	DET
ejpam-6776	129	12	lyapunov	lyapunov	ADJ
ejpam-6776	129	13	function	function	NOUN
ejpam-6776	129	14	:	:	PUNCT
ejpam-6776	130	1	w	w	X
ejpam-6776	130	2	(	(	PUNCT
ejpam-6776	130	3	s	s	PROPN
ejpam-6776	130	4	,	,	PUNCT
ejpam-6776	130	5	i	i	NOUN
ejpam-6776	130	6	)	)	PUNCT
ejpam-6776	130	7	=	=	PUNCT
ejpam-6776	130	8	(	(	PUNCT
ejpam-6776	130	9	1	1	NUM
ejpam-6776	130	10	+	+	NUM
ejpam-6776	130	11	λ	λ	X
ejpam-6776	130	12	δ	δ	X
ejpam-6776	130	13	−	−	PROPN
ejpam-6776	130	14	s	s	PART
ejpam-6776	130	15	)	)	PUNCT
ejpam-6776	130	16	i−θ	i−θ	PROPN
ejpam-6776	130	17	,	,	PUNCT
ejpam-6776	130	18	where	where	SCONJ
ejpam-6776	130	19	θ	θ	PROPN
ejpam-6776	130	20	>	>	X
ejpam-6776	130	21	0	0	NUM
ejpam-6776	130	22	satisfies	satisfie	NOUN
ejpam-6776	130	23	:	:	PUNCT
ejpam-6776	130	24	θ	θ	X
ejpam-6776	130	25	<	<	X
ejpam-6776	130	26	2ξ	2ξ	PROPN
ejpam-6776	130	27	σ2	σ2	PROPN
ejpam-6776	130	28	.	.	PUNCT
ejpam-6776	131	1	by	by	ADP
ejpam-6776	131	2	itô	itô	PROPN
ejpam-6776	131	3	’s	’s	PART
ejpam-6776	131	4	lemma	lemma	PROPN
ejpam-6776	131	5	:	:	PUNCT
ejpam-6776	131	6	dw	dw	PROPN
ejpam-6776	131	7	=	=	PUNCT
ejpam-6776	131	8	lwdt+	lwdt+	X
ejpam-6776	131	9	σsi−θ	σsi−θ	NOUN
ejpam-6776	131	10	1	1	NUM
ejpam-6776	132	1	+	+	NUM
ejpam-6776	132	2	ki	ki	PROPN
ejpam-6776	132	3	[	[	PUNCT
ejpam-6776	132	4	i	i	PRON
ejpam-6776	132	5	−	−	PROPN
ejpam-6776	132	6	θ	θ	NOUN
ejpam-6776	132	7	(	(	PUNCT
ejpam-6776	132	8	1	1	NUM
ejpam-6776	133	1	+	+	NUM
ejpam-6776	133	2	λ	λ	X
ejpam-6776	133	3	δ	δ	X
ejpam-6776	133	4	−	−	PROPN
ejpam-6776	133	5	s	s	PART
ejpam-6776	133	6	)	)	PUNCT
ejpam-6776	133	7	]	]	PUNCT
ejpam-6776	133	8	db(t	db(t	NOUN
ejpam-6776	133	9	)	)	PUNCT
ejpam-6776	133	10	,	,	PUNCT
ejpam-6776	133	11	where	where	SCONJ
ejpam-6776	133	12	:	:	PUNCT
ejpam-6776	133	13	lw	lw	PROPN
ejpam-6776	133	14	=	=	PRON
ejpam-6776	133	15	(	(	PUNCT
ejpam-6776	133	16	λ−	λ−	PROPN
ejpam-6776	133	17	βsi	βsi	NOUN
ejpam-6776	133	18	1	1	NUM
ejpam-6776	133	19	+	+	NUM
ejpam-6776	133	20	ki	ki	PROPN
ejpam-6776	133	21	−	−	PROPN
ejpam-6776	133	22	δs	δs	PROPN
ejpam-6776	133	23	)	)	PUNCT
ejpam-6776	133	24	i−θ−θ	i−θ−θ	NOUN
ejpam-6776	134	1	(	(	PUNCT
ejpam-6776	134	2	1	1	NUM
ejpam-6776	134	3	+	+	NUM
ejpam-6776	134	4	λ	λ	X
ejpam-6776	134	5	δ	δ	X
ejpam-6776	134	6	−	−	PROPN
ejpam-6776	134	7	s	s	PART
ejpam-6776	134	8	)	)	PUNCT
ejpam-6776	134	9	i−θ	i−θ	PROPN
ejpam-6776	134	10	(	(	PUNCT
ejpam-6776	134	11	βs	βs	ADP
ejpam-6776	134	12	1	1	NUM
ejpam-6776	134	13	+	+	CCONJ
ejpam-6776	134	14	ki	ki	PROPN
ejpam-6776	134	15	−	−	PROPN
ejpam-6776	134	16	(	(	PUNCT
ejpam-6776	134	17	δ	δ	PROPN
ejpam-6776	134	18	+	+	CCONJ
ejpam-6776	134	19	γ	γ	PROPN
ejpam-6776	134	20	+	+	X
ejpam-6776	134	21	ϵ)−	ϵ)−	ADJ
ejpam-6776	134	22	α	α	NOUN
ejpam-6776	134	23	λ+	λ+	PUNCT
ejpam-6776	134	24	i	i	PRON
ejpam-6776	134	25	+	+	NUM
ejpam-6776	134	26	σ2s2(1	σ2s2(1	NOUN
ejpam-6776	134	27	+	+	CCONJ
ejpam-6776	134	28	θ	θ	NOUN
ejpam-6776	134	29	)	)	PUNCT
ejpam-6776	134	30	2(1	2(1	NUM
ejpam-6776	135	1	+	+	CCONJ
ejpam-6776	135	2	ki)2	ki)2	PROPN
ejpam-6776	135	3	)	)	PUNCT
ejpam-6776	135	4	.	.	PUNCT
ejpam-6776	136	1	bounding	bound	VERB
ejpam-6776	136	2	lw	lw	NOUN
ejpam-6776	136	3	:	:	PUNCT
ejpam-6776	136	4	lw	lw	PROPN
ejpam-6776	136	5	≤	≤	NUM
ejpam-6776	136	6	κ1	κ1	PROPN
ejpam-6776	136	7	−	−	PROPN
ejpam-6776	136	8	κ2w	κ2w	NOUN
ejpam-6776	136	9	,	,	PUNCT
ejpam-6776	136	10	with	with	ADP
ejpam-6776	136	11	:	:	PUNCT
ejpam-6776	136	12	κ1	κ1	NOUN
ejpam-6776	136	13	=	=	SYM
ejpam-6776	136	14	λ	λ	PROPN
ejpam-6776	136	15	(	(	PUNCT
ejpam-6776	136	16	λ	λ	X
ejpam-6776	136	17	δ	δ	PROPN
ejpam-6776	136	18	)	)	PUNCT
ejpam-6776	136	19	−θ	−θ	ADJ
ejpam-6776	136	20	,	,	PUNCT
ejpam-6776	136	21	κ2	κ2	PROPN
ejpam-6776	136	22	=	=	SYM
ejpam-6776	136	23	θξ	θξ	ADP
ejpam-6776	136	24	.	.	PUNCT
ejpam-6776	136	25	applying	apply	VERB
ejpam-6776	136	26	itô	itô	PROPN
ejpam-6776	136	27	’s	’s	PART
ejpam-6776	136	28	lemma	lemma	PROPN
ejpam-6776	136	29	to	to	ADP
ejpam-6776	136	30	eκ2tw	eκ2tw	PROPN
ejpam-6776	136	31	and	and	CCONJ
ejpam-6776	136	32	taking	take	VERB
ejpam-6776	136	33	expectations	expectation	NOUN
ejpam-6776	136	34	:	:	PUNCT
ejpam-6776	136	35	e[eκ2tw	e[eκ2tw	PROPN
ejpam-6776	136	36	(	(	PUNCT
ejpam-6776	136	37	t	t	PROPN
ejpam-6776	136	38	)	)	PUNCT
ejpam-6776	136	39	]	]	X
ejpam-6776	137	1	≤w	≤w	INTJ
ejpam-6776	137	2	(	(	PUNCT
ejpam-6776	137	3	0	0	NUM
ejpam-6776	137	4	)	)	PUNCT
ejpam-6776	137	5	+	+	CCONJ
ejpam-6776	137	6	κ1	κ1	PROPN
ejpam-6776	137	7	κ2	κ2	NOUN
ejpam-6776	137	8	(	(	PUNCT
ejpam-6776	137	9	eκ2	eκ2	PROPN
ejpam-6776	137	10	t	t	PROPN
ejpam-6776	137	11	−	−	NOUN
ejpam-6776	137	12	1	1	NUM
ejpam-6776	137	13	)	)	PUNCT
ejpam-6776	137	14	.	.	PUNCT
ejpam-6776	138	1	thus	thus	ADV
ejpam-6776	138	2	:	:	PUNCT
ejpam-6776	138	3	e[i−θ(t	e[i−θ(t	NOUN
ejpam-6776	138	4	)	)	PUNCT
ejpam-6776	138	5	]	]	PUNCT
ejpam-6776	139	1	≤	≤	NUM
ejpam-6776	139	2	w	w	NOUN
ejpam-6776	139	3	(	(	PUNCT
ejpam-6776	139	4	0)e−κ2	0)e−κ2	NOUN
ejpam-6776	139	5	t	t	NOUN
ejpam-6776	139	6	+	+	CCONJ
ejpam-6776	139	7	κ1	κ1	PROPN
ejpam-6776	139	8	κ2	κ2	NOUN
ejpam-6776	139	9	(	(	PUNCT
ejpam-6776	139	10	1−	1−	NUM
ejpam-6776	139	11	e−κ2	e−κ2	NUM
ejpam-6776	139	12	t	t	NOUN
ejpam-6776	139	13	)	)	PUNCT
ejpam-6776	139	14	1	1	NUM
ejpam-6776	139	15	+	+	NUM
ejpam-6776	139	16	λ	λ	PROPN
ejpam-6776	139	17	δ	δ	PROPN
ejpam-6776	139	18	.	.	PUNCT
ejpam-6776	140	1	by	by	ADP
ejpam-6776	140	2	jensen	jensen	PROPN
ejpam-6776	140	3	’s	’s	PART
ejpam-6776	140	4	inequality	inequality	NOUN
ejpam-6776	140	5	:	:	PUNCT
ejpam-6776	140	6	e[i(t	e[i(t	PROPN
ejpam-6776	140	7	)	)	PUNCT
ejpam-6776	140	8	]	]	PUNCT
ejpam-6776	140	9	≥	≥	PRON
ejpam-6776	140	10	(	(	PUNCT
ejpam-6776	140	11	κ1	κ1	NOUN
ejpam-6776	140	12	κ2	κ2	PROPN
ejpam-6776	140	13	)	)	PUNCT
ejpam-6776	140	14	−1	−1	NOUN
ejpam-6776	140	15	/	/	SYM
ejpam-6776	140	16	θ	θ	PROPN
ejpam-6776	140	17	as	as	ADP
ejpam-6776	140	18	t→	t→	X
ejpam-6776	140	19	∞.	∞.	PROPN
ejpam-6776	140	20	hence	hence	ADV
ejpam-6776	140	21	,	,	PUNCT
ejpam-6776	140	22	lim	lim	PROPN
ejpam-6776	140	23	inft→∞	inft→∞	PROPN
ejpam-6776	140	24	e[i(t	e[i(t	PROPN
ejpam-6776	140	25	)	)	PUNCT
ejpam-6776	140	26	]	]	PUNCT
ejpam-6776	141	1	≥	≥	X
ejpam-6776	141	2	mi	mi	X
ejpam-6776	141	3	=	=	PUNCT
ejpam-6776	141	4	(	(	PUNCT
ejpam-6776	141	5	κ1	κ1	NOUN
ejpam-6776	141	6	κ2	κ2	PROPN
ejpam-6776	141	7	)	)	PUNCT
ejpam-6776	141	8	−1	−1	NOUN
ejpam-6776	141	9	/	/	SYM
ejpam-6776	141	10	θ	θ	PROPN
ejpam-6776	141	11	.	.	PUNCT
ejpam-6776	142	1	j.	j.	PROPN
ejpam-6776	142	2	leo	leo	PROPN
ejpam-6776	142	3	amalraj	amalraj	PROPN
ejpam-6776	142	4	et	et	PROPN
ejpam-6776	142	5	al	al	PROPN
ejpam-6776	142	6	.	.	PUNCT
ejpam-6776	142	7	/	/	SYM
ejpam-6776	142	8	eur	eur	PROPN
ejpam-6776	142	9	.	.	PUNCT
ejpam-6776	143	1	j.	j.	PROPN
ejpam-6776	143	2	pure	pure	PROPN
ejpam-6776	143	3	appl	appl	PROPN
ejpam-6776	143	4	.	.	PROPN
ejpam-6776	143	5	math	math	PROPN
ejpam-6776	143	6	,	,	PUNCT
ejpam-6776	143	7	18	18	NUM
ejpam-6776	143	8	(	(	PUNCT
ejpam-6776	143	9	4	4	NUM
ejpam-6776	143	10	)	)	PUNCT
ejpam-6776	143	11	(	(	PUNCT
ejpam-6776	143	12	2025	2025	NUM
ejpam-6776	143	13	)	)	PUNCT
ejpam-6776	143	14	,	,	PUNCT
ejpam-6776	143	15	6776	6776	NUM
ejpam-6776	143	16	7	7	NUM
ejpam-6776	143	17	of	of	ADP
ejpam-6776	143	18	22	22	NUM
ejpam-6776	143	19	proposition	proposition	NOUN
ejpam-6776	143	20	1	1	NUM
ejpam-6776	143	21	.	.	PUNCT
ejpam-6776	144	1	for	for	ADP
ejpam-6776	144	2	any	any	DET
ejpam-6776	144	3	initial	initial	ADJ
ejpam-6776	144	4	condition	condition	NOUN
ejpam-6776	144	5	(	(	PUNCT
ejpam-6776	144	6	s(0	s(0	PROPN
ejpam-6776	144	7	)	)	PUNCT
ejpam-6776	144	8	,	,	PUNCT
ejpam-6776	144	9	i(0	i(0	PROPN
ejpam-6776	144	10	)	)	PUNCT
ejpam-6776	144	11	)	)	PUNCT
ejpam-6776	144	12	∈	∈	PROPN
ejpam-6776	145	1	d	d	PROPN
ejpam-6776	145	2	,	,	PUNCT
ejpam-6776	145	3	lim	lim	PROPN
ejpam-6776	145	4	inf	inf	PROPN
ejpam-6776	145	5	t→∞	t→∞	NUM
ejpam-6776	145	6	e[s(t	e[s(t	NOUN
ejpam-6776	145	7	)	)	PUNCT
ejpam-6776	145	8	]	]	PUNCT
ejpam-6776	145	9	≥	≥	X
ejpam-6776	145	10	λ	λ	X
ejpam-6776	145	11	δ	δ	PROPN
ejpam-6776	145	12	+	+	X
ejpam-6776	145	13	β	β	X
ejpam-6776	145	14	λ	λ	X
ejpam-6776	145	15	δ	δ	PROPN
ejpam-6776	145	16	.	.	PUNCT
ejpam-6776	146	1	this	this	PRON
ejpam-6776	146	2	provides	provide	VERB
ejpam-6776	146	3	a	a	DET
ejpam-6776	146	4	lower	low	ADJ
ejpam-6776	146	5	bound	bind	VERB
ejpam-6776	146	6	on	on	ADP
ejpam-6776	146	7	the	the	DET
ejpam-6776	146	8	expected	expect	VERB
ejpam-6776	146	9	susceptible	susceptible	ADJ
ejpam-6776	146	10	population	population	NOUN
ejpam-6776	146	11	,	,	PUNCT
ejpam-6776	146	12	assuming	assume	VERB
ejpam-6776	146	13	the	the	DET
ejpam-6776	146	14	infected	infected	ADJ
ejpam-6776	146	15	population	population	NOUN
ejpam-6776	146	16	is	be	AUX
ejpam-6776	146	17	bounded	bound	VERB
ejpam-6776	146	18	above	above	ADV
ejpam-6776	146	19	by	by	ADP
ejpam-6776	146	20	λ	λ	PROPN
ejpam-6776	146	21	δ	δ	PROPN
ejpam-6776	146	22	.	.	PUNCT
ejpam-6776	147	1	proof	proof	NOUN
ejpam-6776	147	2	.	.	PUNCT
ejpam-6776	148	1	from	from	ADP
ejpam-6776	148	2	(	(	PUNCT
ejpam-6776	148	3	1	1	NUM
ejpam-6776	148	4	)	)	PUNCT
ejpam-6776	148	5	,	,	PUNCT
ejpam-6776	148	6	d	d	X
ejpam-6776	148	7	dt	dt	X
ejpam-6776	148	8	e[s(t	e[s(t	X
ejpam-6776	148	9	)	)	PUNCT
ejpam-6776	148	10	]	]	PUNCT
ejpam-6776	149	1	=	=	PUNCT
ejpam-6776	149	2	e	e	X
ejpam-6776	149	3	[	[	PUNCT
ejpam-6776	149	4	λ−	λ−	PROPN
ejpam-6776	149	5	βs(t)i(t	βs(t)i(t	ADV
ejpam-6776	149	6	)	)	PUNCT
ejpam-6776	149	7	1	1	NUM
ejpam-6776	149	8	+	+	CCONJ
ejpam-6776	149	9	ki(t	ki(t	NOUN
ejpam-6776	149	10	)	)	PUNCT
ejpam-6776	149	11	−	−	NOUN
ejpam-6776	149	12	δs(t	δs(t	PUNCT
ejpam-6776	149	13	)	)	PUNCT
ejpam-6776	149	14	]	]	PUNCT
ejpam-6776	149	15	.	.	PUNCT
ejpam-6776	150	1	since	since	SCONJ
ejpam-6776	150	2	i(t	i(t	NOUN
ejpam-6776	150	3	)	)	PUNCT
ejpam-6776	150	4	≤	≤	PUNCT
ejpam-6776	150	5	λ	λ	PROPN
ejpam-6776	150	6	δ	δ	PROPN
ejpam-6776	150	7	and	and	CCONJ
ejpam-6776	150	8	i(t	i(t	NOUN
ejpam-6776	150	9	)	)	PUNCT
ejpam-6776	150	10	1+ki(t	1+ki(t	NUM
ejpam-6776	150	11	)	)	PUNCT
ejpam-6776	150	12	≤	≤	NUM
ejpam-6776	150	13	i(t	i(t	NOUN
ejpam-6776	150	14	)	)	PUNCT
ejpam-6776	150	15	ki(t	ki(t	NOUN
ejpam-6776	150	16	)	)	PUNCT
ejpam-6776	150	17	=	=	SYM
ejpam-6776	150	18	1	1	NUM
ejpam-6776	150	19	k	k	NOUN
ejpam-6776	150	20	for	for	ADP
ejpam-6776	150	21	large	large	ADJ
ejpam-6776	150	22	i	i	PROPN
ejpam-6776	150	23	,	,	PUNCT
ejpam-6776	150	24	but	but	CCONJ
ejpam-6776	150	25	more	more	ADV
ejpam-6776	150	26	tightly	tightly	ADV
ejpam-6776	150	27	,	,	PUNCT
ejpam-6776	150	28	βsi	βsi	NOUN
ejpam-6776	150	29	1+ki	1+ki	NUM
ejpam-6776	150	30	≤	≤	NUM
ejpam-6776	150	31	βsi	βsi	NOUN
ejpam-6776	150	32	≤	≤	NUM
ejpam-6776	150	33	βs	β	NOUN
ejpam-6776	150	34	λ	λ	X
ejpam-6776	150	35	δ	δ	PROPN
ejpam-6776	150	36	,	,	PUNCT
ejpam-6776	150	37	d	d	X
ejpam-6776	150	38	dt	dt	X
ejpam-6776	150	39	e[s(t	e[s(t	X
ejpam-6776	150	40	)	)	PUNCT
ejpam-6776	150	41	]	]	PUNCT
ejpam-6776	150	42	≥	≥	X
ejpam-6776	150	43	λ−	λ−	PROPN
ejpam-6776	150	44	δe[s(t)]−	δe[s(t)]−	ADV
ejpam-6776	150	45	β	β	X
ejpam-6776	150	46	λ	λ	PROPN
ejpam-6776	150	47	δ	δ	PROPN
ejpam-6776	150	48	e[s(t	e[s(t	X
ejpam-6776	150	49	)	)	PUNCT
ejpam-6776	150	50	]	]	PUNCT
ejpam-6776	150	51	.	.	PUNCT
ejpam-6776	151	1	solving	solve	VERB
ejpam-6776	151	2	the	the	DET
ejpam-6776	151	3	comparison	comparison	NOUN
ejpam-6776	151	4	ode	ode	ADJ
ejpam-6776	151	5	yields	yield	NOUN
ejpam-6776	151	6	the	the	DET
ejpam-6776	151	7	bound	bind	VERB
ejpam-6776	151	8	as	as	ADP
ejpam-6776	151	9	t→	t→	X
ejpam-6776	151	10	∞.	∞.	PROPN
ejpam-6776	151	11	proposition	proposition	NOUN
ejpam-6776	151	12	2	2	NUM
ejpam-6776	151	13	.	.	PUNCT
ejpam-6776	152	1	for	for	ADP
ejpam-6776	152	2	(	(	PUNCT
ejpam-6776	152	3	s(0	s(0	PROPN
ejpam-6776	152	4	)	)	PUNCT
ejpam-6776	152	5	,	,	PUNCT
ejpam-6776	152	6	i(0	i(0	PROPN
ejpam-6776	152	7	)	)	PUNCT
ejpam-6776	152	8	)	)	PUNCT
ejpam-6776	152	9	∈	∈	PROPN
ejpam-6776	153	1	d	d	NOUN
ejpam-6776	153	2	:	:	PUNCT
ejpam-6776	153	3	lim	lim	PROPN
ejpam-6776	153	4	sup	sup	PROPN
ejpam-6776	153	5	t→∞	t→∞	X
ejpam-6776	153	6	e[s−1(t	e[s−1(t	ADJ
ejpam-6776	153	7	)	)	PUNCT
ejpam-6776	153	8	]	]	PUNCT
ejpam-6776	154	1	≤	≤	NUM
ejpam-6776	154	2	δ	δ	PROPN
ejpam-6776	154	3	+	+	CCONJ
ejpam-6776	154	4	βλ	βλ	PROPN
ejpam-6776	154	5	δ	δ	PROPN
ejpam-6776	154	6	+	+	CCONJ
ejpam-6776	154	7	σ2λ2	σ2λ2	PROPN
ejpam-6776	154	8	δ2	δ2	VERB
ejpam-6776	154	9	λ	λ	NOUN
ejpam-6776	154	10	.	.	PUNCT
ejpam-6776	155	1	proof	proof	NOUN
ejpam-6776	155	2	.	.	PUNCT
ejpam-6776	156	1	apply	apply	VERB
ejpam-6776	156	2	itô	itô	PROPN
ejpam-6776	156	3	’s	’s	PART
ejpam-6776	156	4	lemma	lemma	PROPN
ejpam-6776	156	5	to	to	ADP
ejpam-6776	156	6	s−1	s−1	PROPN
ejpam-6776	156	7	:	:	PUNCT
ejpam-6776	156	8	d(s−1	d(s−1	NOUN
ejpam-6776	156	9	)	)	PUNCT
ejpam-6776	156	10	=	=	SYM
ejpam-6776	156	11	(	(	PUNCT
ejpam-6776	156	12	−λs−2	−λs−2	NUM
ejpam-6776	157	1	+	+	CCONJ
ejpam-6776	158	1	βis−1	βis−1	X
ejpam-6776	158	2	1	1	NUM
ejpam-6776	158	3	+	+	NUM
ejpam-6776	158	4	ki	ki	PROPN
ejpam-6776	158	5	+	+	CCONJ
ejpam-6776	158	6	δs−1	δs−1	PROPN
ejpam-6776	158	7	+	+	NUM
ejpam-6776	158	8	σ2i2s−1	σ2i2s−1	NOUN
ejpam-6776	158	9	(	(	PUNCT
ejpam-6776	158	10	1	1	NUM
ejpam-6776	158	11	+	+	CCONJ
ejpam-6776	158	12	ki)2	ki)2	ADJ
ejpam-6776	158	13	)	)	PUNCT
ejpam-6776	158	14	dt+	dt+	NOUN
ejpam-6776	158	15	σis−1	σis−1	NOUN
ejpam-6776	158	16	1	1	NUM
ejpam-6776	158	17	+	+	NUM
ejpam-6776	158	18	ki	ki	PROPN
ejpam-6776	158	19	db(t	db(t	PROPN
ejpam-6776	158	20	)	)	PUNCT
ejpam-6776	158	21	.	.	PUNCT
ejpam-6776	159	1	since	since	SCONJ
ejpam-6776	159	2	i	i	PRON
ejpam-6776	159	3	≤	≤	X
ejpam-6776	159	4	λ	λ	PROPN
ejpam-6776	159	5	δ	δ	PROPN
ejpam-6776	159	6	:	:	PUNCT
ejpam-6776	159	7	βi	βi	PROPN
ejpam-6776	159	8	1	1	NUM
ejpam-6776	159	9	+	+	CCONJ
ejpam-6776	159	10	ki	ki	PROPN
ejpam-6776	159	11	+	+	CCONJ
ejpam-6776	159	12	σ2i2	σ2i2	X
ejpam-6776	159	13	(	(	PUNCT
ejpam-6776	159	14	1	1	NUM
ejpam-6776	159	15	+	+	CCONJ
ejpam-6776	159	16	ki)2	ki)2	PROPN
ejpam-6776	159	17	≤	≤	PROPN
ejpam-6776	159	18	βλ	βλ	PROPN
ejpam-6776	159	19	δ	δ	PROPN
ejpam-6776	159	20	+	+	CCONJ
ejpam-6776	159	21	σ2λ2	σ2λ2	PROPN
ejpam-6776	159	22	δ2	δ2	VERB
ejpam-6776	159	23	.	.	PUNCT
ejpam-6776	160	1	thus	thus	ADV
ejpam-6776	160	2	:	:	PUNCT
ejpam-6776	160	3	d(s−1	d(s−1	NOUN
ejpam-6776	160	4	)	)	PUNCT
ejpam-6776	160	5	≤	≤	NOUN
ejpam-6776	160	6	(	(	PUNCT
ejpam-6776	160	7	−λs−2	−λs−2	NUM
ejpam-6776	160	8	+	+	CCONJ
ejpam-6776	160	9	(	(	PUNCT
ejpam-6776	160	10	δ	δ	PROPN
ejpam-6776	160	11	+	+	NUM
ejpam-6776	160	12	βλ	βλ	PROPN
ejpam-6776	160	13	δ	δ	PROPN
ejpam-6776	160	14	+	+	CCONJ
ejpam-6776	160	15	σ2λ2	σ2λ2	PROPN
ejpam-6776	160	16	δ2	δ2	ADJ
ejpam-6776	160	17	)	)	PUNCT
ejpam-6776	160	18	s−1	s−1	PROPN
ejpam-6776	160	19	)	)	PUNCT
ejpam-6776	160	20	dt+	dt+	NOUN
ejpam-6776	160	21	stochastic	stochastic	ADJ
ejpam-6776	160	22	term	term	NOUN
ejpam-6776	160	23	.	.	PUNCT
ejpam-6776	161	1	using	use	VERB
ejpam-6776	161	2	the	the	DET
ejpam-6776	161	3	inequality	inequality	NOUN
ejpam-6776	161	4	−λx−2	−λx−2	X
ejpam-6776	161	5	+	+	CCONJ
ejpam-6776	161	6	ax−1	ax−1	VERB
ejpam-6776	161	7	≤	≤	NOUN
ejpam-6776	161	8	a2	a2	PROPN
ejpam-6776	161	9	4λ	4λ	PROPN
ejpam-6776	161	10	(	(	PUNCT
ejpam-6776	161	11	derived	derive	VERB
ejpam-6776	161	12	by	by	ADP
ejpam-6776	161	13	completing	complete	VERB
ejpam-6776	161	14	the	the	DET
ejpam-6776	161	15	square	square	NOUN
ejpam-6776	161	16	:	:	PUNCT
ejpam-6776	161	17	let	let	VERB
ejpam-6776	161	18	f(x	f(x	PROPN
ejpam-6776	161	19	)	)	PUNCT
ejpam-6776	162	1	=	=	PRON
ejpam-6776	163	1	−λx−2	−λx−2	X
ejpam-6776	163	2	+	+	CCONJ
ejpam-6776	163	3	ax−1	ax−1	VERB
ejpam-6776	163	4	,	,	PUNCT
ejpam-6776	163	5	maximum	maximum	ADJ
ejpam-6776	163	6	at	at	ADP
ejpam-6776	163	7	x−1	x−1	PROPN
ejpam-6776	163	8	=	=	PUNCT
ejpam-6776	163	9	a	a	DET
ejpam-6776	163	10	2λ	2λ	NOUN
ejpam-6776	163	11	,	,	PUNCT
ejpam-6776	163	12	yielding	yield	VERB
ejpam-6776	163	13	a2	a2	PROPN
ejpam-6776	163	14	4λ	4λ	PROPN
ejpam-6776	163	15	)	)	PUNCT
ejpam-6776	163	16	,	,	PUNCT
ejpam-6776	163	17	d	d	NOUN
ejpam-6776	163	18	dt	dt	X
ejpam-6776	163	19	e[s−1	e[s−1	PROPN
ejpam-6776	163	20	]	]	PUNCT
ejpam-6776	163	21	≤	≤	NUM
ejpam-6776	163	22	(	(	PUNCT
ejpam-6776	163	23	δ	δ	NOUN
ejpam-6776	163	24	+	+	X
ejpam-6776	163	25	β	β	X
ejpam-6776	163	26	λ	λ	X
ejpam-6776	163	27	δ	δ	PROPN
ejpam-6776	163	28	+	+	PROPN
ejpam-6776	163	29	σ2	σ2	PROPN
ejpam-6776	163	30	λ	λ	PROPN
ejpam-6776	163	31	2	2	NUM
ejpam-6776	163	32	δ2	δ2	ADJ
ejpam-6776	163	33	)	)	PUNCT
ejpam-6776	163	34	2	2	NUM
ejpam-6776	163	35	4λ	4λ	NOUN
ejpam-6776	163	36	−	−	PROPN
ejpam-6776	164	1	(	(	PUNCT
ejpam-6776	164	2	δ	δ	PROPN
ejpam-6776	164	3	+	+	X
ejpam-6776	164	4	β	β	X
ejpam-6776	164	5	λ	λ	X
ejpam-6776	164	6	δ	δ	PROPN
ejpam-6776	164	7	+	+	PROPN
ejpam-6776	164	8	σ2	σ2	PROPN
ejpam-6776	164	9	λ2	λ2	PROPN
ejpam-6776	164	10	δ2	δ2	VERB
ejpam-6776	164	11	)	)	PUNCT
ejpam-6776	164	12	e[s−1	e[s−1	NOUN
ejpam-6776	164	13	]	]	PUNCT
ejpam-6776	164	14	.	.	PUNCT
ejpam-6776	165	1	the	the	DET
ejpam-6776	165	2	equilibrium	equilibrium	NOUN
ejpam-6776	165	3	yields	yield	VERB
ejpam-6776	165	4	:	:	PUNCT
ejpam-6776	165	5	lim	lim	PROPN
ejpam-6776	165	6	sup	sup	NOUN
ejpam-6776	165	7	t→∞	t→∞	X
ejpam-6776	165	8	e[s−1(t	e[s−1(t	ADJ
ejpam-6776	165	9	)	)	PUNCT
ejpam-6776	165	10	]	]	PUNCT
ejpam-6776	166	1	≤	≤	NUM
ejpam-6776	166	2	δ	δ	PROPN
ejpam-6776	166	3	+	+	CCONJ
ejpam-6776	166	4	βλ	βλ	PROPN
ejpam-6776	166	5	δ	δ	PROPN
ejpam-6776	166	6	+	+	CCONJ
ejpam-6776	166	7	σ2λ2	σ2λ2	PROPN
ejpam-6776	166	8	δ2	δ2	VERB
ejpam-6776	166	9	λ	λ	PROPN
ejpam-6776	166	10	.	.	PUNCT
ejpam-6776	167	1	j.	j.	PROPN
ejpam-6776	167	2	leo	leo	PROPN
ejpam-6776	167	3	amalraj	amalraj	PROPN
ejpam-6776	167	4	et	et	PROPN
ejpam-6776	167	5	al	al	PROPN
ejpam-6776	167	6	.	.	PUNCT
ejpam-6776	167	7	/	/	SYM
ejpam-6776	167	8	eur	eur	PROPN
ejpam-6776	167	9	.	.	PUNCT
ejpam-6776	168	1	j.	j.	PROPN
ejpam-6776	168	2	pure	pure	PROPN
ejpam-6776	168	3	appl	appl	PROPN
ejpam-6776	168	4	.	.	PROPN
ejpam-6776	168	5	math	math	PROPN
ejpam-6776	168	6	,	,	PUNCT
ejpam-6776	168	7	18	18	NUM
ejpam-6776	168	8	(	(	PUNCT
ejpam-6776	168	9	4	4	NUM
ejpam-6776	168	10	)	)	PUNCT
ejpam-6776	168	11	(	(	PUNCT
ejpam-6776	168	12	2025	2025	NUM
ejpam-6776	168	13	)	)	PUNCT
ejpam-6776	168	14	,	,	PUNCT
ejpam-6776	168	15	6776	6776	NUM
ejpam-6776	168	16	8	8	NUM
ejpam-6776	168	17	of	of	ADP
ejpam-6776	168	18	22	22	NUM
ejpam-6776	168	19	remark	remark	NOUN
ejpam-6776	168	20	1	1	NUM
ejpam-6776	168	21	.	.	PUNCT
ejpam-6776	169	1	from	from	ADP
ejpam-6776	169	2	proposition	proposition	NOUN
ejpam-6776	169	3	2	2	NUM
ejpam-6776	169	4	and	and	CCONJ
ejpam-6776	169	5	jensen	jensen	PROPN
ejpam-6776	169	6	’s	’s	PART
ejpam-6776	169	7	inequality	inequality	NOUN
ejpam-6776	169	8	:	:	PUNCT
ejpam-6776	169	9	lim	lim	PROPN
ejpam-6776	169	10	inf	inf	PROPN
ejpam-6776	169	11	t→∞	t→∞	NUM
ejpam-6776	169	12	e[s(t	e[s(t	NOUN
ejpam-6776	169	13	)	)	PUNCT
ejpam-6776	169	14	]	]	PUNCT
ejpam-6776	170	1	≥	≥	X
ejpam-6776	170	2	λ	λ	X
ejpam-6776	170	3	δ	δ	PROPN
ejpam-6776	170	4	+	+	CCONJ
ejpam-6776	170	5	βλ	βλ	PROPN
ejpam-6776	170	6	δ	δ	PROPN
ejpam-6776	170	7	+	+	CCONJ
ejpam-6776	170	8	σ2λ2	σ2λ2	PROPN
ejpam-6776	170	9	δ2	δ2	VERB
ejpam-6776	170	10	,	,	PUNCT
ejpam-6776	170	11	a	a	PRON
ejpam-6776	170	12	weaker	weak	ADJ
ejpam-6776	170	13	bound	bind	VERB
ejpam-6776	170	14	than	than	ADP
ejpam-6776	170	15	proposition	proposition	NOUN
ejpam-6776	170	16	1	1	NUM
ejpam-6776	170	17	,	,	PUNCT
ejpam-6776	170	18	but	but	CCONJ
ejpam-6776	170	19	useful	useful	ADJ
ejpam-6776	170	20	for	for	ADP
ejpam-6776	170	21	later	later	ADJ
ejpam-6776	170	22	analysis	analysis	NOUN
ejpam-6776	170	23	.	.	PUNCT
ejpam-6776	171	1	proposition	proposition	NOUN
ejpam-6776	171	2	3	3	NUM
ejpam-6776	171	3	.	.	PUNCT
ejpam-6776	172	1	under	under	ADP
ejpam-6776	172	2	condition	condition	NOUN
ejpam-6776	172	3	(	(	PUNCT
ejpam-6776	172	4	3	3	NUM
ejpam-6776	172	5	)	)	PUNCT
ejpam-6776	172	6	,	,	PUNCT
ejpam-6776	172	7	for	for	ADP
ejpam-6776	172	8	(	(	PUNCT
ejpam-6776	172	9	s(0	s(0	PROPN
ejpam-6776	172	10	)	)	PUNCT
ejpam-6776	172	11	,	,	PUNCT
ejpam-6776	172	12	i(0	i(0	PROPN
ejpam-6776	172	13	)	)	PUNCT
ejpam-6776	172	14	)	)	PUNCT
ejpam-6776	172	15	∈	∈	PROPN
ejpam-6776	173	1	d	d	NOUN
ejpam-6776	173	2	:	:	PUNCT
ejpam-6776	173	3	lim	lim	NOUN
ejpam-6776	173	4	sup	sup	VERB
ejpam-6776	173	5	t→∞	t→∞	NUM
ejpam-6776	173	6	e	e	NOUN
ejpam-6776	174	1	[	[	X
ejpam-6776	174	2	(	(	PUNCT
ejpam-6776	174	3	λ	λ	X
ejpam-6776	174	4	δ	δ	PROPN
ejpam-6776	174	5	−	−	PROPN
ejpam-6776	174	6	s(t)−	s(t)−	PROPN
ejpam-6776	174	7	i(t	i(t	PROPN
ejpam-6776	174	8	)	)	PUNCT
ejpam-6776	174	9	)	)	PUNCT
ejpam-6776	175	1	−θ	−θ	X
ejpam-6776	175	2	]	]	PUNCT
ejpam-6776	175	3	≤	≤	NUM
ejpam-6776	175	4	mθ	mθ	NOUN
ejpam-6776	175	5	,	,	PUNCT
ejpam-6776	175	6	where	where	SCONJ
ejpam-6776	175	7	θ	θ	PROPN
ejpam-6776	175	8	satisfies	satisfy	VERB
ejpam-6776	175	9	:	:	PUNCT
ejpam-6776	175	10	θ	θ	PROPN
ejpam-6776	175	11	<	<	X
ejpam-6776	175	12	2	2	NUM
ejpam-6776	175	13	σ2	σ2	PROPN
ejpam-6776	175	14	(	(	PUNCT
ejpam-6776	175	15	ξ	ξ	PROPN
ejpam-6776	175	16	+	+	X
ejpam-6776	175	17	β	β	X
ejpam-6776	175	18	λ	λ	X
ejpam-6776	175	19	δ	δ	PROPN
ejpam-6776	175	20	)	)	PUNCT
ejpam-6776	175	21	,	,	PUNCT
ejpam-6776	175	22	and	and	CCONJ
ejpam-6776	175	23	mθ	mθ	INTJ
ejpam-6776	175	24	>	>	X
ejpam-6776	175	25	0	0	NUM
ejpam-6776	175	26	is	be	AUX
ejpam-6776	175	27	determined	determine	VERB
ejpam-6776	175	28	below	below	ADV
ejpam-6776	175	29	.	.	PUNCT
ejpam-6776	176	1	proof	proof	NOUN
ejpam-6776	176	2	.	.	PUNCT
ejpam-6776	177	1	let	let	VERB
ejpam-6776	177	2	z	z	NOUN
ejpam-6776	177	3	=	=	SYM
ejpam-6776	177	4	s	s	PART
ejpam-6776	177	5	+	+	NUM
ejpam-6776	177	6	i.	i.	NOUN
ejpam-6776	177	7	from	from	ADP
ejpam-6776	177	8	(	(	PUNCT
ejpam-6776	177	9	1	1	NUM
ejpam-6776	177	10	):	):	PUNCT
ejpam-6776	178	1	d	d	X
ejpam-6776	178	2	dt	dt	X
ejpam-6776	178	3	(	(	PUNCT
ejpam-6776	178	4	λ	λ	X
ejpam-6776	178	5	δ	δ	X
ejpam-6776	178	6	−z	−z	NOUN
ejpam-6776	178	7	)	)	PUNCT
ejpam-6776	178	8	−θ	−θ	PROPN
ejpam-6776	178	9	=	=	SYM
ejpam-6776	179	1	θδ	θδ	PROPN
ejpam-6776	179	2	(	(	PUNCT
ejpam-6776	179	3	λ	λ	X
ejpam-6776	179	4	δ	δ	PROPN
ejpam-6776	179	5	−z	−z	NOUN
ejpam-6776	179	6	)	)	PUNCT
ejpam-6776	180	1	−θ	−θ	ADJ
ejpam-6776	180	2	−	−	PROPN
ejpam-6776	180	3	θ	θ	PROPN
ejpam-6776	180	4	(	(	PUNCT
ejpam-6776	180	5	γ	γ	X
ejpam-6776	180	6	+	+	X
ejpam-6776	180	7	ϵ+	ϵ+	PUNCT
ejpam-6776	180	8	α	α	NOUN
ejpam-6776	180	9	λ+	λ+	PUNCT
ejpam-6776	180	10	i	i	PRON
ejpam-6776	180	11	)	)	PUNCT
ejpam-6776	181	1	i	i	PRON
ejpam-6776	181	2	(	(	PUNCT
ejpam-6776	181	3	λ	λ	X
ejpam-6776	181	4	δ	δ	PROPN
ejpam-6776	181	5	−z	−z	NOUN
ejpam-6776	181	6	)	)	PUNCT
ejpam-6776	181	7	−θ−1	−θ−1	PROPN
ejpam-6776	181	8	.	.	PUNCT
ejpam-6776	182	1	since	since	SCONJ
ejpam-6776	182	2	i	i	PRON
ejpam-6776	182	3	≤	≤	X
ejpam-6776	182	4	λ	λ	X
ejpam-6776	182	5	δ	δ	PROPN
ejpam-6776	182	6	:	:	PUNCT
ejpam-6776	182	7	d	d	X
ejpam-6776	182	8	dt	dt	X
ejpam-6776	182	9	(	(	PUNCT
ejpam-6776	182	10	λ	λ	X
ejpam-6776	182	11	δ	δ	X
ejpam-6776	182	12	−z	−z	NOUN
ejpam-6776	182	13	)	)	PUNCT
ejpam-6776	182	14	−θ	−θ	ADV
ejpam-6776	182	15	≤	≤	NOUN
ejpam-6776	182	16	δ(θ	δ(θ	ADP
ejpam-6776	182	17	+	+	CCONJ
ejpam-6776	182	18	1	1	NUM
ejpam-6776	182	19	)	)	PUNCT
ejpam-6776	182	20	(	(	PUNCT
ejpam-6776	182	21	λ	λ	X
ejpam-6776	182	22	δ	δ	PROPN
ejpam-6776	182	23	−z	−z	NOUN
ejpam-6776	182	24	)	)	PUNCT
ejpam-6776	182	25	−θ	−θ	ADJ
ejpam-6776	182	26	−	−	PROPN
ejpam-6776	182	27	θ	θ	PROPN
ejpam-6776	182	28	(	(	PUNCT
ejpam-6776	182	29	γ	γ	X
ejpam-6776	182	30	+	+	X
ejpam-6776	182	31	ϵ+	ϵ+	PUNCT
ejpam-6776	182	32	α	α	NOUN
ejpam-6776	182	33	λ+	λ+	PUNCT
ejpam-6776	182	34	λ	λ	X
ejpam-6776	182	35	δ	δ	PROPN
ejpam-6776	182	36	)	)	PUNCT
ejpam-6776	183	1	i	i	PRON
ejpam-6776	183	2	(	(	PUNCT
ejpam-6776	183	3	λ	λ	X
ejpam-6776	183	4	δ	δ	PROPN
ejpam-6776	183	5	−z	−z	NOUN
ejpam-6776	183	6	)	)	PUNCT
ejpam-6776	183	7	−θ−1	−θ−1	NUM
ejpam-6776	183	8	.	.	PUNCT
ejpam-6776	184	1	using	use	VERB
ejpam-6776	184	2	the	the	DET
ejpam-6776	184	3	inequality	inequality	NOUN
ejpam-6776	184	4	a(θ	a(θ	PUNCT
ejpam-6776	185	1	+	+	PUNCT
ejpam-6776	185	2	1)x−θ	1)x−θ	NUM
ejpam-6776	185	3	−	−	NOUN
ejpam-6776	185	4	bx−θ−1	bx−θ−1	VERB
ejpam-6776	185	5	≤	≤	PUNCT
ejpam-6776	185	6	aθ+1	aθ+1	PROPN
ejpam-6776	185	7	bθ	bθ	PROPN
ejpam-6776	185	8	:	:	PUNCT
ejpam-6776	185	9	d	d	X
ejpam-6776	185	10	dt	dt	X
ejpam-6776	185	11	(	(	PUNCT
ejpam-6776	185	12	λ	λ	X
ejpam-6776	185	13	δ	δ	X
ejpam-6776	185	14	−z	−z	NOUN
ejpam-6776	185	15	)	)	PUNCT
ejpam-6776	185	16	−θ	−θ	ADJ
ejpam-6776	185	17	≤	≤	NUM
ejpam-6776	185	18	δθ+1i−θ	δθ+1i−θ	PROPN
ejpam-6776	185	19	(	(	PUNCT
ejpam-6776	185	20	γ	γ	X
ejpam-6776	185	21	+	+	X
ejpam-6776	185	22	ϵ+	ϵ+	PUNCT
ejpam-6776	185	23	α	α	X
ejpam-6776	185	24	λ+λ	λ+λ	VERB
ejpam-6776	185	25	δ	δ	NOUN
ejpam-6776	185	26	)	)	PUNCT
ejpam-6776	185	27	θ	θ	PROPN
ejpam-6776	186	1	−	−	PROPN
ejpam-6776	186	2	δ	δ	PROPN
ejpam-6776	186	3	(	(	PUNCT
ejpam-6776	186	4	λ	λ	PROPN
ejpam-6776	186	5	δ	δ	PROPN
ejpam-6776	186	6	−z	−z	NOUN
ejpam-6776	186	7	)	)	PUNCT
ejpam-6776	186	8	−θ	−θ	ADV
ejpam-6776	186	9	.	.	PUNCT
ejpam-6776	187	1	taking	take	VERB
ejpam-6776	187	2	expectations	expectation	NOUN
ejpam-6776	187	3	:	:	PUNCT
ejpam-6776	188	1	d	d	X
ejpam-6776	188	2	dt	dt	X
ejpam-6776	188	3	e	e	X
ejpam-6776	188	4	[	[	X
ejpam-6776	188	5	(	(	PUNCT
ejpam-6776	188	6	λ	λ	X
ejpam-6776	188	7	δ	δ	PROPN
ejpam-6776	188	8	−z	−z	NOUN
ejpam-6776	188	9	)	)	PUNCT
ejpam-6776	188	10	−θ	−θ	X
ejpam-6776	188	11	]	]	PUNCT
ejpam-6776	188	12	≤	≤	ADJ
ejpam-6776	188	13	δθ+1e[i−θ	δθ+1e[i−θ	NUM
ejpam-6776	188	14	]	]	PUNCT
ejpam-6776	188	15	(	(	PUNCT
ejpam-6776	188	16	γ	γ	X
ejpam-6776	188	17	+	+	X
ejpam-6776	189	1	ϵ+	ϵ+	PUNCT
ejpam-6776	189	2	α	α	X
ejpam-6776	189	3	λ+λ	λ+λ	VERB
ejpam-6776	189	4	δ	δ	NOUN
ejpam-6776	189	5	)	)	PUNCT
ejpam-6776	189	6	θ	θ	PROPN
ejpam-6776	189	7	−	−	NOUN
ejpam-6776	189	8	δe	δe	DET
ejpam-6776	189	9	[	[	X
ejpam-6776	189	10	(	(	PUNCT
ejpam-6776	189	11	λ	λ	X
ejpam-6776	189	12	δ	δ	PROPN
ejpam-6776	189	13	−z	−z	NOUN
ejpam-6776	189	14	)	)	PUNCT
ejpam-6776	189	15	−θ	−θ	ADV
ejpam-6776	189	16	]	]	PUNCT
ejpam-6776	189	17	.	.	PUNCT
ejpam-6776	190	1	from	from	ADP
ejpam-6776	190	2	theorem	theorem	ADJ
ejpam-6776	190	3	1	1	NUM
ejpam-6776	190	4	:	:	PUNCT
ejpam-6776	190	5	lim	lim	PROPN
ejpam-6776	190	6	sup	sup	NOUN
ejpam-6776	190	7	t→∞	t→∞	NUM
ejpam-6776	190	8	e[i−θ(t	e[i−θ(t	NOUN
ejpam-6776	190	9	)	)	PUNCT
ejpam-6776	190	10	]	]	PUNCT
ejpam-6776	190	11	≤	≤	NUM
ejpam-6776	190	12	κ1	κ1	NOUN
ejpam-6776	190	13	κ2	κ2	NOUN
ejpam-6776	190	14	.	.	PUNCT
ejpam-6776	191	1	thus	thus	ADV
ejpam-6776	191	2	:	:	PUNCT
ejpam-6776	191	3	lim	lim	PROPN
ejpam-6776	191	4	sup	sup	VERB
ejpam-6776	191	5	t→∞	t→∞	NUM
ejpam-6776	191	6	e	e	NOUN
ejpam-6776	192	1	[	[	X
ejpam-6776	192	2	(	(	PUNCT
ejpam-6776	192	3	λ	λ	X
ejpam-6776	192	4	δ	δ	PROPN
ejpam-6776	192	5	−z	−z	NOUN
ejpam-6776	192	6	)	)	PUNCT
ejpam-6776	192	7	−θ	−θ	ADV
ejpam-6776	192	8	]	]	PUNCT
ejpam-6776	192	9	≤	≤	NUM
ejpam-6776	192	10	δθ	δθ	ADP
ejpam-6776	192	11	κ1	κ1	PROPN
ejpam-6776	192	12	κ2	κ2	PROPN
ejpam-6776	192	13	(	(	PUNCT
ejpam-6776	192	14	γ	γ	X
ejpam-6776	192	15	+	+	X
ejpam-6776	192	16	ϵ+	ϵ+	PUNCT
ejpam-6776	192	17	α	α	X
ejpam-6776	192	18	λ+λ	λ+λ	VERB
ejpam-6776	192	19	δ	δ	NOUN
ejpam-6776	192	20	)	)	PUNCT
ejpam-6776	192	21	θ	θ	PROPN
ejpam-6776	192	22	≜	≜	PROPN
ejpam-6776	192	23	mθ	mθ	PROPN
ejpam-6776	192	24	.	.	PROPN
ejpam-6776	192	25	j.	j.	PROPN
ejpam-6776	192	26	leo	leo	PROPN
ejpam-6776	193	1	amalraj	amalraj	PROPN
ejpam-6776	193	2	et	et	PROPN
ejpam-6776	193	3	al	al	PROPN
ejpam-6776	193	4	.	.	PUNCT
ejpam-6776	193	5	/	/	SYM
ejpam-6776	193	6	eur	eur	PROPN
ejpam-6776	193	7	.	.	PUNCT
ejpam-6776	194	1	j.	j.	PROPN
ejpam-6776	194	2	pure	pure	PROPN
ejpam-6776	194	3	appl	appl	PROPN
ejpam-6776	194	4	.	.	PROPN
ejpam-6776	194	5	math	math	PROPN
ejpam-6776	194	6	,	,	PUNCT
ejpam-6776	194	7	18	18	NUM
ejpam-6776	194	8	(	(	PUNCT
ejpam-6776	194	9	4	4	NUM
ejpam-6776	194	10	)	)	PUNCT
ejpam-6776	194	11	(	(	PUNCT
ejpam-6776	194	12	2025	2025	NUM
ejpam-6776	194	13	)	)	PUNCT
ejpam-6776	194	14	,	,	PUNCT
ejpam-6776	194	15	6776	6776	NUM
ejpam-6776	194	16	9	9	NUM
ejpam-6776	194	17	of	of	ADP
ejpam-6776	194	18	22	22	NUM
ejpam-6776	194	19	to	to	PART
ejpam-6776	194	20	explore	explore	VERB
ejpam-6776	194	21	the	the	DET
ejpam-6776	194	22	asymptotic	asymptotic	ADJ
ejpam-6776	194	23	distribution	distribution	NOUN
ejpam-6776	194	24	,	,	PUNCT
ejpam-6776	194	25	we	we	PRON
ejpam-6776	194	26	analyze	analyze	VERB
ejpam-6776	194	27	the	the	DET
ejpam-6776	194	28	transition	transition	NOUN
ejpam-6776	194	29	probability	probability	NOUN
ejpam-6776	194	30	function	function	NOUN
ejpam-6776	194	31	:	:	PUNCT
ejpam-6776	194	32	p	p	X
ejpam-6776	194	33	(	(	PUNCT
ejpam-6776	194	34	t	t	PROPN
ejpam-6776	194	35	,	,	PUNCT
ejpam-6776	194	36	s0	s0	PROPN
ejpam-6776	194	37	,	,	PUNCT
ejpam-6776	194	38	i0	i0	PROPN
ejpam-6776	194	39	,	,	PUNCT
ejpam-6776	194	40	b	b	NOUN
ejpam-6776	194	41	)	)	PUNCT
ejpam-6776	194	42	=	=	SYM
ejpam-6776	194	43	p((s(t	p((s(t	NOUN
ejpam-6776	194	44	)	)	PUNCT
ejpam-6776	194	45	,	,	PUNCT
ejpam-6776	194	46	i(t	i(t	PROPN
ejpam-6776	194	47	)	)	PUNCT
ejpam-6776	194	48	)	)	PUNCT
ejpam-6776	195	1	∈	∈	PROPN
ejpam-6776	195	2	b	b	PROPN
ejpam-6776	195	3	|	|	ADV
ejpam-6776	195	4	s(0	s(0	PROPN
ejpam-6776	195	5	)	)	PUNCT
ejpam-6776	195	6	=	=	SYM
ejpam-6776	195	7	s0	s0	PROPN
ejpam-6776	195	8	,	,	PUNCT
ejpam-6776	195	9	i(0	i(0	PROPN
ejpam-6776	195	10	)	)	PUNCT
ejpam-6776	195	11	=	=	SYM
ejpam-6776	195	12	i0	i0	PROPN
ejpam-6776	195	13	)	)	PUNCT
ejpam-6776	195	14	,	,	PUNCT
ejpam-6776	195	15	for	for	ADP
ejpam-6776	195	16	b	b	PROPN
ejpam-6776	195	17	∈	∈	PROPN
ejpam-6776	195	18	b(d	b(d	PROPN
ejpam-6776	195	19	)	)	PUNCT
ejpam-6776	195	20	,	,	PUNCT
ejpam-6776	195	21	the	the	DET
ejpam-6776	195	22	borel	borel	PROPN
ejpam-6776	195	23	σ	σ	PROPN
ejpam-6776	195	24	-	-	PROPN
ejpam-6776	195	25	algebra	algebra	PROPN
ejpam-6776	195	26	on	on	ADP
ejpam-6776	195	27	d.	d.	PROPN
ejpam-6776	195	28	proposition	proposition	PROPN
ejpam-6776	195	29	4	4	NUM
ejpam-6776	195	30	.	.	PUNCT
ejpam-6776	196	1	for	for	ADP
ejpam-6776	196	2	all	all	DET
ejpam-6776	196	3	t	t	PROPN
ejpam-6776	196	4	>	>	X
ejpam-6776	196	5	0	0	NUM
ejpam-6776	196	6	,	,	PUNCT
ejpam-6776	196	7	(	(	PUNCT
ejpam-6776	196	8	s0	s0	PROPN
ejpam-6776	196	9	,	,	PUNCT
ejpam-6776	196	10	i0	i0	PROPN
ejpam-6776	196	11	)	)	PUNCT
ejpam-6776	196	12	∈	∈	PROPN
ejpam-6776	197	1	d	d	NOUN
ejpam-6776	197	2	,	,	PUNCT
ejpam-6776	197	3	the	the	DET
ejpam-6776	197	4	transition	transition	NOUN
ejpam-6776	197	5	probability	probability	NOUN
ejpam-6776	197	6	p	p	X
ejpam-6776	197	7	(	(	PUNCT
ejpam-6776	197	8	t	t	PROPN
ejpam-6776	197	9	,	,	PUNCT
ejpam-6776	197	10	s0	s0	PROPN
ejpam-6776	197	11	,	,	PUNCT
ejpam-6776	197	12	i0	i0	PROPN
ejpam-6776	197	13	,	,	PUNCT
ejpam-6776	197	14	·	·	PUNCT
ejpam-6776	197	15	)	)	PUNCT
ejpam-6776	197	16	has	have	VERB
ejpam-6776	197	17	a	a	DET
ejpam-6776	197	18	smooth	smooth	ADJ
ejpam-6776	197	19	density	density	NOUN
ejpam-6776	197	20	π(t	π(t	PROPN
ejpam-6776	197	21	,	,	PUNCT
ejpam-6776	197	22	s	s	PROPN
ejpam-6776	197	23	,	,	PUNCT
ejpam-6776	197	24	i	i	PROPN
ejpam-6776	197	25	,	,	PUNCT
ejpam-6776	197	26	s0	s0	PROPN
ejpam-6776	197	27	,	,	PUNCT
ejpam-6776	197	28	i0	i0	PROPN
ejpam-6776	197	29	)	)	PUNCT
ejpam-6776	197	30	∈	∈	PROPN
ejpam-6776	197	31	c∞(r+	c∞(r+	PROPN
ejpam-6776	197	32	×d	×d	NOUN
ejpam-6776	197	33	×d	×d	NOUN
ejpam-6776	197	34	)	)	PUNCT
ejpam-6776	197	35	.	.	PUNCT
ejpam-6776	198	1	proof	proof	NOUN
ejpam-6776	198	2	.	.	PUNCT
ejpam-6776	199	1	rewrite	rewrite	VERB
ejpam-6776	199	2	(	(	PUNCT
ejpam-6776	199	3	1	1	NUM
ejpam-6776	199	4	)	)	PUNCT
ejpam-6776	199	5	in	in	ADP
ejpam-6776	199	6	stratonovich	stratonovich	NOUN
ejpam-6776	199	7	form:ds	form:ds	NOUN
ejpam-6776	199	8	=	=	SYM
ejpam-6776	199	9	(	(	PUNCT
ejpam-6776	199	10	λ−	λ−	PROPN
ejpam-6776	199	11	βsi	βsi	NOUN
ejpam-6776	199	12	1+ki	1+ki	NUM
ejpam-6776	199	13	−	−	NOUN
ejpam-6776	199	14	δs	δs	NOUN
ejpam-6776	199	15	+	+	CCONJ
ejpam-6776	199	16	σ2si(s−i	σ2si(s−i	X
ejpam-6776	199	17	)	)	PUNCT
ejpam-6776	199	18	2(1+ki)2	2(1+ki)2	NUM
ejpam-6776	199	19	)	)	PUNCT
ejpam-6776	200	1	dt−	dt−	PUNCT
ejpam-6776	200	2	σsi	σsi	VERB
ejpam-6776	200	3	1+ki	1+ki	NUM
ejpam-6776	200	4	◦	◦	NOUN
ejpam-6776	200	5	db	db	PROPN
ejpam-6776	200	6	,	,	PUNCT
ejpam-6776	200	7	di	di	X
ejpam-6776	200	8	=	=	PUNCT
ejpam-6776	200	9	(	(	PUNCT
ejpam-6776	200	10	βsi	βsi	NOUN
ejpam-6776	200	11	1+ki	1+ki	NUM
ejpam-6776	200	12	−	−	PROPN
ejpam-6776	200	13	(	(	PUNCT
ejpam-6776	200	14	δ	δ	PROPN
ejpam-6776	200	15	+	+	CCONJ
ejpam-6776	200	16	γ	γ	X
ejpam-6776	200	17	+	+	X
ejpam-6776	200	18	ϵ)i	ϵ)i	AUX
ejpam-6776	200	19	−	−	PROPN
ejpam-6776	200	20	αi	αi	VERB
ejpam-6776	200	21	λ+i	λ+i	PUNCT
ejpam-6776	200	22	−	−	NOUN
ejpam-6776	200	23	σ2si(s−i	σ2si(s−i	NOUN
ejpam-6776	200	24	)	)	PUNCT
ejpam-6776	200	25	2(1+ki)2	2(1+ki)2	NOUN
ejpam-6776	200	26	)	)	PUNCT
ejpam-6776	201	1	dt+	dt+	NOUN
ejpam-6776	201	2	σsi	σsi	VERB
ejpam-6776	201	3	1+ki	1+ki	NUM
ejpam-6776	201	4	◦	◦	NOUN
ejpam-6776	201	5	db	db	PROPN
ejpam-6776	201	6	.	.	NOUN
ejpam-6776	202	1	define	define	VERB
ejpam-6776	202	2	vector	vector	NOUN
ejpam-6776	202	3	fields	field	NOUN
ejpam-6776	202	4	:	:	PUNCT
ejpam-6776	202	5	a(s	a(s	NUM
ejpam-6776	202	6	,	,	PUNCT
ejpam-6776	202	7	i	i	NOUN
ejpam-6776	202	8	)	)	PUNCT
ejpam-6776	203	1	=	=	SYM
ejpam-6776	203	2	(	(	PUNCT
ejpam-6776	203	3	λ−	λ−	PROPN
ejpam-6776	203	4	βsi	βsi	NOUN
ejpam-6776	203	5	1+ki	1+ki	NUM
ejpam-6776	203	6	−	−	PROPN
ejpam-6776	203	7	δs+	δs+	NOUN
ejpam-6776	203	8	σ2si(s−i	σ2si(s−i	X
ejpam-6776	203	9	)	)	PUNCT
ejpam-6776	203	10	2(1+ki)2	2(1+ki)2	NUM
ejpam-6776	203	11	βsi	βsi	NOUN
ejpam-6776	203	12	1+ki	1+ki	NUM
ejpam-6776	203	13	−	−	PROPN
ejpam-6776	203	14	(	(	PUNCT
ejpam-6776	203	15	δ	δ	PROPN
ejpam-6776	203	16	+	+	CCONJ
ejpam-6776	203	17	γ	γ	PROPN
ejpam-6776	203	18	+	+	X
ejpam-6776	203	19	ϵ)i−	ϵ)i−	NOUN
ejpam-6776	203	20	αi	αi	NOUN
ejpam-6776	203	21	λ+i	λ+i	PUNCT
ejpam-6776	203	22	−	−	PROPN
ejpam-6776	203	23	σ2si(s−i	σ2si(s−i	NOUN
ejpam-6776	203	24	)	)	PUNCT
ejpam-6776	203	25	2(1+ki)2	2(1+ki)2	NUM
ejpam-6776	203	26	)	)	PUNCT
ejpam-6776	203	27	,	,	PUNCT
ejpam-6776	203	28	b(s	b(	NOUN
ejpam-6776	203	29	,	,	PUNCT
ejpam-6776	203	30	i	i	NOUN
ejpam-6776	203	31	)	)	PUNCT
ejpam-6776	203	32	=	=	SYM
ejpam-6776	204	1	(	(	PUNCT
ejpam-6776	204	2	−	−	NOUN
ejpam-6776	204	3	σsi	σsi	VERB
ejpam-6776	204	4	1+ki	1+ki	NUM
ejpam-6776	204	5	σsi	σsi	NOUN
ejpam-6776	204	6	1+ki	1+ki	NUM
ejpam-6776	204	7	)	)	PUNCT
ejpam-6776	204	8	.	.	PUNCT
ejpam-6776	205	1	compute	compute	VERB
ejpam-6776	205	2	the	the	DET
ejpam-6776	205	3	lie	lie	NOUN
ejpam-6776	205	4	bracket	bracket	NOUN
ejpam-6776	206	1	[	[	X
ejpam-6776	206	2	a	a	X
ejpam-6776	206	3	,	,	PUNCT
ejpam-6776	206	4	b	b	NOUN
ejpam-6776	206	5	]	]	PUNCT
ejpam-6776	206	6	and	and	CCONJ
ejpam-6776	206	7	evaluate	evaluate	VERB
ejpam-6776	206	8	:	:	PUNCT
ejpam-6776	206	9	det([a	det([a	PROPN
ejpam-6776	206	10	,	,	PUNCT
ejpam-6776	206	11	b	b	NOUN
ejpam-6776	206	12	]	]	X
ejpam-6776	206	13	,	,	PUNCT
ejpam-6776	206	14	b	b	NOUN
ejpam-6776	206	15	)	)	PUNCT
ejpam-6776	206	16	=	=	SYM
ejpam-6776	207	1	(	(	PUNCT
ejpam-6776	207	2	σsi	σsi	VERB
ejpam-6776	207	3	1	1	NUM
ejpam-6776	207	4	+	+	NUM
ejpam-6776	207	5	ki	ki	PROPN
ejpam-6776	207	6	)	)	PUNCT
ejpam-6776	207	7	2	2	NUM
ejpam-6776	207	8	(	(	PUNCT
ejpam-6776	207	9	γ	γ	X
ejpam-6776	207	10	+	+	X
ejpam-6776	207	11	ϵ+	ϵ+	PUNCT
ejpam-6776	207	12	αλ	αλ	PRON
ejpam-6776	207	13	(	(	PUNCT
ejpam-6776	207	14	λ+	λ+	X
ejpam-6776	207	15	i)2	i)2	ADJ
ejpam-6776	207	16	)	)	PUNCT
ejpam-6776	207	17	>	>	X
ejpam-6776	207	18	0	0	NUM
ejpam-6776	207	19	,	,	PUNCT
ejpam-6776	207	20	for	for	ADP
ejpam-6776	207	21	(	(	PUNCT
ejpam-6776	207	22	s	s	PROPN
ejpam-6776	207	23	,	,	PUNCT
ejpam-6776	207	24	i	i	NOUN
ejpam-6776	207	25	)	)	PUNCT
ejpam-6776	207	26	∈	∈	PROPN
ejpam-6776	207	27	d.	d.	PROPN
ejpam-6776	207	28	thus	thus	ADV
ejpam-6776	207	29	,	,	PUNCT
ejpam-6776	207	30	[	[	X
ejpam-6776	207	31	a	a	X
ejpam-6776	207	32	,	,	PUNCT
ejpam-6776	207	33	b	b	NOUN
ejpam-6776	207	34	]	]	PUNCT
ejpam-6776	207	35	and	and	CCONJ
ejpam-6776	207	36	b	b	PROPN
ejpam-6776	207	37	span	span	NOUN
ejpam-6776	207	38	r2	r2	NOUN
ejpam-6776	207	39	.	.	PUNCT
ejpam-6776	208	1	by	by	ADP
ejpam-6776	208	2	hörmander	hörmander	PROPN
ejpam-6776	208	3	’s	’s	PART
ejpam-6776	208	4	theorem	theorem	NOUN
ejpam-6776	208	5	[	[	X
ejpam-6776	208	6	35	35	NUM
ejpam-6776	208	7	]	]	PUNCT
ejpam-6776	208	8	,	,	PUNCT
ejpam-6776	208	9	the	the	DET
ejpam-6776	208	10	transition	transition	NOUN
ejpam-6776	208	11	probability	probability	NOUN
ejpam-6776	208	12	has	have	VERB
ejpam-6776	208	13	a	a	DET
ejpam-6776	208	14	smooth	smooth	ADJ
ejpam-6776	208	15	density	density	NOUN
ejpam-6776	208	16	.	.	PUNCT
ejpam-6776	209	1	theorem	theorem	NOUN
ejpam-6776	209	2	2	2	NUM
ejpam-6776	209	3	.	.	X
ejpam-6776	209	4	for	for	ADP
ejpam-6776	209	5	any	any	DET
ejpam-6776	209	6	(	(	PUNCT
ejpam-6776	209	7	s0	s0	PROPN
ejpam-6776	209	8	,	,	PUNCT
ejpam-6776	209	9	i0	i0	PROPN
ejpam-6776	209	10	)	)	PUNCT
ejpam-6776	209	11	,	,	PUNCT
ejpam-6776	209	12	(	(	PUNCT
ejpam-6776	209	13	s1	s1	NOUN
ejpam-6776	209	14	,	,	PUNCT
ejpam-6776	209	15	i1	i1	PROPN
ejpam-6776	209	16	)	)	PUNCT
ejpam-6776	210	1	∈	∈	PROPN
ejpam-6776	211	1	d	d	NOUN
ejpam-6776	211	2	,	,	PUNCT
ejpam-6776	211	3	there	there	PRON
ejpam-6776	211	4	exists	exist	VERB
ejpam-6776	211	5	t	t	PROPN
ejpam-6776	211	6	>	>	X
ejpam-6776	211	7	0	0	NUM
ejpam-6776	212	1	such	such	ADJ
ejpam-6776	212	2	that	that	SCONJ
ejpam-6776	212	3	:	:	PUNCT
ejpam-6776	212	4	π(t	π(t	PROPN
ejpam-6776	212	5	,	,	PUNCT
ejpam-6776	212	6	s1	s1	PROPN
ejpam-6776	212	7	,	,	PUNCT
ejpam-6776	212	8	i1	i1	PROPN
ejpam-6776	212	9	|	|	PROPN
ejpam-6776	212	10	s0	s0	PROPN
ejpam-6776	212	11	,	,	PUNCT
ejpam-6776	212	12	i0	i0	PROPN
ejpam-6776	212	13	)	)	PUNCT
ejpam-6776	212	14	>	>	X
ejpam-6776	212	15	0	0	X
ejpam-6776	212	16	.	.	PUNCT
ejpam-6776	212	17	proof	proof	NOUN
ejpam-6776	212	18	.	.	PUNCT
ejpam-6776	213	1	consider	consider	VERB
ejpam-6776	213	2	the	the	DET
ejpam-6776	213	3	control	control	NOUN
ejpam-6776	213	4	system	system	NOUN
ejpam-6776	213	5	:	:	PUNCT
ejpam-6776	213	6	{	{	PUNCT
ejpam-6776	213	7	dsφ	dsφ	NOUN
ejpam-6776	213	8	dt	dt	NOUN
ejpam-6776	213	9	=	=	SYM
ejpam-6776	213	10	a1(sφ	a1(sφ	PROPN
ejpam-6776	213	11	,	,	PUNCT
ejpam-6776	213	12	iφ	iφ	NOUN
ejpam-6776	213	13	)	)	PUNCT
ejpam-6776	214	1	+	+	NUM
ejpam-6776	214	2	b1(sφ	b1(sφ	PROPN
ejpam-6776	214	3	,	,	PUNCT
ejpam-6776	214	4	iφ)φ	iφ)φ	PROPN
ejpam-6776	214	5	,	,	PUNCT
ejpam-6776	214	6	diφ	diφ	NOUN
ejpam-6776	214	7	dt	dt	NOUN
ejpam-6776	214	8	=	=	SYM
ejpam-6776	214	9	a2(sφ	a2(sφ	NOUN
ejpam-6776	214	10	,	,	PUNCT
ejpam-6776	214	11	iφ	iφ	NOUN
ejpam-6776	214	12	)	)	PUNCT
ejpam-6776	214	13	+	+	NUM
ejpam-6776	214	14	b2(sφ	b2(sφ	PROPN
ejpam-6776	214	15	,	,	PUNCT
ejpam-6776	214	16	iφ)φ	iφ)φ	PROPN
ejpam-6776	214	17	,	,	PUNCT
ejpam-6776	214	18	with	with	ADP
ejpam-6776	214	19	sφ(0	sφ(0	NOUN
ejpam-6776	214	20	)	)	PUNCT
ejpam-6776	214	21	=	=	SYM
ejpam-6776	214	22	s0	s0	PROPN
ejpam-6776	214	23	,	,	PUNCT
ejpam-6776	214	24	iφ(0	iφ(0	NOUN
ejpam-6776	214	25	)	)	PUNCT
ejpam-6776	214	26	=	=	SYM
ejpam-6776	214	27	i0	i0	PROPN
ejpam-6776	214	28	,	,	PUNCT
ejpam-6776	214	29	and	and	CCONJ
ejpam-6776	214	30	coefficients	coefficient	NOUN
ejpam-6776	214	31	from	from	ADP
ejpam-6776	214	32	proposition	proposition	NOUN
ejpam-6776	214	33	4	4	NUM
ejpam-6776	214	34	.	.	PUNCT
ejpam-6776	214	35	define	define	VERB
ejpam-6776	214	36	zφ	zφ	PROPN
ejpam-6776	215	1	=	=	SYM
ejpam-6776	215	2	sφ	sφ	PROPN
ejpam-6776	215	3	+	+	NUM
ejpam-6776	215	4	iφ	iφ	NOUN
ejpam-6776	215	5	:	:	PUNCT
ejpam-6776	215	6	dzφ	dzφ	NOUN
ejpam-6776	215	7	dt	dt	NOUN
ejpam-6776	216	1	=	=	SYM
ejpam-6776	216	2	λ−	λ−	PROPN
ejpam-6776	216	3	δzφ	δzφ	PROPN
ejpam-6776	216	4	−	−	NOUN
ejpam-6776	216	5	(	(	PUNCT
ejpam-6776	216	6	γ	γ	X
ejpam-6776	216	7	+	+	NOUN
ejpam-6776	216	8	ϵ)iφ	ϵ)iφ	PROPN
ejpam-6776	216	9	−	−	PROPN
ejpam-6776	216	10	αiφ	αiφ	NOUN
ejpam-6776	216	11	λ+	λ+	PUNCT
ejpam-6776	216	12	iφ	iφ	NOUN
ejpam-6776	216	13	.	.	PUNCT
ejpam-6776	217	1	construct	construct	VERB
ejpam-6776	217	2	a	a	DET
ejpam-6776	217	3	trajectory	trajectory	NOUN
ejpam-6776	217	4	from	from	ADP
ejpam-6776	217	5	(	(	PUNCT
ejpam-6776	217	6	s0	s0	PROPN
ejpam-6776	217	7	,	,	PUNCT
ejpam-6776	217	8	i0	i0	PROPN
ejpam-6776	217	9	)	)	PUNCT
ejpam-6776	217	10	to	to	ADP
ejpam-6776	217	11	(	(	PUNCT
ejpam-6776	217	12	s1	s1	PROPN
ejpam-6776	217	13	,	,	PUNCT
ejpam-6776	217	14	i1	i1	PROPN
ejpam-6776	217	15	)	)	PUNCT
ejpam-6776	217	16	.	.	PUNCT
ejpam-6776	218	1	define	define	VERB
ejpam-6776	218	2	:	:	PUNCT
ejpam-6776	218	3	z1(t	z1(t	NUM
ejpam-6776	218	4	)	)	PUNCT
ejpam-6776	218	5	=	=	SYM
ejpam-6776	218	6	z(t	z(t	NOUN
ejpam-6776	218	7	)	)	PUNCT
ejpam-6776	219	1	+	+	CCONJ
ejpam-6776	219	2	g(z0)−	g(z0)−	X
ejpam-6776	219	3	g(i0	g(i0	NOUN
ejpam-6776	219	4	)	)	PUNCT
ejpam-6776	219	5	g(z0	g(z0	NOUN
ejpam-6776	219	6	)	)	PUNCT
ejpam-6776	219	7	(	(	PUNCT
ejpam-6776	219	8	z̄(t)−z(t	z̄(t)−z(t	PROPN
ejpam-6776	219	9	)	)	PUNCT
ejpam-6776	219	10	)	)	PUNCT
ejpam-6776	219	11	,	,	PUNCT
ejpam-6776	219	12	j.	j.	PROPN
ejpam-6776	219	13	leo	leo	PROPN
ejpam-6776	219	14	amalraj	amalraj	PROPN
ejpam-6776	219	15	et	et	PROPN
ejpam-6776	219	16	al	al	PROPN
ejpam-6776	219	17	.	.	PUNCT
ejpam-6776	219	18	/	/	SYM
ejpam-6776	219	19	eur	eur	PROPN
ejpam-6776	219	20	.	.	PUNCT
ejpam-6776	220	1	j.	j.	PROPN
ejpam-6776	220	2	pure	pure	PROPN
ejpam-6776	220	3	appl	appl	PROPN
ejpam-6776	220	4	.	.	PROPN
ejpam-6776	220	5	math	math	PROPN
ejpam-6776	220	6	,	,	PUNCT
ejpam-6776	220	7	18	18	NUM
ejpam-6776	220	8	(	(	PUNCT
ejpam-6776	220	9	4	4	NUM
ejpam-6776	220	10	)	)	PUNCT
ejpam-6776	220	11	(	(	PUNCT
ejpam-6776	220	12	2025	2025	NUM
ejpam-6776	220	13	)	)	PUNCT
ejpam-6776	220	14	,	,	PUNCT
ejpam-6776	220	15	6776	6776	NUM
ejpam-6776	220	16	10	10	NUM
ejpam-6776	220	17	of	of	ADP
ejpam-6776	220	18	22	22	NUM
ejpam-6776	220	19	where	where	SCONJ
ejpam-6776	220	20	z	z	NOUN
ejpam-6776	220	21	,	,	PUNCT
ejpam-6776	220	22	z̄	z̄	X
ejpam-6776	220	23	solve	solve	NOUN
ejpam-6776	220	24	:	:	PUNCT
ejpam-6776	220	25	dz	dz	ADJ
ejpam-6776	220	26	dt	dt	NOUN
ejpam-6776	220	27	=	=	SYM
ejpam-6776	220	28	ψ(z	ψ(z	PROPN
ejpam-6776	220	29	)	)	PUNCT
ejpam-6776	220	30	,	,	PUNCT
ejpam-6776	220	31	dz̄	dz̄	NOUN
ejpam-6776	220	32	dt	dt	NOUN
ejpam-6776	220	33	=	=	SYM
ejpam-6776	220	34	λ−	λ−	PROPN
ejpam-6776	220	35	δz̄	δz̄	NOUN
ejpam-6776	220	36	,	,	PUNCT
ejpam-6776	220	37	with	with	ADP
ejpam-6776	220	38	z(0	z(0	ADV
ejpam-6776	220	39	)	)	PUNCT
ejpam-6776	220	40	=	=	PUNCT
ejpam-6776	220	41	z̄(0	z̄(0	NUM
ejpam-6776	220	42	)	)	PUNCT
ejpam-6776	220	43	=	=	SYM
ejpam-6776	220	44	z0	z0	NOUN
ejpam-6776	220	45	=	=	SYM
ejpam-6776	220	46	s0	s0	PROPN
ejpam-6776	220	47	+	+	CCONJ
ejpam-6776	220	48	i0	i0	PROPN
ejpam-6776	220	49	,	,	PUNCT
ejpam-6776	220	50	and	and	CCONJ
ejpam-6776	220	51	g(x	g(x	NOUN
ejpam-6776	220	52	)	)	PUNCT
ejpam-6776	221	1	=	=	SYM
ejpam-6776	221	2	(	(	PUNCT
ejpam-6776	221	3	γ	γ	X
ejpam-6776	221	4	+	+	X
ejpam-6776	221	5	ϵ)x+	ϵ)x+	X
ejpam-6776	221	6	αx	αx	X
ejpam-6776	221	7	λ+x	λ+x	PROPN
ejpam-6776	221	8	.	.	PUNCT
ejpam-6776	222	1	then	then	ADV
ejpam-6776	222	2	:	:	PUNCT
ejpam-6776	222	3	z1(0	z1(0	X
ejpam-6776	222	4	)	)	PUNCT
ejpam-6776	222	5	=	=	SYM
ejpam-6776	222	6	z0	z0	PROPN
ejpam-6776	222	7	,	,	PUNCT
ejpam-6776	222	8	dz1	dz1	ADJ
ejpam-6776	222	9	dt	dt	X
ejpam-6776	222	10	(	(	PUNCT
ejpam-6776	222	11	0	0	NUM
ejpam-6776	222	12	)	)	PUNCT
ejpam-6776	222	13	=	=	SYM
ejpam-6776	223	1	λ−	λ−	PROPN
ejpam-6776	223	2	δz0	δz0	NOUN
ejpam-6776	223	3	−	−	NOUN
ejpam-6776	223	4	g(i0	g(i0	NOUN
ejpam-6776	223	5	)	)	PUNCT
ejpam-6776	223	6	.	.	PUNCT
ejpam-6776	224	1	since	since	SCONJ
ejpam-6776	224	2	g	g	PROPN
ejpam-6776	224	3	is	be	AUX
ejpam-6776	224	4	increasing	increase	VERB
ejpam-6776	224	5	and	and	CCONJ
ejpam-6776	224	6	ψ(z1	ψ(z1	ADJ
ejpam-6776	224	7	)	)	PUNCT
ejpam-6776	224	8	<	<	X
ejpam-6776	224	9	dz1	dz1	VERB
ejpam-6776	224	10	dt	dt	X
ejpam-6776	224	11	<	<	X
ejpam-6776	224	12	λ−	λ−	PROPN
ejpam-6776	224	13	δz1	δz1	PROPN
ejpam-6776	224	14	,	,	PUNCT
ejpam-6776	224	15	z1(t	z1(t	NUM
ejpam-6776	224	16	)	)	PUNCT
ejpam-6776	224	17	∈	∈	PROPN
ejpam-6776	224	18	(	(	PUNCT
ejpam-6776	224	19	z∗,λ	z∗,λ	PROPN
ejpam-6776	224	20	/	/	SYM
ejpam-6776	224	21	δ	δ	PROPN
ejpam-6776	224	22	)	)	PUNCT
ejpam-6776	224	23	.	.	PUNCT
ejpam-6776	225	1	similarly	similarly	ADV
ejpam-6776	225	2	,	,	PUNCT
ejpam-6776	225	3	define	define	VERB
ejpam-6776	225	4	:	:	PUNCT
ejpam-6776	225	5	z3(t	z3(t	NUM
ejpam-6776	225	6	)	)	PUNCT
ejpam-6776	225	7	=	=	SYM
ejpam-6776	225	8	z̄(t	z̄(t	ADJ
ejpam-6776	225	9	)	)	PUNCT
ejpam-6776	226	1	+	+	CCONJ
ejpam-6776	226	2	g(z1)−	g(z1)−	PROPN
ejpam-6776	226	3	g(i1	g(i1	NOUN
ejpam-6776	226	4	)	)	PUNCT
ejpam-6776	226	5	g(z1	g(z1	NOUN
ejpam-6776	226	6	)	)	PUNCT
ejpam-6776	226	7	(	(	PUNCT
ejpam-6776	226	8	z̄(t	z̄(t	PROPN
ejpam-6776	226	9	−	−	ADP
ejpam-6776	226	10	t)−z(t	t)−z(t	SYM
ejpam-6776	226	11	−	−	PROPN
ejpam-6776	226	12	t	t	PROPN
ejpam-6776	226	13	)	)	PUNCT
ejpam-6776	226	14	)	)	PUNCT
ejpam-6776	226	15	,	,	PUNCT
ejpam-6776	226	16	with	with	ADP
ejpam-6776	226	17	z3(t	z3(t	PROPN
ejpam-6776	226	18	)	)	PUNCT
ejpam-6776	227	1	=	=	SYM
ejpam-6776	227	2	z1	z1	PROPN
ejpam-6776	227	3	=	=	SYM
ejpam-6776	227	4	s1+i1	s1+i1	PROPN
ejpam-6776	227	5	.	.	PUNCT
ejpam-6776	227	6	choose	choose	VERB
ejpam-6776	227	7	z2(t	z2(t	PROPN
ejpam-6776	227	8	)	)	PUNCT
ejpam-6776	227	9	on	on	ADP
ejpam-6776	227	10	[	[	PUNCT
ejpam-6776	227	11	η	η	PROPN
ejpam-6776	227	12	,	,	PUNCT
ejpam-6776	227	13	t	t	NOUN
ejpam-6776	227	14	−η	−η	NOUN
ejpam-6776	227	15	]	]	PUNCT
ejpam-6776	227	16	such	such	ADJ
ejpam-6776	227	17	that	that	SCONJ
ejpam-6776	227	18	zφ(t	zφ(t	VERB
ejpam-6776	227	19	)	)	PUNCT
ejpam-6776	227	20	=	=	SYM
ejpam-6776	227	21	z1(t),z2(t),z3(t	z1(t),z2(t),z3(t	X
ejpam-6776	227	22	)	)	PUNCT
ejpam-6776	227	23	is	be	AUX
ejpam-6776	227	24	c1	c1	PROPN
ejpam-6776	227	25	.	.	PUNCT
ejpam-6776	228	1	set	set	PROPN
ejpam-6776	228	2	:	:	PUNCT
ejpam-6776	228	3	iφ(t	iφ(t	NUM
ejpam-6776	228	4	)	)	PUNCT
ejpam-6776	228	5	=	=	SYM
ejpam-6776	229	1	g−1	g−1	PROPN
ejpam-6776	229	2	(	(	PUNCT
ejpam-6776	229	3	λ−	λ−	PROPN
ejpam-6776	229	4	δzφ	δzφ	VERB
ejpam-6776	229	5	−	−	PROPN
ejpam-6776	229	6	dzφ	dzφ	NOUN
ejpam-6776	229	7	dt	dt	NOUN
ejpam-6776	229	8	)	)	PUNCT
ejpam-6776	229	9	,	,	PUNCT
ejpam-6776	229	10	and	and	CCONJ
ejpam-6776	229	11	compute	compute	PROPN
ejpam-6776	229	12	φ	φ	PROPN
ejpam-6776	229	13	.	.	PUNCT
ejpam-6776	230	1	this	this	DET
ejpam-6776	230	2	trajectory	trajectory	NOUN
ejpam-6776	230	3	connects	connect	VERB
ejpam-6776	230	4	(	(	PUNCT
ejpam-6776	230	5	s0	s0	PROPN
ejpam-6776	230	6	,	,	PUNCT
ejpam-6776	230	7	i0	i0	PROPN
ejpam-6776	230	8	)	)	PUNCT
ejpam-6776	230	9	to	to	ADP
ejpam-6776	230	10	(	(	PUNCT
ejpam-6776	230	11	s1	s1	PROPN
ejpam-6776	230	12	,	,	PUNCT
ejpam-6776	230	13	i1	i1	PROPN
ejpam-6776	230	14	)	)	PUNCT
ejpam-6776	230	15	,	,	PUNCT
ejpam-6776	230	16	ensuring	ensure	VERB
ejpam-6776	230	17	positive	positive	ADJ
ejpam-6776	230	18	density	density	NOUN
ejpam-6776	230	19	by	by	ADP
ejpam-6776	230	20	support	support	NOUN
ejpam-6776	230	21	theorems	theorem	NOUN
ejpam-6776	230	22	[	[	X
ejpam-6776	230	23	35	35	NUM
ejpam-6776	230	24	]	]	PUNCT
ejpam-6776	230	25	.	.	PUNCT
ejpam-6776	231	1	theorem	theorem	NOUN
ejpam-6776	231	2	3	3	NUM
ejpam-6776	231	3	.	.	PUNCT
ejpam-6776	232	1	under	under	ADP
ejpam-6776	232	2	condition	condition	NOUN
ejpam-6776	232	3	(	(	PUNCT
ejpam-6776	232	4	3	3	NUM
ejpam-6776	232	5	)	)	PUNCT
ejpam-6776	232	6	,	,	PUNCT
ejpam-6776	232	7	for	for	ADP
ejpam-6776	232	8	(	(	PUNCT
ejpam-6776	232	9	s0	s0	PROPN
ejpam-6776	232	10	,	,	PUNCT
ejpam-6776	232	11	i0	i0	PROPN
ejpam-6776	232	12	)	)	PUNCT
ejpam-6776	232	13	∈	∈	PROPN
ejpam-6776	232	14	d	d	NOUN
ejpam-6776	232	15	,	,	PUNCT
ejpam-6776	232	16	there	there	PRON
ejpam-6776	232	17	exists	exist	VERB
ejpam-6776	232	18	a	a	DET
ejpam-6776	232	19	compact	compact	ADJ
ejpam-6776	232	20	set	set	NOUN
ejpam-6776	232	21	k	k	PROPN
ejpam-6776	232	22	⊂	⊂	PROPN
ejpam-6776	233	1	d	d	X
ejpam-6776	233	2	such	such	ADJ
ejpam-6776	233	3	that	that	PRON
ejpam-6776	233	4	:	:	PUNCT
ejpam-6776	233	5	lim	lim	PROPN
ejpam-6776	233	6	inf	inf	PROPN
ejpam-6776	233	7	t→∞	t→∞	ADV
ejpam-6776	233	8	1	1	NUM
ejpam-6776	233	9	t	t	NOUN
ejpam-6776	233	10	∫	∫	PROPN
ejpam-6776	233	11	t	t	PROPN
ejpam-6776	233	12	0	0	NUM
ejpam-6776	234	1	p	p	X
ejpam-6776	234	2	(	(	PUNCT
ejpam-6776	234	3	u	u	NOUN
ejpam-6776	234	4	,	,	PUNCT
ejpam-6776	234	5	(	(	PUNCT
ejpam-6776	234	6	s0	s0	PROPN
ejpam-6776	234	7	,	,	PUNCT
ejpam-6776	234	8	i0),k)du	i0),k)du	PROPN
ejpam-6776	234	9	>	>	X
ejpam-6776	234	10	0	0	NUM
ejpam-6776	234	11	,	,	PUNCT
ejpam-6776	234	12	and	and	CCONJ
ejpam-6776	234	13	a	a	DET
ejpam-6776	234	14	unique	unique	ADJ
ejpam-6776	234	15	stationary	stationary	ADJ
ejpam-6776	234	16	density	density	NOUN
ejpam-6776	234	17	π∗	π∗	PROPN
ejpam-6776	234	18	satisfying	satisfying	PROPN
ejpam-6776	234	19	:	:	PUNCT
ejpam-6776	234	20	lim	lim	PROPN
ejpam-6776	234	21	t→∞	t→∞	X
ejpam-6776	234	22	∫	∫	PROPN
ejpam-6776	234	23	d	d	X
ejpam-6776	234	24	|π(t	|π(t	PROPN
ejpam-6776	234	25	,	,	PUNCT
ejpam-6776	234	26	x	x	PRON
ejpam-6776	234	27	,	,	PUNCT
ejpam-6776	234	28	(	(	PUNCT
ejpam-6776	234	29	s0	s0	NOUN
ejpam-6776	234	30	,	,	PUNCT
ejpam-6776	234	31	i0))−	i0))−	NOUN
ejpam-6776	234	32	π∗(x)|dx	π∗(x)|dx	NOUN
ejpam-6776	234	33	=	=	SYM
ejpam-6776	234	34	0	0	X
ejpam-6776	234	35	.	.	PUNCT
ejpam-6776	234	36	proof	proof	NOUN
ejpam-6776	234	37	.	.	PUNCT
ejpam-6776	235	1	let	let	VERB
ejpam-6776	235	2	z	z	NOUN
ejpam-6776	235	3	=	=	SYM
ejpam-6776	235	4	s	s	PART
ejpam-6776	235	5	+	+	NUM
ejpam-6776	235	6	i.	i.	NOUN
ejpam-6776	235	7	from	from	ADP
ejpam-6776	235	8	(	(	PUNCT
ejpam-6776	235	9	1	1	NUM
ejpam-6776	235	10	):	):	PUNCT
ejpam-6776	235	11	dz	dz	PROPN
ejpam-6776	235	12	dt	dt	PROPN
ejpam-6776	235	13	≥	≥	PROPN
ejpam-6776	235	14	ψ(z	ψ(z	PROPN
ejpam-6776	235	15	)	)	PUNCT
ejpam-6776	235	16	.	.	PUNCT
ejpam-6776	236	1	choose	choose	VERB
ejpam-6776	236	2	h	h	NOUN
ejpam-6776	236	3	>	>	X
ejpam-6776	236	4	0	0	PUNCT
ejpam-6776	237	1	small	small	ADJ
ejpam-6776	237	2	such	such	ADJ
ejpam-6776	237	3	that	that	DET
ejpam-6776	237	4	ψ(z∗+h	ψ(z∗+h	NOUN
ejpam-6776	237	5	)	)	PUNCT
ejpam-6776	237	6	<	<	X
ejpam-6776	237	7	−(γ+ϵ)ms	−(γ+ϵ)ms	X
ejpam-6776	237	8	,	,	PUNCT
ejpam-6776	237	9	where	where	SCONJ
ejpam-6776	237	10	ms	ms	PROPN
ejpam-6776	237	11	=	=	PROPN
ejpam-6776	237	12	λ	λ	PROPN
ejpam-6776	237	13	δ+βλ	δ+βλ	ADJ
ejpam-6776	237	14	δ	δ	PROPN
ejpam-6776	237	15	.	.	PUNCT
ejpam-6776	238	1	by	by	ADP
ejpam-6776	238	2	proposition	proposition	NOUN
ejpam-6776	238	3	1	1	NUM
ejpam-6776	238	4	:	:	PUNCT
ejpam-6776	238	5	lim	lim	PROPN
ejpam-6776	238	6	inf	inf	PROPN
ejpam-6776	238	7	t→∞	t→∞	ADV
ejpam-6776	238	8	1	1	NUM
ejpam-6776	238	9	t	t	NOUN
ejpam-6776	238	10	∫	∫	PROPN
ejpam-6776	239	1	t	t	PROPN
ejpam-6776	239	2	0	0	NUM
ejpam-6776	239	3	−ψ(z(u))du	−ψ(z(u))du	PROPN
ejpam-6776	239	4	≥	≥	NUM
ejpam-6776	239	5	(	(	PUNCT
ejpam-6776	239	6	γ	γ	X
ejpam-6776	239	7	+	+	X
ejpam-6776	239	8	ϵ)ms	ϵ)ms	PROPN
ejpam-6776	239	9	.	.	PUNCT
ejpam-6776	240	1	using	use	VERB
ejpam-6776	240	2	hölder	hölder	NOUN
ejpam-6776	240	3	’s	’s	PART
ejpam-6776	240	4	inequality	inequality	NOUN
ejpam-6776	240	5	:	:	PUNCT
ejpam-6776	240	6	1	1	NUM
ejpam-6776	240	7	t	t	NOUN
ejpam-6776	240	8	∫	∫	PROPN
ejpam-6776	240	9	t	t	PROPN
ejpam-6776	240	10	0	0	NUM
ejpam-6776	240	11	−⊮{z(u)≥z∗+h}ψ(z(u))du	−⊮{z(u)≥z∗+h}ψ(z(u))du	PROPN
ejpam-6776	240	12	≤	≤	PROPN
ejpam-6776	240	13	−ψ	−ψ	NOUN
ejpam-6776	240	14	(	(	PUNCT
ejpam-6776	240	15	λ	λ	X
ejpam-6776	240	16	δ	δ	NOUN
ejpam-6776	240	17	)	)	PUNCT
ejpam-6776	240	18	(	(	PUNCT
ejpam-6776	240	19	1	1	NUM
ejpam-6776	240	20	t	t	NOUN
ejpam-6776	240	21	∫	∫	PROPN
ejpam-6776	240	22	t	t	PROPN
ejpam-6776	240	23	0	0	NUM
ejpam-6776	240	24	⊮{z(u)≥z∗+h}du	⊮{z(u)≥z∗+h}du	ADV
ejpam-6776	240	25	)	)	PUNCT
ejpam-6776	240	26	1/2	1/2	NUM
ejpam-6776	240	27	.	.	PUNCT
ejpam-6776	241	1	thus	thus	ADV
ejpam-6776	241	2	:	:	PUNCT
ejpam-6776	241	3	lim	lim	PROPN
ejpam-6776	241	4	inf	inf	PROPN
ejpam-6776	241	5	t→∞	t→∞	ADV
ejpam-6776	241	6	1	1	NUM
ejpam-6776	241	7	t	t	NOUN
ejpam-6776	241	8	∫	∫	PROPN
ejpam-6776	241	9	t	t	PROPN
ejpam-6776	241	10	0	0	NUM
ejpam-6776	241	11	⊮{z(u)≥z∗+h}du	⊮{z(u)≥z∗+h}du	VERB
ejpam-6776	241	12	≥	≥	NOUN
ejpam-6776	241	13	[	[	PUNCT
ejpam-6776	241	14	ψ	ψ	X
ejpam-6776	241	15	(	(	PUNCT
ejpam-6776	241	16	λ	λ	X
ejpam-6776	241	17	δ	δ	PROPN
ejpam-6776	241	18	)	)	PUNCT
ejpam-6776	241	19	]	]	X
ejpam-6776	241	20	−2	−2	X
ejpam-6776	242	1	[	[	X
ejpam-6776	242	2	(	(	PUNCT
ejpam-6776	242	3	γ	γ	X
ejpam-6776	242	4	+	+	X
ejpam-6776	242	5	ϵ)ms	ϵ)ms	PROPN
ejpam-6776	242	6	+	+	PUNCT
ejpam-6776	242	7	ψ(z∗	ψ(z∗	X
ejpam-6776	242	8	+	+	NUM
ejpam-6776	242	9	h)]2	h)]2	NUM
ejpam-6776	242	10	.	.	PUNCT
ejpam-6776	243	1	j.	j.	PROPN
ejpam-6776	243	2	leo	leo	PROPN
ejpam-6776	243	3	amalraj	amalraj	PROPN
ejpam-6776	243	4	et	et	PROPN
ejpam-6776	243	5	al	al	PROPN
ejpam-6776	243	6	.	.	PUNCT
ejpam-6776	243	7	/	/	SYM
ejpam-6776	243	8	eur	eur	PROPN
ejpam-6776	243	9	.	.	PUNCT
ejpam-6776	244	1	j.	j.	PROPN
ejpam-6776	244	2	pure	pure	PROPN
ejpam-6776	244	3	appl	appl	PROPN
ejpam-6776	244	4	.	.	PROPN
ejpam-6776	244	5	math	math	PROPN
ejpam-6776	244	6	,	,	PUNCT
ejpam-6776	244	7	18	18	NUM
ejpam-6776	244	8	(	(	PUNCT
ejpam-6776	244	9	4	4	NUM
ejpam-6776	244	10	)	)	PUNCT
ejpam-6776	244	11	(	(	PUNCT
ejpam-6776	244	12	2025	2025	NUM
ejpam-6776	244	13	)	)	PUNCT
ejpam-6776	244	14	,	,	PUNCT
ejpam-6776	244	15	6776	6776	NUM
ejpam-6776	244	16	11	11	NUM
ejpam-6776	244	17	of	of	ADP
ejpam-6776	244	18	22	22	NUM
ejpam-6776	244	19	define	define	NOUN
ejpam-6776	244	20	sets	set	NOUN
ejpam-6776	244	21	:	:	PUNCT
ejpam-6776	244	22	k1	k1	NOUN
ejpam-6776	244	23	=	=	SYM
ejpam-6776	244	24	{	{	PUNCT
ejpam-6776	244	25	(	(	PUNCT
ejpam-6776	244	26	s	s	X
ejpam-6776	244	27	,	,	PUNCT
ejpam-6776	244	28	i	i	PROPN
ejpam-6776	244	29	)	)	PUNCT
ejpam-6776	244	30	:	:	PUNCT
ejpam-6776	244	31	s+	s+	ADV
ejpam-6776	244	32	i	i	PRON
ejpam-6776	244	33	≥	≥	VERB
ejpam-6776	244	34	z∗+h	z∗+h	PROPN
ejpam-6776	244	35	}	}	PUNCT
ejpam-6776	244	36	,	,	PUNCT
ejpam-6776	244	37	k2	k2	NOUN
ejpam-6776	244	38	=	=	PUNCT
ejpam-6776	244	39	{	{	PUNCT
ejpam-6776	244	40	s	s	NOUN
ejpam-6776	244	41	≥	≥	NUM
ejpam-6776	244	42	h2	h2	NOUN
ejpam-6776	244	43	}	}	PUNCT
ejpam-6776	244	44	,	,	PUNCT
ejpam-6776	244	45	k3	k3	PROPN
ejpam-6776	244	46	=	=	SYM
ejpam-6776	244	47	{	{	PUNCT
ejpam-6776	244	48	i	i	PRON
ejpam-6776	244	49	≥	≥	NOUN
ejpam-6776	244	50	h3	h3	NOUN
ejpam-6776	244	51	}	}	PUNCT
ejpam-6776	244	52	,	,	PUNCT
ejpam-6776	244	53	k4	k4	NOUN
ejpam-6776	244	54	=	=	PUNCT
ejpam-6776	244	55	{	{	PUNCT
ejpam-6776	244	56	s+	s+	ADV
ejpam-6776	244	57	i	i	PRON
ejpam-6776	244	58	≤	≤	VERB
ejpam-6776	244	59	λ	λ	PROPN
ejpam-6776	244	60	δ	δ	PROPN
ejpam-6776	244	61	−h4	−h4	PROPN
ejpam-6776	244	62	}	}	PUNCT
ejpam-6776	244	63	.	.	PUNCT
ejpam-6776	245	1	using	use	VERB
ejpam-6776	245	2	propositions	proposition	NOUN
ejpam-6776	245	3	2	2	NUM
ejpam-6776	245	4	,	,	PUNCT
ejpam-6776	245	5	3	3	NUM
ejpam-6776	245	6	,	,	PUNCT
ejpam-6776	245	7	and	and	CCONJ
ejpam-6776	245	8	markov	markov	PROPN
ejpam-6776	245	9	’s	’s	PART
ejpam-6776	245	10	inequality	inequality	NOUN
ejpam-6776	245	11	,	,	PUNCT
ejpam-6776	245	12	choose	choose	VERB
ejpam-6776	245	13	h2	h2	PROPN
ejpam-6776	245	14	,	,	PUNCT
ejpam-6776	245	15	h3	h3	NOUN
ejpam-6776	245	16	,	,	PUNCT
ejpam-6776	245	17	h4	h4	NOUN
ejpam-6776	245	18	to	to	PART
ejpam-6776	245	19	ensure	ensure	VERB
ejpam-6776	245	20	:	:	PUNCT
ejpam-6776	245	21	lim	lim	PROPN
ejpam-6776	245	22	inf	inf	PROPN
ejpam-6776	246	1	t→∞	t→∞	ADV
ejpam-6776	246	2	1	1	NUM
ejpam-6776	246	3	t	t	NOUN
ejpam-6776	246	4	∫	∫	PROPN
ejpam-6776	246	5	t	t	PROPN
ejpam-6776	246	6	0	0	NUM
ejpam-6776	247	1	p	p	X
ejpam-6776	247	2	(	(	PUNCT
ejpam-6776	247	3	u	u	NOUN
ejpam-6776	247	4	,	,	PUNCT
ejpam-6776	247	5	(	(	PUNCT
ejpam-6776	247	6	s0	s0	PROPN
ejpam-6776	247	7	,	,	PUNCT
ejpam-6776	247	8	i0),ki)du	i0),ki)du	PROPN
ejpam-6776	247	9	≥	≥	NOUN
ejpam-6776	247	10	1−	1−	NUM
ejpam-6776	247	11	small	small	ADJ
ejpam-6776	247	12	terms	term	NOUN
ejpam-6776	247	13	.	.	PUNCT
ejpam-6776	248	1	set	set	VERB
ejpam-6776	248	2	k	k	X
ejpam-6776	249	1	=	=	PUNCT
ejpam-6776	249	2	⋂4	⋂4	PROPN
ejpam-6776	249	3	i=1ki	i=1ki	NOUN
ejpam-6776	249	4	.	.	PUNCT
ejpam-6776	250	1	then	then	ADV
ejpam-6776	250	2	:	:	PUNCT
ejpam-6776	250	3	lim	lim	PROPN
ejpam-6776	250	4	inf	inf	PROPN
ejpam-6776	250	5	t→∞	t→∞	ADV
ejpam-6776	250	6	1	1	NUM
ejpam-6776	250	7	t	t	NOUN
ejpam-6776	250	8	∫	∫	PROPN
ejpam-6776	250	9	t	t	PROPN
ejpam-6776	250	10	0	0	NUM
ejpam-6776	251	1	p	p	X
ejpam-6776	251	2	(	(	PUNCT
ejpam-6776	251	3	u	u	NOUN
ejpam-6776	251	4	,	,	PUNCT
ejpam-6776	251	5	(	(	PUNCT
ejpam-6776	251	6	s0	s0	PROPN
ejpam-6776	251	7	,	,	PUNCT
ejpam-6776	251	8	i0),k)du	i0),k)du	PROPN
ejpam-6776	251	9	>	>	X
ejpam-6776	251	10	0	0	X
ejpam-6776	251	11	.	.	PUNCT
ejpam-6776	252	1	by	by	ADP
ejpam-6776	252	2	proposition	proposition	NOUN
ejpam-6776	252	3	4	4	NUM
ejpam-6776	252	4	and	and	CCONJ
ejpam-6776	252	5	theorem	theorem	VERB
ejpam-6776	252	6	2	2	NUM
ejpam-6776	252	7	,	,	PUNCT
ejpam-6776	252	8	the	the	DET
ejpam-6776	252	9	markov	markov	NOUN
ejpam-6776	252	10	semigroup	semigroup	NOUN
ejpam-6776	252	11	is	be	AUX
ejpam-6776	252	12	asymptotically	asymptotically	ADV
ejpam-6776	252	13	stable	stable	ADJ
ejpam-6776	252	14	[	[	X
ejpam-6776	252	15	35	35	NUM
ejpam-6776	252	16	]	]	PUNCT
ejpam-6776	252	17	,	,	PUNCT
ejpam-6776	252	18	yielding	yield	VERB
ejpam-6776	252	19	a	a	DET
ejpam-6776	252	20	unique	unique	ADJ
ejpam-6776	252	21	π∗.	π∗.	ADJ
ejpam-6776	252	22	3	3	NUM
ejpam-6776	252	23	.	.	PUNCT
ejpam-6776	252	24	conditions	condition	NOUN
ejpam-6776	252	25	for	for	ADP
ejpam-6776	252	26	disease	disease	NOUN
ejpam-6776	252	27	elimination	elimination	NOUN
ejpam-6776	252	28	recent	recent	ADJ
ejpam-6776	252	29	studies	study	NOUN
ejpam-6776	252	30	on	on	ADP
ejpam-6776	252	31	stochastic	stochastic	ADJ
ejpam-6776	252	32	extinction	extinction	NOUN
ejpam-6776	252	33	conditions	condition	NOUN
ejpam-6776	252	34	,	,	PUNCT
ejpam-6776	252	35	such	such	ADJ
ejpam-6776	252	36	as	as	ADP
ejpam-6776	252	37	in	in	ADP
ejpam-6776	252	38	seir	seir	ADJ
ejpam-6776	252	39	models	model	NOUN
ejpam-6776	252	40	with	with	ADP
ejpam-6776	252	41	delays	delay	NOUN
ejpam-6776	252	42	and	and	CCONJ
ejpam-6776	252	43	noise	noise	NOUN
ejpam-6776	252	44	[	[	X
ejpam-6776	252	45	36	36	NUM
ejpam-6776	252	46	]	]	PUNCT
ejpam-6776	252	47	and	and	CCONJ
ejpam-6776	252	48	sivr	sivr	VERB
ejpam-6776	252	49	models	model	NOUN
ejpam-6776	252	50	with	with	ADP
ejpam-6776	252	51	vaccination	vaccination	NOUN
ejpam-6776	252	52	perturbations	perturbation	NOUN
ejpam-6776	252	53	[	[	X
ejpam-6776	252	54	37	37	NUM
ejpam-6776	252	55	]	]	PUNCT
ejpam-6776	252	56	,	,	PUNCT
ejpam-6776	252	57	provide	provide	VERB
ejpam-6776	252	58	context	context	NOUN
ejpam-6776	252	59	for	for	ADP
ejpam-6776	252	60	our	our	PRON
ejpam-6776	252	61	analysis	analysis	NOUN
ejpam-6776	252	62	of	of	ADP
ejpam-6776	252	63	disease	disease	NOUN
ejpam-6776	252	64	elimination	elimination	NOUN
ejpam-6776	252	65	under	under	ADP
ejpam-6776	252	66	resource	resource	NOUN
ejpam-6776	252	67	constraints	constraint	NOUN
ejpam-6776	252	68	.	.	PUNCT
ejpam-6776	253	1	we	we	PRON
ejpam-6776	253	2	investigate	investigate	VERB
ejpam-6776	253	3	the	the	DET
ejpam-6776	253	4	longterm	longterm	ADJ
ejpam-6776	253	5	dynamics	dynamic	NOUN
ejpam-6776	253	6	of	of	ADP
ejpam-6776	253	7	a	a	DET
ejpam-6776	253	8	stochastic	stochastic	ADJ
ejpam-6776	253	9	epidemic	epidemic	NOUN
ejpam-6776	253	10	model	model	NOUN
ejpam-6776	253	11	governing	govern	VERB
ejpam-6776	253	12	susceptible	susceptible	ADJ
ejpam-6776	253	13	(	(	PUNCT
ejpam-6776	253	14	s(t	s(t	PROPN
ejpam-6776	253	15	)	)	PUNCT
ejpam-6776	253	16	)	)	PUNCT
ejpam-6776	253	17	and	and	CCONJ
ejpam-6776	253	18	infected	infect	VERB
ejpam-6776	253	19	(	(	PUNCT
ejpam-6776	253	20	i(t	i(t	PROPN
ejpam-6776	253	21	)	)	PUNCT
ejpam-6776	253	22	)	)	PUNCT
ejpam-6776	253	23	populations	population	NOUN
ejpam-6776	253	24	,	,	PUNCT
ejpam-6776	253	25	initialized	initialize	VERB
ejpam-6776	253	26	at	at	ADP
ejpam-6776	253	27	x0	x0	PROPN
ejpam-6776	253	28	=	=	SYM
ejpam-6776	253	29	(	(	PUNCT
ejpam-6776	253	30	s0	s0	PROPN
ejpam-6776	253	31	,	,	PUNCT
ejpam-6776	253	32	i0	i0	PROPN
ejpam-6776	253	33	)	)	PUNCT
ejpam-6776	253	34	∈	∈	PROPN
ejpam-6776	253	35	r2	r2	NOUN
ejpam-6776	253	36	+	+	PROPN
ejpam-6776	253	37	,	,	PUNCT
ejpam-6776	253	38	where	where	SCONJ
ejpam-6776	253	39	:	:	PUNCT
ejpam-6776	253	40	r2	r2	PROPN
ejpam-6776	253	41	+	+	CCONJ
ejpam-6776	254	1	=	=	SYM
ejpam-6776	254	2	{	{	PUNCT
ejpam-6776	254	3	(	(	PUNCT
ejpam-6776	254	4	s	s	X
ejpam-6776	254	5	,	,	PUNCT
ejpam-6776	254	6	i	i	NOUN
ejpam-6776	254	7	)	)	PUNCT
ejpam-6776	254	8	∈	∈	PROPN
ejpam-6776	254	9	r2	r2	PROPN
ejpam-6776	254	10	:	:	PUNCT
ejpam-6776	254	11	s	s	X
ejpam-6776	254	12	>	>	X
ejpam-6776	254	13	0	0	PROPN
ejpam-6776	254	14	,	,	PUNCT
ejpam-6776	254	15	i	i	PRON
ejpam-6776	254	16	>	>	X
ejpam-6776	254	17	0	0	NUM
ejpam-6776	254	18	}	}	PUNCT
ejpam-6776	254	19	.	.	PUNCT
ejpam-6776	255	1	prior	prior	ADJ
ejpam-6776	255	2	analysis	analysis	NOUN
ejpam-6776	255	3	(	(	PUNCT
ejpam-6776	255	4	analogous	analogous	ADJ
ejpam-6776	255	5	to	to	ADP
ejpam-6776	255	6	earlier	early	ADV
ejpam-6776	255	7	lemmas	lemma	NOUN
ejpam-6776	255	8	)	)	PUNCT
ejpam-6776	255	9	guarantees	guarantee	VERB
ejpam-6776	255	10	that	that	SCONJ
ejpam-6776	255	11	the	the	DET
ejpam-6776	255	12	solution	solution	NOUN
ejpam-6776	255	13	(	(	PUNCT
ejpam-6776	255	14	s(t	s(t	PROPN
ejpam-6776	255	15	)	)	PUNCT
ejpam-6776	255	16	,	,	PUNCT
ejpam-6776	255	17	i(t	i(t	PROPN
ejpam-6776	255	18	)	)	PUNCT
ejpam-6776	255	19	)	)	PUNCT
ejpam-6776	255	20	remains	remain	VERB
ejpam-6776	255	21	in	in	ADP
ejpam-6776	255	22	r2	r2	PROPN
ejpam-6776	255	23	+	+	CCONJ
ejpam-6776	255	24	with	with	ADP
ejpam-6776	255	25	probability	probability	NOUN
ejpam-6776	255	26	1	1	NUM
ejpam-6776	255	27	.	.	PUNCT
ejpam-6776	256	1	furthermore	furthermore	ADV
ejpam-6776	256	2	,	,	PUNCT
ejpam-6776	256	3	employing	employ	VERB
ejpam-6776	256	4	techniques	technique	NOUN
ejpam-6776	256	5	similar	similar	ADJ
ejpam-6776	256	6	to	to	ADP
ejpam-6776	256	7	those	those	PRON
ejpam-6776	256	8	establishing	establish	VERB
ejpam-6776	256	9	invariant	invariant	ADJ
ejpam-6776	256	10	regions	region	NOUN
ejpam-6776	256	11	,	,	PUNCT
ejpam-6776	256	12	we	we	PRON
ejpam-6776	256	13	identify	identify	VERB
ejpam-6776	256	14	a	a	PRON
ejpam-6776	256	15	compact	compact	ADJ
ejpam-6776	256	16	,	,	PUNCT
ejpam-6776	256	17	positively	positively	ADV
ejpam-6776	256	18	invariant	invariant	ADJ
ejpam-6776	256	19	,	,	PUNCT
ejpam-6776	256	20	and	and	CCONJ
ejpam-6776	256	21	attractive	attractive	ADJ
ejpam-6776	256	22	set	set	NOUN
ejpam-6776	256	23	:	:	PUNCT
ejpam-6776	256	24	a	a	DET
ejpam-6776	256	25	=	=	X
ejpam-6776	256	26	{	{	PUNCT
ejpam-6776	256	27	(	(	PUNCT
ejpam-6776	256	28	s	s	X
ejpam-6776	256	29	,	,	PUNCT
ejpam-6776	256	30	i	i	NOUN
ejpam-6776	256	31	)	)	PUNCT
ejpam-6776	256	32	∈	∈	PROPN
ejpam-6776	256	33	r2	r2	NOUN
ejpam-6776	256	34	+	+	CCONJ
ejpam-6776	256	35	:	:	PUNCT
ejpam-6776	256	36	x∗	x∗	PROPN
ejpam-6776	256	37	≤	≤	PROPN
ejpam-6776	256	38	s+	s+	PUNCT
ejpam-6776	256	39	i	i	PRON
ejpam-6776	256	40	≤	≤	VERB
ejpam-6776	256	41	λ	λ	X
ejpam-6776	256	42	δ	δ	PROPN
ejpam-6776	256	43	}	}	PUNCT
ejpam-6776	256	44	,	,	PUNCT
ejpam-6776	256	45	where	where	SCONJ
ejpam-6776	256	46	x∗	x∗	PROPN
ejpam-6776	256	47	is	be	AUX
ejpam-6776	256	48	the	the	DET
ejpam-6776	256	49	unique	unique	ADJ
ejpam-6776	256	50	root	root	NOUN
ejpam-6776	256	51	of	of	ADP
ejpam-6776	256	52	the	the	DET
ejpam-6776	256	53	function	function	NOUN
ejpam-6776	256	54	ϕ(x	ϕ(x	X
ejpam-6776	256	55	)	)	PUNCT
ejpam-6776	257	1	=	=	SYM
ejpam-6776	257	2	λ−	λ−	PROPN
ejpam-6776	257	3	(	(	PUNCT
ejpam-6776	257	4	δ	δ	PROPN
ejpam-6776	257	5	+	+	CCONJ
ejpam-6776	257	6	γ	γ	PROPN
ejpam-6776	257	7	+	+	NOUN
ejpam-6776	257	8	ϵ)x−	ϵ)x−	NOUN
ejpam-6776	257	9	αx	αx	X
ejpam-6776	257	10	λ+x	λ+x	PROPN
ejpam-6776	257	11	.	.	PUNCT
ejpam-6776	258	1	consequently	consequently	ADV
ejpam-6776	258	2	,	,	PUNCT
ejpam-6776	258	3	we	we	PRON
ejpam-6776	258	4	restrict	restrict	VERB
ejpam-6776	258	5	our	our	PRON
ejpam-6776	258	6	study	study	NOUN
ejpam-6776	258	7	of	of	ADP
ejpam-6776	258	8	the	the	DET
ejpam-6776	258	9	system	system	NOUN
ejpam-6776	258	10	’s	’s	PART
ejpam-6776	258	11	asymptotic	asymptotic	ADJ
ejpam-6776	258	12	behavior	behavior	NOUN
ejpam-6776	258	13	to	to	ADP
ejpam-6776	258	14	the	the	DET
ejpam-6776	258	15	state	state	NOUN
ejpam-6776	258	16	space	space	NOUN
ejpam-6776	258	17	a.	a.	NOUN
ejpam-6776	258	18	in	in	ADP
ejpam-6776	258	19	this	this	DET
ejpam-6776	258	20	section	section	NOUN
ejpam-6776	258	21	,	,	PUNCT
ejpam-6776	258	22	we	we	PRON
ejpam-6776	258	23	derive	derive	VERB
ejpam-6776	258	24	conditions	condition	NOUN
ejpam-6776	258	25	ensuring	ensure	VERB
ejpam-6776	258	26	disease	disease	NOUN
ejpam-6776	258	27	extinction	extinction	NOUN
ejpam-6776	258	28	by	by	ADP
ejpam-6776	258	29	examining	examine	VERB
ejpam-6776	258	30	the	the	DET
ejpam-6776	258	31	stability	stability	NOUN
ejpam-6776	258	32	of	of	ADP
ejpam-6776	258	33	the	the	DET
ejpam-6776	258	34	disease	disease	NOUN
ejpam-6776	258	35	-	-	PUNCT
ejpam-6776	258	36	free	free	ADJ
ejpam-6776	258	37	equilibrium	equilibrium	NOUN
ejpam-6776	258	38	e0	e0	PROPN
ejpam-6776	258	39	=	=	PUNCT
ejpam-6776	258	40	(	(	PUNCT
ejpam-6776	258	41	λ	λ	X
ejpam-6776	258	42	δ	δ	PROPN
ejpam-6776	258	43	,	,	PUNCT
ejpam-6776	258	44	0	0	NUM
ejpam-6776	258	45	)	)	PUNCT
ejpam-6776	258	46	.	.	PUNCT
ejpam-6776	259	1	we	we	PRON
ejpam-6776	259	2	denote	denote	VERB
ejpam-6776	259	3	the	the	DET
ejpam-6776	259	4	solution	solution	NOUN
ejpam-6776	259	5	with	with	ADP
ejpam-6776	259	6	initial	initial	ADJ
ejpam-6776	259	7	condition	condition	NOUN
ejpam-6776	259	8	x0	x0	PROPN
ejpam-6776	259	9	=	=	PRON
ejpam-6776	259	10	(	(	PUNCT
ejpam-6776	259	11	s0	s0	PROPN
ejpam-6776	259	12	,	,	PUNCT
ejpam-6776	259	13	i0	i0	PROPN
ejpam-6776	259	14	)	)	PUNCT
ejpam-6776	259	15	∈	∈	PROPN
ejpam-6776	259	16	a	a	PRON
ejpam-6776	259	17	as	as	ADP
ejpam-6776	259	18	x	x	PROPN
ejpam-6776	259	19	x0(t	x0(t	PROPN
ejpam-6776	259	20	)	)	PUNCT
ejpam-6776	259	21	=	=	SYM
ejpam-6776	259	22	(	(	PUNCT
ejpam-6776	259	23	s(t	s(t	PROPN
ejpam-6776	259	24	)	)	PUNCT
ejpam-6776	259	25	,	,	PUNCT
ejpam-6776	259	26	i(t	i(t	PROPN
ejpam-6776	259	27	)	)	PUNCT
ejpam-6776	259	28	)	)	PUNCT
ejpam-6776	259	29	,	,	PUNCT
ejpam-6776	259	30	and	and	CCONJ
ejpam-6776	259	31	use	use	VERB
ejpam-6776	259	32	x	x	PROPN
ejpam-6776	259	33	u	u	NOUN
ejpam-6776	259	34	,	,	PUNCT
ejpam-6776	259	35	x(t	x(t	PROPN
ejpam-6776	259	36	)	)	PUNCT
ejpam-6776	259	37	to	to	PART
ejpam-6776	259	38	indicate	indicate	VERB
ejpam-6776	259	39	the	the	DET
ejpam-6776	259	40	solution	solution	NOUN
ejpam-6776	259	41	satisfying	satisfy	VERB
ejpam-6776	259	42	x	x	X
ejpam-6776	259	43	(	(	PUNCT
ejpam-6776	259	44	u	u	NOUN
ejpam-6776	259	45	)	)	PUNCT
ejpam-6776	259	46	=	=	PUNCT
ejpam-6776	260	1	x.	x.	NOUN
ejpam-6776	261	1	the	the	DET
ejpam-6776	261	2	euclidean	euclidean	ADJ
ejpam-6776	261	3	norm	norm	NOUN
ejpam-6776	261	4	in	in	ADP
ejpam-6776	261	5	r2	r2	PROPN
ejpam-6776	261	6	is	be	AUX
ejpam-6776	261	7	denoted	denote	VERB
ejpam-6776	261	8	by	by	ADP
ejpam-6776	261	9	∥	∥	X
ejpam-6776	261	10	·	·	PUNCT
ejpam-6776	261	11	∥.	∥.	X
ejpam-6776	262	1	drawing	draw	VERB
ejpam-6776	262	2	on	on	ADP
ejpam-6776	262	3	stochastic	stochastic	ADJ
ejpam-6776	262	4	stability	stability	NOUN
ejpam-6776	262	5	theory	theory	NOUN
ejpam-6776	262	6	[	[	X
ejpam-6776	262	7	38	38	NUM
ejpam-6776	262	8	,	,	PUNCT
ejpam-6776	262	9	39	39	NUM
ejpam-6776	262	10	]	]	PUNCT
ejpam-6776	262	11	,	,	PUNCT
ejpam-6776	262	12	we	we	PRON
ejpam-6776	262	13	establish	establish	VERB
ejpam-6776	262	14	an	an	DET
ejpam-6776	262	15	almost	almost	ADV
ejpam-6776	262	16	necessary	necessary	ADJ
ejpam-6776	262	17	and	and	CCONJ
ejpam-6776	262	18	sufficient	sufficient	ADJ
ejpam-6776	262	19	condition	condition	NOUN
ejpam-6776	262	20	for	for	SCONJ
ejpam-6776	262	21	the	the	DET
ejpam-6776	262	22	disease	disease	NOUN
ejpam-6776	262	23	to	to	PART
ejpam-6776	262	24	vanish	vanish	VERB
ejpam-6776	262	25	,	,	PUNCT
ejpam-6776	262	26	as	as	SCONJ
ejpam-6776	262	27	formalized	formalize	VERB
ejpam-6776	262	28	below	below	ADV
ejpam-6776	262	29	.	.	PUNCT
ejpam-6776	263	1	theorem	theorem	ADJ
ejpam-6776	263	2	4	4	NUM
ejpam-6776	263	3	.	.	PUNCT
ejpam-6776	264	1	assume	assume	VERB
ejpam-6776	264	2	the	the	DET
ejpam-6776	264	3	parameter	parameter	NOUN
ejpam-6776	264	4	condition	condition	NOUN
ejpam-6776	264	5	:	:	PUNCT
ejpam-6776	264	6	η	η	PROPN
ejpam-6776	264	7	≜	≜	PROPN
ejpam-6776	264	8	βλ	βλ	PROPN
ejpam-6776	264	9	δ	δ	PROPN
ejpam-6776	264	10	−	−	PROPN
ejpam-6776	265	1	(	(	PUNCT
ejpam-6776	265	2	δ	δ	PROPN
ejpam-6776	265	3	+	+	CCONJ
ejpam-6776	265	4	γ	γ	X
ejpam-6776	265	5	+	+	X
ejpam-6776	265	6	ϵ+	ϵ+	PUNCT
ejpam-6776	265	7	α	α	X
ejpam-6776	265	8	λ	λ	X
ejpam-6776	265	9	+	+	NOUN
ejpam-6776	265	10	1	1	NUM
ejpam-6776	265	11	2	2	NUM
ejpam-6776	265	12	(	(	PUNCT
ejpam-6776	265	13	σλ	σλ	NOUN
ejpam-6776	265	14	δ	δ	PROPN
ejpam-6776	265	15	)	)	PUNCT
ejpam-6776	265	16	2	2	X
ejpam-6776	265	17	)	)	PUNCT
ejpam-6776	265	18	<	<	X
ejpam-6776	265	19	0	0	X
ejpam-6776	265	20	.	.	PUNCT
ejpam-6776	266	1	(	(	PUNCT
ejpam-6776	266	2	4	4	X
ejpam-6776	266	3	)	)	PUNCT
ejpam-6776	266	4	j.	j.	PROPN
ejpam-6776	266	5	leo	leo	PROPN
ejpam-6776	266	6	amalraj	amalraj	PROPN
ejpam-6776	266	7	et	et	PROPN
ejpam-6776	266	8	al	al	PROPN
ejpam-6776	266	9	.	.	PUNCT
ejpam-6776	266	10	/	/	SYM
ejpam-6776	266	11	eur	eur	PROPN
ejpam-6776	266	12	.	.	PUNCT
ejpam-6776	267	1	j.	j.	PROPN
ejpam-6776	267	2	pure	pure	PROPN
ejpam-6776	267	3	appl	appl	PROPN
ejpam-6776	267	4	.	.	PROPN
ejpam-6776	267	5	math	math	PROPN
ejpam-6776	267	6	,	,	PUNCT
ejpam-6776	267	7	18	18	NUM
ejpam-6776	267	8	(	(	PUNCT
ejpam-6776	267	9	4	4	NUM
ejpam-6776	267	10	)	)	PUNCT
ejpam-6776	267	11	(	(	PUNCT
ejpam-6776	267	12	2025	2025	NUM
ejpam-6776	267	13	)	)	PUNCT
ejpam-6776	267	14	,	,	PUNCT
ejpam-6776	267	15	6776	6776	NUM
ejpam-6776	267	16	12	12	NUM
ejpam-6776	267	17	of	of	ADP
ejpam-6776	267	18	22	22	NUM
ejpam-6776	267	19	then	then	ADV
ejpam-6776	267	20	,	,	PUNCT
ejpam-6776	267	21	the	the	DET
ejpam-6776	267	22	disease	disease	NOUN
ejpam-6776	267	23	-	-	PUNCT
ejpam-6776	267	24	free	free	ADJ
ejpam-6776	267	25	equilibrium	equilibrium	NOUN
ejpam-6776	267	26	e0	e0	PROPN
ejpam-6776	267	27	=	=	PUNCT
ejpam-6776	267	28	(	(	PUNCT
ejpam-6776	267	29	λ	λ	X
ejpam-6776	267	30	δ	δ	PROPN
ejpam-6776	267	31	,	,	PUNCT
ejpam-6776	267	32	0	0	NUM
ejpam-6776	267	33	)	)	PUNCT
ejpam-6776	267	34	is	be	AUX
ejpam-6776	267	35	asymptotically	asymptotically	ADV
ejpam-6776	267	36	stable	stable	ADJ
ejpam-6776	267	37	in	in	ADP
ejpam-6776	267	38	the	the	DET
ejpam-6776	267	39	large	large	ADJ
ejpam-6776	267	40	in	in	ADP
ejpam-6776	267	41	the	the	DET
ejpam-6776	267	42	stochastic	stochastic	ADJ
ejpam-6776	267	43	sense	sense	NOUN
ejpam-6776	267	44	.	.	PUNCT
ejpam-6776	268	1	specifically	specifically	ADV
ejpam-6776	268	2	,	,	PUNCT
ejpam-6776	268	3	e0	e0	PROPN
ejpam-6776	268	4	is	be	AUX
ejpam-6776	268	5	stochastically	stochastically	ADV
ejpam-6776	268	6	stable	stable	ADJ
ejpam-6776	268	7	,	,	PUNCT
ejpam-6776	268	8	and	and	CCONJ
ejpam-6776	268	9	for	for	ADP
ejpam-6776	268	10	all	all	DET
ejpam-6776	268	11	initial	initial	ADJ
ejpam-6776	268	12	conditions	condition	NOUN
ejpam-6776	268	13	x0	x0	PROPN
ejpam-6776	268	14	=	=	SYM
ejpam-6776	268	15	(	(	PUNCT
ejpam-6776	268	16	s0	s0	PROPN
ejpam-6776	268	17	,	,	PUNCT
ejpam-6776	268	18	i0	i0	PROPN
ejpam-6776	268	19	)	)	PUNCT
ejpam-6776	268	20	∈	∈	PROPN
ejpam-6776	269	1	a	a	PRON
ejpam-6776	269	2	:	:	PUNCT
ejpam-6776	269	3	p	p	X
ejpam-6776	269	4	(	(	PUNCT
ejpam-6776	269	5	lim	lim	PROPN
ejpam-6776	269	6	t→∞	t→∞	NUM
ejpam-6776	269	7	x	x	PROPN
ejpam-6776	269	8	x0(t	x0(t	PROPN
ejpam-6776	269	9	)	)	PUNCT
ejpam-6776	269	10	=	=	SYM
ejpam-6776	269	11	e0	e0	PROPN
ejpam-6776	269	12	)	)	PUNCT
ejpam-6776	270	1	=	=	PUNCT
ejpam-6776	270	2	1	1	X
ejpam-6776	270	3	.	.	PUNCT
ejpam-6776	270	4	proof	proof	NOUN
ejpam-6776	270	5	.	.	PUNCT
ejpam-6776	271	1	to	to	PART
ejpam-6776	271	2	demonstrate	demonstrate	VERB
ejpam-6776	271	3	asymptotic	asymptotic	ADJ
ejpam-6776	271	4	stability	stability	NOUN
ejpam-6776	271	5	,	,	PUNCT
ejpam-6776	271	6	we	we	PRON
ejpam-6776	271	7	follow	follow	VERB
ejpam-6776	271	8	the	the	DET
ejpam-6776	271	9	approach	approach	NOUN
ejpam-6776	271	10	outlined	outline	VERB
ejpam-6776	271	11	in	in	ADP
ejpam-6776	271	12	[	[	X
ejpam-6776	271	13	38	38	NUM
ejpam-6776	271	14	]	]	PUNCT
ejpam-6776	271	15	,	,	PUNCT
ejpam-6776	271	16	which	which	PRON
ejpam-6776	271	17	equates	equate	VERB
ejpam-6776	271	18	the	the	DET
ejpam-6776	271	19	stability	stability	NOUN
ejpam-6776	271	20	of	of	ADP
ejpam-6776	271	21	the	the	DET
ejpam-6776	271	22	nonlinear	nonlinear	ADJ
ejpam-6776	271	23	system	system	NOUN
ejpam-6776	271	24	to	to	ADP
ejpam-6776	271	25	that	that	PRON
ejpam-6776	271	26	of	of	ADP
ejpam-6776	271	27	its	its	PRON
ejpam-6776	271	28	linearization	linearization	NOUN
ejpam-6776	271	29	at	at	ADP
ejpam-6776	271	30	e0	e0	PROPN
ejpam-6776	271	31	.	.	PUNCT
ejpam-6776	272	1	introduce	introduce	VERB
ejpam-6776	272	2	transformed	transform	VERB
ejpam-6776	272	3	variables	variable	NOUN
ejpam-6776	272	4	:	:	PUNCT
ejpam-6776	273	1	x1	x1	PROPN
ejpam-6776	273	2	=	=	PUNCT
ejpam-6776	273	3	λ	λ	PART
ejpam-6776	273	4	δ	δ	X
ejpam-6776	273	5	−	−	PROPN
ejpam-6776	274	1	s	s	PROPN
ejpam-6776	274	2	,	,	PUNCT
ejpam-6776	274	3	x2	x2	PROPN
ejpam-6776	274	4	=	=	SYM
ejpam-6776	274	5	i.	i.	NOUN
ejpam-6776	274	6	linearizing	linearize	VERB
ejpam-6776	274	7	the	the	DET
ejpam-6776	274	8	system	system	NOUN
ejpam-6776	274	9	around	around	ADP
ejpam-6776	274	10	e0	e0	PROPN
ejpam-6776	274	11	,	,	PUNCT
ejpam-6776	274	12	we	we	PRON
ejpam-6776	274	13	obtain:dx1	obtain:dx1	NUM
ejpam-6776	274	14	=	=	SYM
ejpam-6776	274	15	(	(	PUNCT
ejpam-6776	274	16	−δx1	−δx1	X
ejpam-6776	274	17	+	+	CCONJ
ejpam-6776	274	18	βλ	βλ	PROPN
ejpam-6776	274	19	δ	δ	NOUN
ejpam-6776	274	20	x2	x2	NOUN
ejpam-6776	274	21	)	)	PUNCT
ejpam-6776	274	22	dt+	dt+	NOUN
ejpam-6776	274	23	σλ	σλ	VERB
ejpam-6776	274	24	δ	δ	PROPN
ejpam-6776	274	25	x2db(t	x2db(t	PROPN
ejpam-6776	274	26	)	)	PUNCT
ejpam-6776	274	27	,	,	PUNCT
ejpam-6776	274	28	dx2	dx2	PROPN
ejpam-6776	275	1	=	=	SYM
ejpam-6776	275	2	[	[	PUNCT
ejpam-6776	275	3	βλ	βλ	X
ejpam-6776	275	4	δ	δ	PROPN
ejpam-6776	275	5	−	−	PROPN
ejpam-6776	275	6	(	(	PUNCT
ejpam-6776	275	7	δ	δ	PROPN
ejpam-6776	275	8	+	+	CCONJ
ejpam-6776	275	9	γ	γ	X
ejpam-6776	275	10	+	+	X
ejpam-6776	275	11	ϵ+	ϵ+	PUNCT
ejpam-6776	275	12	α	α	X
ejpam-6776	275	13	λ	λ	PROPN
ejpam-6776	275	14	)	)	PUNCT
ejpam-6776	275	15	]	]	PUNCT
ejpam-6776	275	16	x2dt+	x2dt+	PROPN
ejpam-6776	275	17	σλ	σλ	VERB
ejpam-6776	275	18	δ	δ	PROPN
ejpam-6776	275	19	x2db(t	x2db(t	PROPN
ejpam-6776	275	20	)	)	PUNCT
ejpam-6776	275	21	.	.	PUNCT
ejpam-6776	276	1	(	(	PUNCT
ejpam-6776	276	2	5	5	X
ejpam-6776	276	3	)	)	PUNCT
ejpam-6776	276	4	define	define	VERB
ejpam-6776	276	5	a	a	DET
ejpam-6776	276	6	positive	positive	ADJ
ejpam-6776	276	7	-	-	PUNCT
ejpam-6776	276	8	definite	definite	ADJ
ejpam-6776	276	9	lyapunov	lyapunov	ADJ
ejpam-6776	276	10	function	function	NOUN
ejpam-6776	276	11	:	:	PUNCT
ejpam-6776	276	12	ψ(x1,x2	ψ(x1,x2	VERB
ejpam-6776	276	13	)	)	PUNCT
ejpam-6776	277	1	=	=	VERB
ejpam-6776	277	2	kx1	kx1	X
ejpam-6776	277	3	+	+	CCONJ
ejpam-6776	278	1	1	1	NUM
ejpam-6776	278	2	p	p	NOUN
ejpam-6776	278	3	x	x	X
ejpam-6776	278	4	p	p	X
ejpam-6776	278	5	2	2	NUM
ejpam-6776	278	6	,	,	PUNCT
ejpam-6776	278	7	(	(	PUNCT
ejpam-6776	278	8	6	6	NUM
ejpam-6776	278	9	)	)	PUNCT
ejpam-6776	278	10	where	where	SCONJ
ejpam-6776	278	11	k	k	NOUN
ejpam-6776	278	12	,	,	PUNCT
ejpam-6776	278	13	p	p	X
ejpam-6776	278	14	>	>	X
ejpam-6776	278	15	0	0	NUM
ejpam-6776	278	16	are	be	AUX
ejpam-6776	278	17	parameters	parameter	NOUN
ejpam-6776	278	18	to	to	PART
ejpam-6776	278	19	be	be	AUX
ejpam-6776	278	20	chosen	choose	VERB
ejpam-6776	278	21	.	.	PUNCT
ejpam-6776	279	1	let	let	VERB
ejpam-6776	279	2	l	l	NOUN
ejpam-6776	279	3	be	be	AUX
ejpam-6776	279	4	the	the	DET
ejpam-6776	279	5	infinitesimal	infinitesimal	ADJ
ejpam-6776	279	6	generator	generator	NOUN
ejpam-6776	279	7	associated	associate	VERB
ejpam-6776	279	8	with	with	ADP
ejpam-6776	279	9	(	(	PUNCT
ejpam-6776	279	10	5	5	NUM
ejpam-6776	279	11	)	)	PUNCT
ejpam-6776	279	12	.	.	PUNCT
ejpam-6776	280	1	compute	compute	NOUN
ejpam-6776	280	2	:	:	PUNCT
ejpam-6776	280	3	lψ	lψ	PROPN
ejpam-6776	280	4	=	=	SYM
ejpam-6776	280	5	k	k	PROPN
ejpam-6776	280	6	(	(	PUNCT
ejpam-6776	280	7	−δx1	−δx1	ADP
ejpam-6776	280	8	+	+	CCONJ
ejpam-6776	280	9	βλ	βλ	PROPN
ejpam-6776	280	10	δ	δ	NOUN
ejpam-6776	280	11	x2	x2	PROPN
ejpam-6776	280	12	)	)	PUNCT
ejpam-6776	281	1	+	+	PUNCT
ejpam-6776	281	2	x	x	PROPN
ejpam-6776	281	3	p−1	p−1	PROPN
ejpam-6776	281	4	2	2	NUM
ejpam-6776	281	5	[	[	PUNCT
ejpam-6776	281	6	βλ	βλ	X
ejpam-6776	281	7	δ	δ	PROPN
ejpam-6776	281	8	−	−	PROPN
ejpam-6776	282	1	(	(	PUNCT
ejpam-6776	282	2	δ	δ	PROPN
ejpam-6776	282	3	+	+	CCONJ
ejpam-6776	282	4	γ	γ	X
ejpam-6776	282	5	+	+	X
ejpam-6776	282	6	ϵ+	ϵ+	PUNCT
ejpam-6776	282	7	α	α	X
ejpam-6776	282	8	λ	λ	PROPN
ejpam-6776	282	9	)	)	PUNCT
ejpam-6776	282	10	]	]	PUNCT
ejpam-6776	283	1	+	+	CCONJ
ejpam-6776	283	2	p(p−	p(p−	VERB
ejpam-6776	283	3	1	1	NUM
ejpam-6776	283	4	)	)	PUNCT
ejpam-6776	283	5	2	2	NUM
ejpam-6776	283	6	(	(	PUNCT
ejpam-6776	283	7	σλ	σλ	NOUN
ejpam-6776	283	8	δ	δ	PROPN
ejpam-6776	283	9	)	)	PUNCT
ejpam-6776	283	10	2	2	NUM
ejpam-6776	283	11	x	x	SYM
ejpam-6776	283	12	p−2	p−2	NOUN
ejpam-6776	283	13	2	2	NUM
ejpam-6776	283	14	·	·	PUNCT
ejpam-6776	283	15	x	x	SYM
ejpam-6776	283	16	2	2	NUM
ejpam-6776	283	17	2	2	NUM
ejpam-6776	283	18	.	.	PUNCT
ejpam-6776	283	19	simplify	simplify	VERB
ejpam-6776	283	20	the	the	DET
ejpam-6776	283	21	stochastic	stochastic	ADJ
ejpam-6776	283	22	term	term	NOUN
ejpam-6776	283	23	:	:	PUNCT
ejpam-6776	283	24	p(p−	p(p−	VERB
ejpam-6776	283	25	1	1	NUM
ejpam-6776	283	26	)	)	SYM
ejpam-6776	283	27	2	2	NUM
ejpam-6776	283	28	(	(	PUNCT
ejpam-6776	283	29	σλ	σλ	NOUN
ejpam-6776	283	30	δ	δ	PROPN
ejpam-6776	283	31	)	)	PUNCT
ejpam-6776	283	32	2	2	NUM
ejpam-6776	283	33	x	x	SYM
ejpam-6776	283	34	p−2	p−2	NOUN
ejpam-6776	283	35	2	2	NUM
ejpam-6776	283	36	·	·	PUNCT
ejpam-6776	283	37	x	x	SYM
ejpam-6776	283	38	2	2	NUM
ejpam-6776	283	39	2	2	NUM
ejpam-6776	283	40	=	=	PUNCT
ejpam-6776	283	41	p(p−	p(p−	VERB
ejpam-6776	283	42	1	1	NUM
ejpam-6776	283	43	)	)	PUNCT
ejpam-6776	283	44	2	2	NUM
ejpam-6776	283	45	(	(	PUNCT
ejpam-6776	283	46	σλ	σλ	NOUN
ejpam-6776	283	47	δ	δ	PROPN
ejpam-6776	283	48	)	)	PUNCT
ejpam-6776	283	49	2	2	NUM
ejpam-6776	283	50	x	x	SYM
ejpam-6776	283	51	p	p	NOUN
ejpam-6776	283	52	2	2	NUM
ejpam-6776	283	53	.	.	PUNCT
ejpam-6776	284	1	thus	thus	ADV
ejpam-6776	284	2	:	:	PUNCT
ejpam-6776	284	3	lψ	lψ	PROPN
ejpam-6776	284	4	=	=	PUNCT
ejpam-6776	284	5	−kδx1	−kδx1	PROPN
ejpam-6776	285	1	+	+	CCONJ
ejpam-6776	285	2	k	k	PROPN
ejpam-6776	285	3	βλ	βλ	PROPN
ejpam-6776	285	4	δ	δ	X
ejpam-6776	285	5	x2	x2	PROPN
ejpam-6776	286	1	+	+	CCONJ
ejpam-6776	286	2	[	[	PUNCT
ejpam-6776	286	3	βλ	βλ	X
ejpam-6776	286	4	δ	δ	PROPN
ejpam-6776	286	5	−	−	PROPN
ejpam-6776	286	6	(	(	PUNCT
ejpam-6776	286	7	δ	δ	PROPN
ejpam-6776	286	8	+	+	CCONJ
ejpam-6776	286	9	γ	γ	X
ejpam-6776	286	10	+	+	X
ejpam-6776	286	11	ϵ+	ϵ+	PUNCT
ejpam-6776	286	12	α	α	X
ejpam-6776	286	13	λ	λ	NOUN
ejpam-6776	286	14	)	)	PUNCT
ejpam-6776	287	1	+	+	CCONJ
ejpam-6776	287	2	p(p−	p(p−	VERB
ejpam-6776	287	3	1	1	NUM
ejpam-6776	287	4	)	)	PUNCT
ejpam-6776	287	5	2	2	NUM
ejpam-6776	287	6	(	(	PUNCT
ejpam-6776	287	7	σλ	σλ	NOUN
ejpam-6776	287	8	δ	δ	PROPN
ejpam-6776	287	9	)	)	PUNCT
ejpam-6776	287	10	2	2	NUM
ejpam-6776	287	11	]	]	PUNCT
ejpam-6776	287	12	x	x	SYM
ejpam-6776	287	13	p	p	NOUN
ejpam-6776	287	14	2	2	NUM
ejpam-6776	287	15	.	.	PUNCT
ejpam-6776	288	1	since	since	ADV
ejpam-6776	288	2	:	:	PUNCT
ejpam-6776	288	3	p(p−	p(p−	VERB
ejpam-6776	288	4	1	1	NUM
ejpam-6776	288	5	)	)	SYM
ejpam-6776	288	6	2	2	NUM
ejpam-6776	288	7	=	=	NOUN
ejpam-6776	288	8	p2	p2	NOUN
ejpam-6776	289	1	−	−	PROPN
ejpam-6776	289	2	p	p	NOUN
ejpam-6776	289	3	2	2	NUM
ejpam-6776	289	4	=	=	SYM
ejpam-6776	289	5	p	p	NOUN
ejpam-6776	289	6	2	2	NUM
ejpam-6776	289	7	(	(	PUNCT
ejpam-6776	289	8	p−	p−	NOUN
ejpam-6776	289	9	1	1	NUM
ejpam-6776	289	10	)	)	PUNCT
ejpam-6776	289	11	≤	≤	NOUN
ejpam-6776	289	12	p	p	X
ejpam-6776	289	13	2	2	NUM
ejpam-6776	289	14	·	·	SYM
ejpam-6776	289	15	0	0	NUM
ejpam-6776	290	1	=	=	SYM
ejpam-6776	290	2	0	0	NUM
ejpam-6776	290	3	for	for	ADP
ejpam-6776	290	4	p	p	PROPN
ejpam-6776	290	5	∈	∈	PROPN
ejpam-6776	290	6	(	(	PUNCT
ejpam-6776	290	7	0	0	NUM
ejpam-6776	290	8	,	,	PUNCT
ejpam-6776	290	9	1	1	NUM
ejpam-6776	290	10	)	)	PUNCT
ejpam-6776	290	11	,	,	PUNCT
ejpam-6776	290	12	and	and	CCONJ
ejpam-6776	290	13	noting	note	VERB
ejpam-6776	290	14	that	that	SCONJ
ejpam-6776	290	15	:	:	PUNCT
ejpam-6776	290	16	βλ	βλ	PROPN
ejpam-6776	290	17	δ	δ	PROPN
ejpam-6776	290	18	−	−	PROPN
ejpam-6776	290	19	(	(	PUNCT
ejpam-6776	290	20	δ	δ	PROPN
ejpam-6776	290	21	+	+	CCONJ
ejpam-6776	290	22	γ	γ	X
ejpam-6776	290	23	+	+	X
ejpam-6776	290	24	ϵ+	ϵ+	PUNCT
ejpam-6776	290	25	α	α	X
ejpam-6776	290	26	λ	λ	NOUN
ejpam-6776	290	27	)	)	PUNCT
ejpam-6776	290	28	=	=	PUNCT
ejpam-6776	290	29	η	η	PROPN
ejpam-6776	290	30	+	+	PROPN
ejpam-6776	290	31	1	1	NUM
ejpam-6776	290	32	2	2	NUM
ejpam-6776	290	33	(	(	PUNCT
ejpam-6776	290	34	σλ	σλ	NOUN
ejpam-6776	290	35	δ	δ	PROPN
ejpam-6776	290	36	)	)	PUNCT
ejpam-6776	290	37	2	2	NUM
ejpam-6776	290	38	,	,	PUNCT
ejpam-6776	290	39	we	we	PRON
ejpam-6776	290	40	rewrite	rewrite	VERB
ejpam-6776	290	41	:	:	PUNCT
ejpam-6776	290	42	lψ	lψ	PROPN
ejpam-6776	290	43	=	=	PROPN
ejpam-6776	290	44	−kδx1	−kδx1	PROPN
ejpam-6776	291	1	+	+	CCONJ
ejpam-6776	291	2	k	k	PROPN
ejpam-6776	291	3	βλ	βλ	PROPN
ejpam-6776	291	4	δ	δ	X
ejpam-6776	291	5	x2	x2	PROPN
ejpam-6776	292	1	+	+	CCONJ
ejpam-6776	292	2	[	[	PUNCT
ejpam-6776	292	3	η	η	X
ejpam-6776	292	4	+	+	PROPN
ejpam-6776	292	5	1	1	NUM
ejpam-6776	292	6	2	2	NUM
ejpam-6776	292	7	(	(	PUNCT
ejpam-6776	292	8	σλ	σλ	NOUN
ejpam-6776	292	9	δ	δ	PROPN
ejpam-6776	292	10	)	)	PUNCT
ejpam-6776	292	11	2	2	NUM
ejpam-6776	293	1	+	+	CCONJ
ejpam-6776	293	2	p(p−	p(p−	VERB
ejpam-6776	293	3	1	1	NUM
ejpam-6776	293	4	)	)	PUNCT
ejpam-6776	293	5	2	2	NUM
ejpam-6776	293	6	(	(	PUNCT
ejpam-6776	293	7	σλ	σλ	NOUN
ejpam-6776	293	8	δ	δ	PROPN
ejpam-6776	293	9	)	)	PUNCT
ejpam-6776	293	10	2	2	NUM
ejpam-6776	293	11	]	]	PUNCT
ejpam-6776	293	12	x	x	SYM
ejpam-6776	293	13	p	p	NOUN
ejpam-6776	293	14	2	2	NUM
ejpam-6776	293	15	.	.	PUNCT
ejpam-6776	294	1	j.	j.	PROPN
ejpam-6776	294	2	leo	leo	PROPN
ejpam-6776	294	3	amalraj	amalraj	PROPN
ejpam-6776	294	4	et	et	PROPN
ejpam-6776	294	5	al	al	PROPN
ejpam-6776	294	6	.	.	PUNCT
ejpam-6776	294	7	/	/	SYM
ejpam-6776	294	8	eur	eur	PROPN
ejpam-6776	294	9	.	.	PUNCT
ejpam-6776	295	1	j.	j.	PROPN
ejpam-6776	295	2	pure	pure	PROPN
ejpam-6776	295	3	appl	appl	PROPN
ejpam-6776	295	4	.	.	PROPN
ejpam-6776	295	5	math	math	PROPN
ejpam-6776	295	6	,	,	PUNCT
ejpam-6776	295	7	18	18	NUM
ejpam-6776	295	8	(	(	PUNCT
ejpam-6776	295	9	4	4	NUM
ejpam-6776	295	10	)	)	PUNCT
ejpam-6776	295	11	(	(	PUNCT
ejpam-6776	295	12	2025	2025	NUM
ejpam-6776	295	13	)	)	PUNCT
ejpam-6776	295	14	,	,	PUNCT
ejpam-6776	295	15	6776	6776	NUM
ejpam-6776	295	16	13	13	NUM
ejpam-6776	295	17	of	of	ADP
ejpam-6776	295	18	22	22	NUM
ejpam-6776	295	19	combine	combine	NOUN
ejpam-6776	295	20	terms	term	NOUN
ejpam-6776	295	21	:	:	PUNCT
ejpam-6776	295	22	1	1	NUM
ejpam-6776	295	23	2	2	NUM
ejpam-6776	295	24	(	(	PUNCT
ejpam-6776	295	25	σλ	σλ	NOUN
ejpam-6776	295	26	δ	δ	PROPN
ejpam-6776	295	27	)	)	PUNCT
ejpam-6776	295	28	2	2	NUM
ejpam-6776	296	1	+	+	CCONJ
ejpam-6776	296	2	p(p−	p(p−	VERB
ejpam-6776	296	3	1	1	NUM
ejpam-6776	296	4	)	)	PUNCT
ejpam-6776	296	5	2	2	NUM
ejpam-6776	296	6	(	(	PUNCT
ejpam-6776	296	7	σλ	σλ	NOUN
ejpam-6776	296	8	δ	δ	PROPN
ejpam-6776	296	9	)	)	PUNCT
ejpam-6776	296	10	2	2	NUM
ejpam-6776	296	11	=	=	SYM
ejpam-6776	296	12	1	1	NUM
ejpam-6776	296	13	2	2	NUM
ejpam-6776	296	14	(	(	PUNCT
ejpam-6776	296	15	σλ	σλ	NOUN
ejpam-6776	296	16	δ	δ	PROPN
ejpam-6776	296	17	)	)	PUNCT
ejpam-6776	296	18	2	2	NUM
ejpam-6776	297	1	[	[	SYM
ejpam-6776	297	2	1	1	NUM
ejpam-6776	297	3	+	+	CCONJ
ejpam-6776	297	4	p(p−	p(p−	VERB
ejpam-6776	297	5	1	1	NUM
ejpam-6776	297	6	)	)	PUNCT
ejpam-6776	297	7	]	]	PUNCT
ejpam-6776	298	1	=	=	SYM
ejpam-6776	298	2	1	1	NUM
ejpam-6776	298	3	2	2	NUM
ejpam-6776	298	4	(	(	PUNCT
ejpam-6776	298	5	σλ	σλ	NOUN
ejpam-6776	298	6	δ	δ	PROPN
ejpam-6776	298	7	)	)	PUNCT
ejpam-6776	298	8	2	2	NUM
ejpam-6776	299	1	p.	p.	NOUN
ejpam-6776	300	1	thus	thus	ADV
ejpam-6776	300	2	:	:	PUNCT
ejpam-6776	300	3	lψ	lψ	PROPN
ejpam-6776	300	4	=	=	PUNCT
ejpam-6776	300	5	−kδx1	−kδx1	PROPN
ejpam-6776	301	1	+	+	CCONJ
ejpam-6776	301	2	k	k	PROPN
ejpam-6776	301	3	βλ	βλ	PROPN
ejpam-6776	301	4	δ	δ	X
ejpam-6776	301	5	x2	x2	PROPN
ejpam-6776	302	1	+	+	CCONJ
ejpam-6776	302	2	[	[	PUNCT
ejpam-6776	302	3	η	η	X
ejpam-6776	302	4	+	+	PROPN
ejpam-6776	302	5	1	1	NUM
ejpam-6776	302	6	2	2	NUM
ejpam-6776	302	7	p	p	NOUN
ejpam-6776	302	8	(	(	PUNCT
ejpam-6776	302	9	σλ	σλ	NOUN
ejpam-6776	302	10	δ	δ	PROPN
ejpam-6776	302	11	)	)	PUNCT
ejpam-6776	302	12	2	2	NUM
ejpam-6776	302	13	]	]	PUNCT
ejpam-6776	302	14	x	x	SYM
ejpam-6776	302	15	p	p	NOUN
ejpam-6776	302	16	2	2	NUM
ejpam-6776	302	17	.	.	PUNCT
ejpam-6776	303	1	(	(	PUNCT
ejpam-6776	303	2	7	7	NUM
ejpam-6776	303	3	)	)	PUNCT
ejpam-6776	303	4	since	since	SCONJ
ejpam-6776	303	5	η	η	PROPN
ejpam-6776	303	6	<	<	X
ejpam-6776	303	7	0	0	NUM
ejpam-6776	303	8	by	by	ADP
ejpam-6776	303	9	(	(	PUNCT
ejpam-6776	303	10	4	4	NUM
ejpam-6776	303	11	)	)	PUNCT
ejpam-6776	303	12	,	,	PUNCT
ejpam-6776	303	13	select	select	VERB
ejpam-6776	303	14	p	p	PROPN
ejpam-6776	303	15	∈	∈	PROPN
ejpam-6776	303	16	(	(	PUNCT
ejpam-6776	303	17	0	0	NUM
ejpam-6776	303	18	,	,	PUNCT
ejpam-6776	303	19	1	1	NUM
ejpam-6776	303	20	)	)	PUNCT
ejpam-6776	303	21	such	such	ADJ
ejpam-6776	303	22	that	that	SCONJ
ejpam-6776	303	23	:	:	PUNCT
ejpam-6776	303	24	η	η	PROPN
ejpam-6776	303	25	+	+	PROPN
ejpam-6776	303	26	1	1	NUM
ejpam-6776	303	27	2	2	NUM
ejpam-6776	303	28	p	p	NOUN
ejpam-6776	303	29	(	(	PUNCT
ejpam-6776	303	30	σλ	σλ	NOUN
ejpam-6776	303	31	δ	δ	PROPN
ejpam-6776	303	32	)	)	PUNCT
ejpam-6776	303	33	2	2	NUM
ejpam-6776	303	34	<	<	X
ejpam-6776	303	35	0	0	NUM
ejpam-6776	303	36	.	.	PUNCT
ejpam-6776	304	1	this	this	PRON
ejpam-6776	304	2	is	be	AUX
ejpam-6776	304	3	feasible	feasible	ADJ
ejpam-6776	304	4	,	,	PUNCT
ejpam-6776	304	5	as	as	ADP
ejpam-6776	304	6	choosing	choose	VERB
ejpam-6776	304	7	p	p	NOUN
ejpam-6776	304	8	small	small	ADJ
ejpam-6776	304	9	ensures	ensure	NOUN
ejpam-6776	304	10	the	the	DET
ejpam-6776	304	11	positive	positive	ADJ
ejpam-6776	304	12	term	term	NOUN
ejpam-6776	304	13	1	1	NUM
ejpam-6776	304	14	2p	2p	NUM
ejpam-6776	304	15	(	(	PUNCT
ejpam-6776	304	16	σλ	σλ	NOUN
ejpam-6776	304	17	δ	δ	PROPN
ejpam-6776	304	18	)	)	PUNCT
ejpam-6776	304	19	2	2	NUM
ejpam-6776	304	20	does	do	AUX
ejpam-6776	304	21	not	not	PART
ejpam-6776	304	22	dominate	dominate	VERB
ejpam-6776	304	23	η	η	PROPN
ejpam-6776	304	24	.	.	PROPN
ejpam-6776	304	25	next	next	ADV
ejpam-6776	304	26	,	,	PUNCT
ejpam-6776	304	27	choose	choose	VERB
ejpam-6776	304	28	k	k	PROPN
ejpam-6776	304	29	>	>	X
ejpam-6776	304	30	0	0	PUNCT
ejpam-6776	304	31	to	to	PART
ejpam-6776	304	32	satisfy	satisfy	VERB
ejpam-6776	304	33	:	:	PUNCT
ejpam-6776	304	34	η	η	PROPN
ejpam-6776	304	35	+	+	PROPN
ejpam-6776	304	36	1	1	NUM
ejpam-6776	304	37	2	2	NUM
ejpam-6776	304	38	p	p	NOUN
ejpam-6776	304	39	(	(	PUNCT
ejpam-6776	304	40	σλ	σλ	NOUN
ejpam-6776	304	41	δ	δ	PROPN
ejpam-6776	304	42	)	)	PUNCT
ejpam-6776	304	43	2	2	PROPN
ejpam-6776	305	1	+	+	CCONJ
ejpam-6776	305	2	k	k	PROPN
ejpam-6776	305	3	βλ	βλ	PROPN
ejpam-6776	305	4	δ	δ	PROPN
ejpam-6776	305	5	<	<	X
ejpam-6776	305	6	0	0	NUM
ejpam-6776	305	7	.	.	PUNCT
ejpam-6776	306	1	(	(	PUNCT
ejpam-6776	306	2	8)	8)	NUM
ejpam-6776	306	3	for	for	ADP
ejpam-6776	306	4	small	small	ADJ
ejpam-6776	306	5	x2	x2	PROPN
ejpam-6776	306	6	,	,	PUNCT
ejpam-6776	306	7	since	since	SCONJ
ejpam-6776	306	8	p	p	X
ejpam-6776	306	9	<	<	X
ejpam-6776	306	10	1	1	NUM
ejpam-6776	306	11	,	,	PUNCT
ejpam-6776	306	12	x	x	PUNCT
ejpam-6776	306	13	p	p	NOUN
ejpam-6776	306	14	2	2	NUM
ejpam-6776	306	15	>	>	X
ejpam-6776	306	16	x2	x2	PROPN
ejpam-6776	306	17	,	,	PUNCT
ejpam-6776	306	18	so	so	ADV
ejpam-6776	306	19	:	:	PUNCT
ejpam-6776	306	20	k	k	PROPN
ejpam-6776	306	21	βλ	βλ	PROPN
ejpam-6776	306	22	δ	δ	X
ejpam-6776	306	23	x2	x2	ADJ
ejpam-6776	306	24	≤	≤	PROPN
ejpam-6776	307	1	[	[	PUNCT
ejpam-6776	307	2	k	k	X
ejpam-6776	307	3	βλ	βλ	PROPN
ejpam-6776	307	4	δ	δ	PROPN
ejpam-6776	307	5	]	]	PUNCT
ejpam-6776	307	6	x	x	PUNCT
ejpam-6776	307	7	p	p	X
ejpam-6776	307	8	2	2	NUM
ejpam-6776	307	9	.	.	PUNCT
ejpam-6776	308	1	thus	thus	ADV
ejpam-6776	308	2	:	:	PUNCT
ejpam-6776	308	3	lψ	lψ	ADJ
ejpam-6776	308	4	≤	≤	PROPN
ejpam-6776	308	5	−kδx1	−kδx1	PROPN
ejpam-6776	309	1	+	+	CCONJ
ejpam-6776	309	2	[	[	PUNCT
ejpam-6776	309	3	η	η	X
ejpam-6776	309	4	+	+	PROPN
ejpam-6776	309	5	1	1	NUM
ejpam-6776	309	6	2	2	NUM
ejpam-6776	309	7	p	p	NOUN
ejpam-6776	309	8	(	(	PUNCT
ejpam-6776	309	9	σλ	σλ	NOUN
ejpam-6776	309	10	δ	δ	PROPN
ejpam-6776	309	11	)	)	PUNCT
ejpam-6776	309	12	2	2	PROPN
ejpam-6776	310	1	+	+	CCONJ
ejpam-6776	310	2	k	k	PROPN
ejpam-6776	310	3	βλ	βλ	PROPN
ejpam-6776	310	4	δ	δ	PROPN
ejpam-6776	310	5	]	]	PUNCT
ejpam-6776	311	1	x	x	PUNCT
ejpam-6776	311	2	p	p	NOUN
ejpam-6776	311	3	2	2	NUM
ejpam-6776	311	4	.	.	PUNCT
ejpam-6776	312	1	by	by	ADP
ejpam-6776	312	2	(	(	PUNCT
ejpam-6776	312	3	8)	8)	NUM
ejpam-6776	312	4	,	,	PUNCT
ejpam-6776	312	5	the	the	DET
ejpam-6776	312	6	coefficient	coefficient	NOUN
ejpam-6776	312	7	of	of	ADP
ejpam-6776	312	8	x	x	PUNCT
ejpam-6776	312	9	p	p	DET
ejpam-6776	312	10	2	2	NUM
ejpam-6776	312	11	is	be	AUX
ejpam-6776	312	12	negative	negative	ADJ
ejpam-6776	312	13	,	,	PUNCT
ejpam-6776	312	14	and	and	CCONJ
ejpam-6776	312	15	since	since	SCONJ
ejpam-6776	312	16	x1	x1	PROPN
ejpam-6776	312	17	≥	≥	NOUN
ejpam-6776	312	18	0	0	NUM
ejpam-6776	312	19	in	in	ADP
ejpam-6776	312	20	a	a	PRON
ejpam-6776	312	21	,	,	PUNCT
ejpam-6776	312	22	we	we	PRON
ejpam-6776	312	23	have	have	VERB
ejpam-6776	312	24	:	:	PUNCT
ejpam-6776	312	25	lψ	lψ	ADJ
ejpam-6776	312	26	≤	≤	NUM
ejpam-6776	312	27	0	0	NUM
ejpam-6776	312	28	.	.	PUNCT
ejpam-6776	313	1	per	per	ADP
ejpam-6776	313	2	[	[	X
ejpam-6776	313	3	39	39	NUM
ejpam-6776	313	4	]	]	PUNCT
ejpam-6776	313	5	,	,	PUNCT
ejpam-6776	313	6	this	this	PRON
ejpam-6776	313	7	implies	imply	VERB
ejpam-6776	313	8	stochastic	stochastic	ADJ
ejpam-6776	313	9	stability	stability	NOUN
ejpam-6776	313	10	of	of	ADP
ejpam-6776	313	11	the	the	DET
ejpam-6776	313	12	origin	origin	NOUN
ejpam-6776	313	13	(	(	PUNCT
ejpam-6776	313	14	0	0	NUM
ejpam-6776	313	15	,	,	PUNCT
ejpam-6776	313	16	0	0	NUM
ejpam-6776	313	17	)	)	PUNCT
ejpam-6776	313	18	for	for	ADP
ejpam-6776	313	19	(	(	PUNCT
ejpam-6776	313	20	5	5	NUM
ejpam-6776	313	21	)	)	PUNCT
ejpam-6776	313	22	.	.	PUNCT
ejpam-6776	314	1	hence	hence	ADV
ejpam-6776	314	2	,	,	PUNCT
ejpam-6776	314	3	for	for	ADP
ejpam-6776	314	4	any	any	DET
ejpam-6776	314	5	ε	ε	PROPN
ejpam-6776	314	6	>	>	X
ejpam-6776	314	7	0	0	PUNCT
ejpam-6776	314	8	and	and	CCONJ
ejpam-6776	314	9	r	r	X
ejpam-6776	314	10	>	>	X
ejpam-6776	314	11	0	0	NUM
ejpam-6776	314	12	,	,	PUNCT
ejpam-6776	314	13	there	there	PRON
ejpam-6776	314	14	exists	exist	VERB
ejpam-6776	314	15	d	d	X
ejpam-6776	314	16	>	>	X
ejpam-6776	314	17	0	0	NUM
ejpam-6776	314	18	such	such	ADJ
ejpam-6776	314	19	that	that	SCONJ
ejpam-6776	314	20	:	:	PUNCT
ejpam-6776	315	1	p	p	X
ejpam-6776	315	2	(	(	PUNCT
ejpam-6776	315	3	sup	sup	NOUN
ejpam-6776	315	4	t≥0	t≥0	NOUN
ejpam-6776	316	1	∥x	∥x	PROPN
ejpam-6776	316	2	x0(t)−	x0(t)−	PROPN
ejpam-6776	316	3	e0∥	e0∥	PROPN
ejpam-6776	316	4	<	<	X
ejpam-6776	316	5	r	r	NOUN
ejpam-6776	316	6	)	)	PUNCT
ejpam-6776	316	7	≥	≥	NOUN
ejpam-6776	316	8	1−	1−	NUM
ejpam-6776	316	9	ε	ε	PROPN
ejpam-6776	316	10	,	,	PUNCT
ejpam-6776	316	11	∀x0	∀x0	PROPN
ejpam-6776	316	12	∈	∈	PROPN
ejpam-6776	316	13	b̃d	b̃d	PROPN
ejpam-6776	316	14	,	,	PUNCT
ejpam-6776	316	15	(	(	PUNCT
ejpam-6776	316	16	9	9	NUM
ejpam-6776	316	17	)	)	PUNCT
ejpam-6776	317	1	where	where	SCONJ
ejpam-6776	317	2	:	:	PUNCT
ejpam-6776	317	3	b̃d	b̃d	PROPN
ejpam-6776	317	4	=	=	PRON
ejpam-6776	317	5	{	{	PUNCT
ejpam-6776	317	6	x	x	PUNCT
ejpam-6776	317	7	∈	∈	PROPN
ejpam-6776	317	8	a	a	PRON
ejpam-6776	317	9	:	:	PUNCT
ejpam-6776	317	10	∥x−	∥x−	PROPN
ejpam-6776	317	11	e0∥	e0∥	PROPN
ejpam-6776	317	12	≤	≤	PROPN
ejpam-6776	317	13	d	d	NOUN
ejpam-6776	317	14	}	}	PUNCT
ejpam-6776	317	15	.	.	PUNCT
ejpam-6776	318	1	to	to	PART
ejpam-6776	318	2	extend	extend	VERB
ejpam-6776	318	3	stability	stability	NOUN
ejpam-6776	318	4	to	to	ADP
ejpam-6776	318	5	global	global	ADJ
ejpam-6776	318	6	convergence	convergence	NOUN
ejpam-6776	318	7	,	,	PUNCT
ejpam-6776	318	8	consider	consider	VERB
ejpam-6776	318	9	any	any	DET
ejpam-6776	318	10	x	x	SYM
ejpam-6776	318	11	∈	∈	NOUN
ejpam-6776	318	12	a.	a.	NOUN
ejpam-6776	318	13	by	by	ADP
ejpam-6776	318	14	prior	prior	ADJ
ejpam-6776	318	15	results	result	NOUN
ejpam-6776	318	16	on	on	ADP
ejpam-6776	318	17	connectivity	connectivity	NOUN
ejpam-6776	318	18	(	(	PUNCT
ejpam-6776	318	19	cf	cf	NOUN
ejpam-6776	318	20	.	.	PUNCT
ejpam-6776	318	21	theorem	theorem	VERB
ejpam-6776	318	22	2.2	2.2	NUM
ejpam-6776	318	23	in	in	ADP
ejpam-6776	318	24	earlier	early	ADJ
ejpam-6776	318	25	sections	section	NOUN
ejpam-6776	318	26	)	)	PUNCT
ejpam-6776	318	27	,	,	PUNCT
ejpam-6776	318	28	there	there	PRON
ejpam-6776	318	29	exists	exist	VERB
ejpam-6776	318	30	tx	tx	PROPN
ejpam-6776	318	31	>	>	X
ejpam-6776	318	32	0	0	NUM
ejpam-6776	319	1	such	such	ADJ
ejpam-6776	319	2	that	that	SCONJ
ejpam-6776	319	3	:	:	PUNCT
ejpam-6776	319	4	p	p	X
ejpam-6776	319	5	(	(	PUNCT
ejpam-6776	319	6	tx	tx	PROPN
ejpam-6776	319	7	,	,	PUNCT
ejpam-6776	319	8	x	x	NOUN
ejpam-6776	319	9	,	,	PUNCT
ejpam-6776	319	10	b̃d	b̃d	NUM
ejpam-6776	319	11	)	)	PUNCT
ejpam-6776	319	12	≥	≥	NOUN
ejpam-6776	319	13	px	px	X
ejpam-6776	319	14	>	>	X
ejpam-6776	319	15	0	0	NUM
ejpam-6776	319	16	.	.	PUNCT
ejpam-6776	319	17	(	(	PUNCT
ejpam-6776	319	18	10	10	NUM
ejpam-6776	319	19	)	)	PUNCT
ejpam-6776	319	20	j.	j.	PROPN
ejpam-6776	319	21	leo	leo	PROPN
ejpam-6776	319	22	amalraj	amalraj	PROPN
ejpam-6776	319	23	et	et	PROPN
ejpam-6776	319	24	al	al	PROPN
ejpam-6776	319	25	.	.	PUNCT
ejpam-6776	319	26	/	/	SYM
ejpam-6776	319	27	eur	eur	PROPN
ejpam-6776	319	28	.	.	PUNCT
ejpam-6776	320	1	j.	j.	PROPN
ejpam-6776	320	2	pure	pure	PROPN
ejpam-6776	320	3	appl	appl	PROPN
ejpam-6776	320	4	.	.	PROPN
ejpam-6776	320	5	math	math	PROPN
ejpam-6776	320	6	,	,	PUNCT
ejpam-6776	320	7	18	18	NUM
ejpam-6776	320	8	(	(	PUNCT
ejpam-6776	320	9	4	4	NUM
ejpam-6776	320	10	)	)	PUNCT
ejpam-6776	320	11	(	(	PUNCT
ejpam-6776	320	12	2025	2025	NUM
ejpam-6776	320	13	)	)	PUNCT
ejpam-6776	320	14	,	,	PUNCT
ejpam-6776	320	15	6776	6776	NUM
ejpam-6776	320	16	14	14	NUM
ejpam-6776	320	17	of	of	ADP
ejpam-6776	320	18	22	22	NUM
ejpam-6776	320	19	the	the	DET
ejpam-6776	320	20	process	process	NOUN
ejpam-6776	320	21	x	x	SYM
ejpam-6776	320	22	(	(	PUNCT
ejpam-6776	320	23	t	t	NOUN
ejpam-6776	320	24	)	)	PUNCT
ejpam-6776	320	25	possesses	possess	VERB
ejpam-6776	320	26	the	the	DET
ejpam-6776	320	27	feller	feller	NOUN
ejpam-6776	320	28	property	property	NOUN
ejpam-6776	320	29	,	,	PUNCT
ejpam-6776	320	30	as	as	SCONJ
ejpam-6776	320	31	established	establish	VERB
ejpam-6776	320	32	by	by	ADP
ejpam-6776	320	33	the	the	DET
ejpam-6776	320	34	smoothness	smoothness	NOUN
ejpam-6776	320	35	of	of	ADP
ejpam-6776	320	36	its	its	PRON
ejpam-6776	320	37	transition	transition	NOUN
ejpam-6776	320	38	density	density	NOUN
ejpam-6776	320	39	(	(	PUNCT
ejpam-6776	320	40	cf	cf	NOUN
ejpam-6776	320	41	.	.	PUNCT
ejpam-6776	321	1	proposition	proposition	NOUN
ejpam-6776	321	2	3	3	NUM
ejpam-6776	321	3	)	)	PUNCT
ejpam-6776	321	4	.	.	PUNCT
ejpam-6776	322	1	thus	thus	ADV
ejpam-6776	322	2	,	,	PUNCT
ejpam-6776	322	3	there	there	PRON
ejpam-6776	322	4	exists	exist	VERB
ejpam-6776	322	5	an	an	DET
ejpam-6776	322	6	open	open	ADJ
ejpam-6776	322	7	neighborhood	neighborhood	NOUN
ejpam-6776	322	8	vx	vx	X
ejpam-6776	322	9	⊂	⊂	PROPN
ejpam-6776	322	10	a	a	PRON
ejpam-6776	322	11	of	of	ADP
ejpam-6776	322	12	x	x	SYM
ejpam-6776	322	13	such	such	ADJ
ejpam-6776	322	14	that	that	SCONJ
ejpam-6776	322	15	:	:	PUNCT
ejpam-6776	322	16	p	p	X
ejpam-6776	322	17	(	(	PUNCT
ejpam-6776	322	18	tx	tx	PROPN
ejpam-6776	322	19	,	,	PUNCT
ejpam-6776	322	20	y	y	PROPN
ejpam-6776	322	21	,	,	PUNCT
ejpam-6776	322	22	b̃d	b̃d	NUM
ejpam-6776	322	23	)	)	PUNCT
ejpam-6776	322	24	≥	≥	NOUN
ejpam-6776	322	25	px	px	X
ejpam-6776	322	26	>	>	X
ejpam-6776	322	27	0	0	NUM
ejpam-6776	322	28	,	,	PUNCT
ejpam-6776	322	29	∀y	∀y	PROPN
ejpam-6776	322	30	∈	∈	PROPN
ejpam-6776	322	31	vx	vx	PROPN
ejpam-6776	322	32	.	.	PROPN
ejpam-6776	322	33	(	(	PUNCT
ejpam-6776	322	34	11	11	NUM
ejpam-6776	322	35	)	)	PUNCT
ejpam-6776	322	36	since	since	SCONJ
ejpam-6776	322	37	a	a	PRON
ejpam-6776	322	38	is	be	AUX
ejpam-6776	322	39	compact	compact	ADJ
ejpam-6776	322	40	,	,	PUNCT
ejpam-6776	322	41	there	there	PRON
ejpam-6776	322	42	exists	exist	VERB
ejpam-6776	322	43	a	a	DET
ejpam-6776	322	44	finite	finite	ADJ
ejpam-6776	322	45	cover	cover	NOUN
ejpam-6776	322	46	:	:	PUNCT
ejpam-6776	322	47	a	a	DET
ejpam-6776	322	48	⊂	⊂	PROPN
ejpam-6776	322	49	m⋃	m⋃	NOUN
ejpam-6776	323	1	i=1	i=1	PROPN
ejpam-6776	323	2	vxi	vxi	INTJ
ejpam-6776	323	3	,	,	PUNCT
ejpam-6776	323	4	(	(	PUNCT
ejpam-6776	323	5	12	12	NUM
ejpam-6776	323	6	)	)	PUNCT
ejpam-6776	323	7	for	for	ADP
ejpam-6776	323	8	some	some	PRON
ejpam-6776	323	9	xi	xi	ADP
ejpam-6776	323	10	∈	∈	PROPN
ejpam-6776	324	1	a	a	PRON
ejpam-6776	324	2	,	,	PUNCT
ejpam-6776	324	3	i	i	NOUN
ejpam-6776	324	4	=	=	NOUN
ejpam-6776	324	5	1	1	NUM
ejpam-6776	324	6	,	,	PUNCT
ejpam-6776	324	7	.	.	PUNCT
ejpam-6776	324	8	.	.	PUNCT
ejpam-6776	324	9	.	.	PUNCT
ejpam-6776	325	1	,	,	PUNCT
ejpam-6776	325	2	m.	m.	NOUN
ejpam-6776	325	3	define	define	NOUN
ejpam-6776	325	4	:	:	PUNCT
ejpam-6776	325	5	t	t	NOUN
ejpam-6776	325	6	∗	∗	NOUN
ejpam-6776	325	7	=	=	SYM
ejpam-6776	325	8	max	max	PROPN
ejpam-6776	325	9	1≤i≤m	1≤i≤m	NUM
ejpam-6776	325	10	txi	txi	NOUN
ejpam-6776	325	11	,	,	PUNCT
ejpam-6776	325	12	p∗	p∗	PROPN
ejpam-6776	325	13	=	=	SYM
ejpam-6776	325	14	min	min	PROPN
ejpam-6776	325	15	1≤i≤m	1≤i≤m	NUM
ejpam-6776	325	16	pxi	pxi	NOUN
ejpam-6776	325	17	.	.	PUNCT
ejpam-6776	326	1	for	for	ADP
ejpam-6776	326	2	any	any	DET
ejpam-6776	326	3	initial	initial	ADJ
ejpam-6776	326	4	condition	condition	NOUN
ejpam-6776	326	5	x0	x0	PROPN
ejpam-6776	326	6	∈	∈	PROPN
ejpam-6776	326	7	a	a	DET
ejpam-6776	326	8	,	,	PUNCT
ejpam-6776	326	9	combining	combine	VERB
ejpam-6776	326	10	(	(	PUNCT
ejpam-6776	326	11	11	11	NUM
ejpam-6776	326	12	)	)	PUNCT
ejpam-6776	326	13	and	and	CCONJ
ejpam-6776	326	14	(	(	PUNCT
ejpam-6776	326	15	12	12	NUM
ejpam-6776	326	16	):	):	PUNCT
ejpam-6776	326	17	p	p	X
ejpam-6776	326	18	(	(	PUNCT
ejpam-6776	326	19	t	t	NOUN
ejpam-6776	326	20	∗	∗	NOUN
ejpam-6776	326	21	,	,	PUNCT
ejpam-6776	326	22	x0	x0	PROPN
ejpam-6776	326	23	,	,	PUNCT
ejpam-6776	326	24	b̃d	b̃d	NUM
ejpam-6776	326	25	)	)	PUNCT
ejpam-6776	326	26	≥	≥	PRON
ejpam-6776	326	27	p∗	p∗	VERB
ejpam-6776	326	28	>	>	X
ejpam-6776	326	29	0	0	NUM
ejpam-6776	326	30	.	.	PUNCT
ejpam-6776	327	1	(	(	PUNCT
ejpam-6776	327	2	13	13	NUM
ejpam-6776	327	3	)	)	PUNCT
ejpam-6776	327	4	introduce	introduce	VERB
ejpam-6776	327	5	the	the	DET
ejpam-6776	327	6	stopping	stopping	NOUN
ejpam-6776	327	7	time	time	NOUN
ejpam-6776	327	8	:	:	PUNCT
ejpam-6776	327	9	τx0	τx0	NOUN
ejpam-6776	327	10	=	=	SYM
ejpam-6776	327	11	inf	inf	PROPN
ejpam-6776	327	12	{	{	PUNCT
ejpam-6776	327	13	t	t	PROPN
ejpam-6776	327	14	≥	≥	NOUN
ejpam-6776	327	15	0	0	NUM
ejpam-6776	327	16	:	:	PUNCT
ejpam-6776	327	17	x	x	X
ejpam-6776	327	18	x0(t	x0(t	PROPN
ejpam-6776	327	19	)	)	PUNCT
ejpam-6776	327	20	∈	∈	PROPN
ejpam-6776	327	21	b̃d	b̃d	PROPN
ejpam-6776	327	22	}	}	PUNCT
ejpam-6776	327	23	.	.	PUNCT
ejpam-6776	328	1	define	define	VERB
ejpam-6776	328	2	a	a	DET
ejpam-6776	328	3	sequence	sequence	NOUN
ejpam-6776	328	4	of	of	ADP
ejpam-6776	328	5	times	time	NOUN
ejpam-6776	328	6	:	:	PUNCT
ejpam-6776	328	7	νx0	νx0	NOUN
ejpam-6776	328	8	n	n	NOUN
ejpam-6776	328	9	=	=	PUNCT
ejpam-6776	328	10	inf	inf	PROPN
ejpam-6776	328	11	{	{	PUNCT
ejpam-6776	328	12	t	t	PROPN
ejpam-6776	328	13	∈	∈	PROPN
ejpam-6776	329	1	[	[	X
ejpam-6776	329	2	(	(	PUNCT
ejpam-6776	329	3	n−	n−	NOUN
ejpam-6776	329	4	1)t	1)t	PROPN
ejpam-6776	329	5	∗	∗	NOUN
ejpam-6776	329	6	,	,	PUNCT
ejpam-6776	329	7	nt	not	PART
ejpam-6776	329	8	∗	∗	NOUN
ejpam-6776	329	9	]	]	PUNCT
ejpam-6776	329	10	:	:	PUNCT
ejpam-6776	329	11	x	x	X
ejpam-6776	329	12	x0(t	x0(t	PROPN
ejpam-6776	329	13	)	)	PUNCT
ejpam-6776	329	14	∈	∈	PROPN
ejpam-6776	329	15	b̃d	b̃d	PROPN
ejpam-6776	329	16	}	}	PUNCT
ejpam-6776	329	17	,	,	PUNCT
ejpam-6776	329	18	with	with	ADP
ejpam-6776	329	19	the	the	DET
ejpam-6776	329	20	convention	convention	NOUN
ejpam-6776	329	21	inf	inf	NOUN
ejpam-6776	329	22	∅	∅	NOUN
ejpam-6776	329	23	=	=	PUNCT
ejpam-6776	329	24	∞.	∞.	PROPN
ejpam-6776	329	25	the	the	DET
ejpam-6776	329	26	probability	probability	NOUN
ejpam-6776	329	27	that	that	SCONJ
ejpam-6776	329	28	the	the	DET
ejpam-6776	329	29	process	process	NOUN
ejpam-6776	329	30	never	never	ADV
ejpam-6776	329	31	enters	enter	VERB
ejpam-6776	329	32	b̃d	b̃d	PROPN
ejpam-6776	329	33	is	be	AUX
ejpam-6776	329	34	:	:	PUNCT
ejpam-6776	329	35	p	p	X
ejpam-6776	329	36	(	(	PUNCT
ejpam-6776	329	37	τx0	τx0	PROPN
ejpam-6776	329	38	=	=	SYM
ejpam-6776	329	39	∞	∞	NUM
ejpam-6776	329	40	)	)	PUNCT
ejpam-6776	330	1	=	=	SYM
ejpam-6776	330	2	p	p	NOUN
ejpam-6776	330	3	(	(	PUNCT
ejpam-6776	330	4	νx0	νx0	NOUN
ejpam-6776	330	5	n	n	NOUN
ejpam-6776	330	6	=	=	SYM
ejpam-6776	330	7	∞	∞	PROPN
ejpam-6776	330	8	,	,	PUNCT
ejpam-6776	330	9	∀n	∀n	NUM
ejpam-6776	330	10	≥	≥	NOUN
ejpam-6776	330	11	1	1	NUM
ejpam-6776	330	12	)	)	PUNCT
ejpam-6776	331	1	=	=	SYM
ejpam-6776	331	2	lim	lim	PROPN
ejpam-6776	331	3	k→∞	k→∞	PROPN
ejpam-6776	332	1	p	p	PROPN
ejpam-6776	332	2	(	(	PUNCT
ejpam-6776	332	3	k⋂	k⋂	NOUN
ejpam-6776	332	4	n=1	n=1	PROPN
ejpam-6776	332	5	νx0	νx0	NOUN
ejpam-6776	332	6	n	n	NOUN
ejpam-6776	332	7	=	=	SYM
ejpam-6776	332	8	∞	∞	NUM
ejpam-6776	332	9	)	)	PUNCT
ejpam-6776	332	10	.	.	PUNCT
ejpam-6776	333	1	compute	compute	NOUN
ejpam-6776	333	2	:	:	PUNCT
ejpam-6776	334	1	p	p	X
ejpam-6776	334	2	(	(	PUNCT
ejpam-6776	334	3	k⋂	k⋂	NOUN
ejpam-6776	334	4	n=1	n=1	PROPN
ejpam-6776	334	5	νx0	νx0	NOUN
ejpam-6776	334	6	n	n	NOUN
ejpam-6776	334	7	=	=	SYM
ejpam-6776	334	8	∞	∞	NUM
ejpam-6776	334	9	)	)	PUNCT
ejpam-6776	335	1	=	=	SYM
ejpam-6776	336	1	p	p	NOUN
ejpam-6776	336	2	(	(	PUNCT
ejpam-6776	336	3	νx0	νx0	NOUN
ejpam-6776	336	4	1	1	NUM
ejpam-6776	336	5	=	=	SYM
ejpam-6776	336	6	∞	∞	NUM
ejpam-6776	336	7	)	)	PUNCT
ejpam-6776	336	8	k∏	k∏	PROPN
ejpam-6776	336	9	n=2	n=2	PRON
ejpam-6776	336	10	p	p	NOUN
ejpam-6776	336	11	(	(	PUNCT
ejpam-6776	336	12	νx0	νx0	NOUN
ejpam-6776	336	13	n	n	NOUN
ejpam-6776	336	14	=	=	SYM
ejpam-6776	336	15	∞	∞	NUM
ejpam-6776	336	16	|	|	ADV
ejpam-6776	336	17	νx0	νx0	NOUN
ejpam-6776	336	18	n−1	n−1	PROPN
ejpam-6776	336	19	=	=	SYM
ejpam-6776	336	20	∞	∞	PROPN
ejpam-6776	336	21	)	)	PUNCT
ejpam-6776	336	22	.	.	PUNCT
ejpam-6776	337	1	(	(	PUNCT
ejpam-6776	337	2	14	14	NUM
ejpam-6776	337	3	)	)	PUNCT
ejpam-6776	337	4	from	from	ADP
ejpam-6776	337	5	(	(	PUNCT
ejpam-6776	337	6	13	13	NUM
ejpam-6776	337	7	):	):	PUNCT
ejpam-6776	337	8	p	p	X
ejpam-6776	337	9	(	(	PUNCT
ejpam-6776	337	10	νx0	νx0	NOUN
ejpam-6776	337	11	1	1	NUM
ejpam-6776	337	12	=	=	SYM
ejpam-6776	337	13	∞	∞	NUM
ejpam-6776	337	14	)	)	PUNCT
ejpam-6776	338	1	=	=	SYM
ejpam-6776	338	2	p	p	X
ejpam-6776	338	3	(	(	PUNCT
ejpam-6776	338	4	x	x	PROPN
ejpam-6776	338	5	x0(t	x0(t	PROPN
ejpam-6776	338	6	)	)	PUNCT
ejpam-6776	338	7	/∈	/∈	PUNCT
ejpam-6776	339	1	b̃d	b̃d	PROPN
ejpam-6776	339	2	,	,	PUNCT
ejpam-6776	339	3	∀t	∀t	PROPN
ejpam-6776	339	4	∈	∈	PROPN
ejpam-6776	340	1	[	[	X
ejpam-6776	340	2	0	0	NUM
ejpam-6776	340	3	,	,	PUNCT
ejpam-6776	340	4	t	t	PROPN
ejpam-6776	340	5	∗	∗	NOUN
ejpam-6776	340	6	]	]	PUNCT
ejpam-6776	340	7	)	)	PUNCT
ejpam-6776	340	8	≤	≤	NOUN
ejpam-6776	340	9	1−	1−	NUM
ejpam-6776	340	10	p∗.	p∗.	NOUN
ejpam-6776	340	11	for	for	ADP
ejpam-6776	340	12	n	n	PRON
ejpam-6776	340	13	≥	≥	NUM
ejpam-6776	340	14	2	2	NUM
ejpam-6776	340	15	,	,	PUNCT
ejpam-6776	340	16	by	by	ADP
ejpam-6776	340	17	the	the	DET
ejpam-6776	340	18	markov	markov	NOUN
ejpam-6776	340	19	property	property	NOUN
ejpam-6776	340	20	:	:	PUNCT
ejpam-6776	341	1	p	p	X
ejpam-6776	341	2	(	(	PUNCT
ejpam-6776	341	3	νx0	νx0	NOUN
ejpam-6776	341	4	n	n	NOUN
ejpam-6776	341	5	=	=	SYM
ejpam-6776	341	6	∞	∞	NUM
ejpam-6776	341	7	|	|	ADV
ejpam-6776	341	8	νx0	νx0	NOUN
ejpam-6776	341	9	n−1	n−1	PROPN
ejpam-6776	341	10	=	=	SYM
ejpam-6776	341	11	∞	∞	PROPN
ejpam-6776	341	12	)	)	PUNCT
ejpam-6776	342	1	=	=	SYM
ejpam-6776	342	2	p	p	X
ejpam-6776	342	3	(	(	PUNCT
ejpam-6776	342	4	x	x	PROPN
ejpam-6776	342	5	x0(t	x0(t	PROPN
ejpam-6776	342	6	)	)	PUNCT
ejpam-6776	342	7	/∈	/∈	PUNCT
ejpam-6776	343	1	b̃d	b̃d	PROPN
ejpam-6776	343	2	,	,	PUNCT
ejpam-6776	343	3	∀t	∀t	PROPN
ejpam-6776	343	4	∈	∈	X
ejpam-6776	344	1	[	[	X
ejpam-6776	344	2	(	(	PUNCT
ejpam-6776	344	3	n−	n−	NOUN
ejpam-6776	344	4	1)t	1)t	PROPN
ejpam-6776	344	5	∗	∗	NOUN
ejpam-6776	344	6	,	,	PUNCT
ejpam-6776	344	7	nt	not	PART
ejpam-6776	344	8	∗	∗	NOUN
ejpam-6776	344	9	]	]	X
ejpam-6776	344	10	|	|	ADV
ejpam-6776	344	11	x	x	X
ejpam-6776	344	12	x0(t	x0(t	PROPN
ejpam-6776	344	13	)	)	PUNCT
ejpam-6776	344	14	/∈	/∈	PUNCT
ejpam-6776	345	1	b̃d	b̃d	PROPN
ejpam-6776	345	2	,	,	PUNCT
ejpam-6776	345	3	∀t	∀t	PROPN
ejpam-6776	345	4	∈	∈	X
ejpam-6776	346	1	[	[	X
ejpam-6776	346	2	(	(	PUNCT
ejpam-6776	346	3	n−	n−	NOUN
ejpam-6776	346	4	2)t	2)t	PROPN
ejpam-6776	346	5	∗	∗	NOUN
ejpam-6776	346	6	,	,	PUNCT
ejpam-6776	346	7	(	(	PUNCT
ejpam-6776	346	8	n−	n−	NOUN
ejpam-6776	346	9	1)t	1)t	NOUN
ejpam-6776	346	10	∗	∗	NOUN
ejpam-6776	346	11	]	]	PUNCT
ejpam-6776	346	12	)	)	PUNCT
ejpam-6776	346	13	.	.	PUNCT
ejpam-6776	347	1	conditioning	condition	VERB
ejpam-6776	347	2	on	on	ADP
ejpam-6776	347	3	x	x	PROPN
ejpam-6776	347	4	x0((n−	x0((n−	PROPN
ejpam-6776	347	5	1)t	1)t	PROPN
ejpam-6776	347	6	∗	∗	NOUN
ejpam-6776	347	7	):	):	PUNCT
ejpam-6776	347	8	p	p	X
ejpam-6776	347	9	(	(	PUNCT
ejpam-6776	347	10	x	x	PROPN
ejpam-6776	347	11	x0(t	x0(t	PROPN
ejpam-6776	347	12	)	)	PUNCT
ejpam-6776	347	13	/∈	/∈	PUNCT
ejpam-6776	348	1	b̃d	b̃d	PROPN
ejpam-6776	348	2	,	,	PUNCT
ejpam-6776	348	3	∀t	∀t	PROPN
ejpam-6776	348	4	∈	∈	X
ejpam-6776	349	1	[	[	X
ejpam-6776	349	2	(	(	PUNCT
ejpam-6776	349	3	n−	n−	NOUN
ejpam-6776	349	4	1)t	1)t	PROPN
ejpam-6776	349	5	∗	∗	NOUN
ejpam-6776	349	6	,	,	PUNCT
ejpam-6776	349	7	nt	not	PART
ejpam-6776	349	8	∗	∗	NOUN
ejpam-6776	349	9	]	]	X
ejpam-6776	349	10	|	|	ADV
ejpam-6776	349	11	x	x	X
ejpam-6776	349	12	x0((n−	x0((n−	PROPN
ejpam-6776	349	13	1)t	1)t	PROPN
ejpam-6776	349	14	∗	∗	NOUN
ejpam-6776	349	15	)	)	PUNCT
ejpam-6776	349	16	=	=	SYM
ejpam-6776	349	17	x	x	X
ejpam-6776	349	18	)	)	PUNCT
ejpam-6776	349	19	=	=	SYM
ejpam-6776	350	1	p	p	X
ejpam-6776	350	2	(	(	PUNCT
ejpam-6776	350	3	x	x	NOUN
ejpam-6776	350	4	0,x(s	0,x(s	PROPN
ejpam-6776	350	5	)	)	PUNCT
ejpam-6776	350	6	/∈	/∈	PUNCT
ejpam-6776	351	1	b̃d	b̃d	PROPN
ejpam-6776	351	2	,	,	PUNCT
ejpam-6776	351	3	∀s	∀s	X
ejpam-6776	351	4	∈	∈	PROPN
ejpam-6776	352	1	[	[	X
ejpam-6776	352	2	0	0	NUM
ejpam-6776	352	3	,	,	PUNCT
ejpam-6776	352	4	t	t	PROPN
ejpam-6776	352	5	∗	∗	NOUN
ejpam-6776	352	6	]	]	PUNCT
ejpam-6776	352	7	)	)	PUNCT
ejpam-6776	352	8	≤	≤	NOUN
ejpam-6776	352	9	1−p∗	1−p∗	NUM
ejpam-6776	352	10	,	,	PUNCT
ejpam-6776	352	11	j.	j.	PROPN
ejpam-6776	352	12	leo	leo	PROPN
ejpam-6776	352	13	amalraj	amalraj	PROPN
ejpam-6776	352	14	et	et	PROPN
ejpam-6776	352	15	al	al	PROPN
ejpam-6776	352	16	.	.	PUNCT
ejpam-6776	352	17	/	/	SYM
ejpam-6776	352	18	eur	eur	PROPN
ejpam-6776	352	19	.	.	PUNCT
ejpam-6776	353	1	j.	j.	PROPN
ejpam-6776	353	2	pure	pure	PROPN
ejpam-6776	353	3	appl	appl	PROPN
ejpam-6776	353	4	.	.	PROPN
ejpam-6776	353	5	math	math	PROPN
ejpam-6776	353	6	,	,	PUNCT
ejpam-6776	353	7	18	18	NUM
ejpam-6776	353	8	(	(	PUNCT
ejpam-6776	353	9	4	4	NUM
ejpam-6776	353	10	)	)	PUNCT
ejpam-6776	353	11	(	(	PUNCT
ejpam-6776	353	12	2025	2025	NUM
ejpam-6776	353	13	)	)	PUNCT
ejpam-6776	353	14	,	,	PUNCT
ejpam-6776	353	15	6776	6776	NUM
ejpam-6776	353	16	15	15	NUM
ejpam-6776	353	17	of	of	ADP
ejpam-6776	353	18	22	22	NUM
ejpam-6776	353	19	since	since	SCONJ
ejpam-6776	353	20	p	p	PROPN
ejpam-6776	353	21	(	(	PUNCT
ejpam-6776	353	22	t	t	NOUN
ejpam-6776	353	23	∗	∗	NOUN
ejpam-6776	353	24	,	,	PUNCT
ejpam-6776	353	25	x	x	NOUN
ejpam-6776	353	26	,	,	PUNCT
ejpam-6776	353	27	b̃d	b̃d	NUM
ejpam-6776	353	28	)	)	PUNCT
ejpam-6776	353	29	≥	≥	NOUN
ejpam-6776	353	30	p∗.	p∗.	NOUN
ejpam-6776	353	31	thus	thus	ADV
ejpam-6776	353	32	:	:	PUNCT
ejpam-6776	353	33	p	p	X
ejpam-6776	353	34	(	(	PUNCT
ejpam-6776	353	35	νx0	νx0	NOUN
ejpam-6776	353	36	n	n	NOUN
ejpam-6776	353	37	=	=	SYM
ejpam-6776	353	38	∞	∞	NUM
ejpam-6776	353	39	|	|	ADV
ejpam-6776	353	40	νx0	νx0	NOUN
ejpam-6776	353	41	n−1	n−1	PROPN
ejpam-6776	353	42	=	=	SYM
ejpam-6776	353	43	∞	∞	PROPN
ejpam-6776	353	44	)	)	PUNCT
ejpam-6776	353	45	≤	≤	NUM
ejpam-6776	354	1	∫	∫	PROPN
ejpam-6776	355	1	a	a	DET
ejpam-6776	355	2	p	p	X
ejpam-6776	355	3	(	(	PUNCT
ejpam-6776	355	4	x	x	NOUN
ejpam-6776	355	5	0,x(s	0,x(s	PROPN
ejpam-6776	355	6	)	)	PUNCT
ejpam-6776	355	7	/∈	/∈	PUNCT
ejpam-6776	356	1	b̃d	b̃d	PROPN
ejpam-6776	356	2	,	,	PUNCT
ejpam-6776	356	3	∀s	∀s	X
ejpam-6776	356	4	∈	∈	PROPN
ejpam-6776	357	1	[	[	X
ejpam-6776	357	2	0	0	NUM
ejpam-6776	357	3	,	,	PUNCT
ejpam-6776	357	4	t	t	PROPN
ejpam-6776	357	5	∗	∗	NOUN
ejpam-6776	357	6	]	]	PUNCT
ejpam-6776	357	7	)	)	PUNCT
ejpam-6776	358	1	π((n−	π((n−	PROPN
ejpam-6776	358	2	1)t	1)t	PROPN
ejpam-6776	358	3	∗	∗	NOUN
ejpam-6776	358	4	,	,	PUNCT
ejpam-6776	358	5	x	x	X
ejpam-6776	358	6	,	,	PUNCT
ejpam-6776	358	7	x0	x0	PROPN
ejpam-6776	358	8	)	)	PUNCT
ejpam-6776	358	9	dx	dx	PROPN
ejpam-6776	358	10	≤	≤	NUM
ejpam-6776	358	11	1−	1−	NUM
ejpam-6776	358	12	p∗.	p∗.	NOUN
ejpam-6776	358	13	substituting	substitute	VERB
ejpam-6776	358	14	into	into	ADP
ejpam-6776	358	15	(	(	PUNCT
ejpam-6776	358	16	14	14	NUM
ejpam-6776	358	17	):	):	PUNCT
ejpam-6776	358	18	p	p	X
ejpam-6776	358	19	(	(	PUNCT
ejpam-6776	358	20	k⋂	k⋂	NOUN
ejpam-6776	358	21	n=1	n=1	PROPN
ejpam-6776	358	22	νx0	νx0	NOUN
ejpam-6776	358	23	n	n	NOUN
ejpam-6776	358	24	=	=	SYM
ejpam-6776	358	25	∞	∞	NUM
ejpam-6776	358	26	)	)	PUNCT
ejpam-6776	358	27	≤	≤	NOUN
ejpam-6776	358	28	(	(	PUNCT
ejpam-6776	358	29	1−	1−	NUM
ejpam-6776	358	30	p∗)k	p∗)k	PROPN
ejpam-6776	358	31	.	.	PUNCT
ejpam-6776	359	1	as	as	ADP
ejpam-6776	359	2	k	k	PROPN
ejpam-6776	359	3	→	→	SYM
ejpam-6776	359	4	∞	∞	PROPN
ejpam-6776	359	5	,	,	PUNCT
ejpam-6776	359	6	(	(	PUNCT
ejpam-6776	359	7	1−	1−	NUM
ejpam-6776	359	8	p∗)k	p∗)k	PROPN
ejpam-6776	359	9	→	→	SYM
ejpam-6776	359	10	0	0	NUM
ejpam-6776	359	11	,	,	PUNCT
ejpam-6776	359	12	so	so	ADV
ejpam-6776	359	13	:	:	PUNCT
ejpam-6776	359	14	p	p	X
ejpam-6776	359	15	(	(	PUNCT
ejpam-6776	359	16	τx0	τx0	PROPN
ejpam-6776	359	17	=	=	SYM
ejpam-6776	359	18	∞	∞	NOUN
ejpam-6776	359	19	)	)	PUNCT
ejpam-6776	359	20	=	=	SYM
ejpam-6776	359	21	0	0	NUM
ejpam-6776	359	22	,	,	PUNCT
ejpam-6776	359	23	i.e.	i.e.	X
ejpam-6776	359	24	,	,	PUNCT
ejpam-6776	359	25	p	p	X
ejpam-6776	359	26	(	(	PUNCT
ejpam-6776	359	27	τx0	τx0	NOUN
ejpam-6776	359	28	<	<	X
ejpam-6776	359	29	∞	∞	X
ejpam-6776	359	30	)	)	PUNCT
ejpam-6776	359	31	=	=	SYM
ejpam-6776	359	32	1	1	X
ejpam-6776	359	33	.	.	PUNCT
ejpam-6776	359	34	by	by	ADP
ejpam-6776	359	35	the	the	DET
ejpam-6776	359	36	strong	strong	ADJ
ejpam-6776	359	37	markov	markov	NOUN
ejpam-6776	359	38	property	property	NOUN
ejpam-6776	359	39	and	and	CCONJ
ejpam-6776	359	40	(	(	PUNCT
ejpam-6776	359	41	9	9	NUM
ejpam-6776	359	42	)	)	PUNCT
ejpam-6776	359	43	,	,	PUNCT
ejpam-6776	359	44	for	for	ADP
ejpam-6776	359	45	any	any	DET
ejpam-6776	359	46	r	r	NOUN
ejpam-6776	359	47	,	,	PUNCT
ejpam-6776	359	48	ε	ε	PROPN
ejpam-6776	359	49	>	>	X
ejpam-6776	359	50	0	0	NUM
ejpam-6776	359	51	:	:	PUNCT
ejpam-6776	360	1	p	p	X
ejpam-6776	360	2	(	(	PUNCT
ejpam-6776	360	3	lim	lim	PROPN
ejpam-6776	360	4	sup	sup	NOUN
ejpam-6776	360	5	t→∞	t→∞	NUM
ejpam-6776	361	1	∥x	∥x	PROPN
ejpam-6776	361	2	x0(t)−	x0(t)−	PROPN
ejpam-6776	361	3	e0∥	e0∥	PROPN
ejpam-6776	361	4	>	>	X
ejpam-6776	361	5	r	r	NOUN
ejpam-6776	361	6	)	)	PUNCT
ejpam-6776	362	1	=	=	PUNCT
ejpam-6776	362	2	e	e	X
ejpam-6776	362	3	[	[	PUNCT
ejpam-6776	362	4	p	p	X
ejpam-6776	362	5	(	(	PUNCT
ejpam-6776	362	6	lim	lim	PROPN
ejpam-6776	362	7	sup	sup	NOUN
ejpam-6776	362	8	t→∞	t→∞	NUM
ejpam-6776	362	9	∥x	∥x	PROPN
ejpam-6776	362	10	x0(t)−	x0(t)−	PROPN
ejpam-6776	362	11	e0∥	e0∥	PROPN
ejpam-6776	362	12	>	>	PUNCT
ejpam-6776	362	13	r	r	NOUN
ejpam-6776	362	14	|	|	ADV
ejpam-6776	362	15	fτx0	fτx0	PROPN
ejpam-6776	362	16	)	)	PUNCT
ejpam-6776	362	17	]	]	PUNCT
ejpam-6776	362	18	.	.	PUNCT
ejpam-6776	363	1	at	at	ADP
ejpam-6776	363	2	τx0	τx0	PROPN
ejpam-6776	363	3	,	,	PUNCT
ejpam-6776	363	4	x	x	NOUN
ejpam-6776	363	5	x0(τx0	x0(τx0	ADV
ejpam-6776	363	6	)	)	PUNCT
ejpam-6776	363	7	∈	∈	PROPN
ejpam-6776	363	8	b̃d	b̃d	PROPN
ejpam-6776	363	9	,	,	PUNCT
ejpam-6776	363	10	so	so	ADV
ejpam-6776	363	11	:	:	PUNCT
ejpam-6776	363	12	p	p	X
ejpam-6776	363	13	(	(	PUNCT
ejpam-6776	363	14	lim	lim	PROPN
ejpam-6776	363	15	sup	sup	NOUN
ejpam-6776	363	16	t→∞	t→∞	NUM
ejpam-6776	364	1	∥x	∥x	PROPN
ejpam-6776	364	2	τx0	τx0	PROPN
ejpam-6776	364	3	,	,	PUNCT
ejpam-6776	364	4	x(t)−	x(t)−	PROPN
ejpam-6776	364	5	e0∥	e0∥	PROPN
ejpam-6776	364	6	>	>	X
ejpam-6776	364	7	r	r	NOUN
ejpam-6776	364	8	)	)	PUNCT
ejpam-6776	364	9	≤	≤	PROPN
ejpam-6776	364	10	ε	ε	PROPN
ejpam-6776	364	11	,	,	PUNCT
ejpam-6776	364	12	∀x	∀x	X
ejpam-6776	364	13	∈	∈	PROPN
ejpam-6776	364	14	b̃d	b̃d	PROPN
ejpam-6776	364	15	.	.	PUNCT
ejpam-6776	365	1	thus	thus	ADV
ejpam-6776	365	2	:	:	PUNCT
ejpam-6776	365	3	p	p	X
ejpam-6776	365	4	(	(	PUNCT
ejpam-6776	365	5	lim	lim	PROPN
ejpam-6776	365	6	sup	sup	NOUN
ejpam-6776	365	7	t→∞	t→∞	NUM
ejpam-6776	366	1	∥x	∥x	PROPN
ejpam-6776	366	2	x0(t)−	x0(t)−	PROPN
ejpam-6776	366	3	e0∥	e0∥	PROPN
ejpam-6776	366	4	>	>	X
ejpam-6776	366	5	r	r	NOUN
ejpam-6776	366	6	)	)	PUNCT
ejpam-6776	366	7	≤	≤	NUM
ejpam-6776	366	8	∫	∫	PROPN
ejpam-6776	367	1	∞	∞	NUM
ejpam-6776	367	2	0	0	NUM
ejpam-6776	368	1	∫	∫	PROPN
ejpam-6776	369	1	b̃d	b̃d	PROPN
ejpam-6776	369	2	p	p	PROPN
ejpam-6776	369	3	(	(	PUNCT
ejpam-6776	369	4	lim	lim	PROPN
ejpam-6776	369	5	sup	sup	NOUN
ejpam-6776	369	6	t→∞	t→∞	NUM
ejpam-6776	369	7	∥x	∥x	PROPN
ejpam-6776	369	8	u	u	NOUN
ejpam-6776	369	9	,	,	PUNCT
ejpam-6776	369	10	x(t)−	x(t)−	PROPN
ejpam-6776	369	11	e0∥	e0∥	PROPN
ejpam-6776	369	12	>	>	X
ejpam-6776	369	13	r	r	NOUN
ejpam-6776	369	14	)	)	PUNCT
ejpam-6776	369	15	p(τx0	p(τx0	PROPN
ejpam-6776	369	16	∈	∈	PROPN
ejpam-6776	369	17	du	du	X
ejpam-6776	369	18	,	,	PUNCT
ejpam-6776	369	19	x	x	NOUN
ejpam-6776	369	20	x0(τx0	x0(τx0	ADV
ejpam-6776	369	21	)	)	PUNCT
ejpam-6776	369	22	∈	∈	PROPN
ejpam-6776	369	23	dx	dx	PROPN
ejpam-6776	369	24	)	)	PUNCT
ejpam-6776	369	25	≤	≤	PROPN
ejpam-6776	369	26	ε	ε	PROPN
ejpam-6776	369	27	.	.	PUNCT
ejpam-6776	370	1	since	since	SCONJ
ejpam-6776	370	2	ε	ε	PROPN
ejpam-6776	370	3	and	and	CCONJ
ejpam-6776	370	4	r	r	NOUN
ejpam-6776	370	5	are	be	AUX
ejpam-6776	370	6	arbitrary	arbitrary	ADJ
ejpam-6776	370	7	:	:	PUNCT
ejpam-6776	370	8	p	p	X
ejpam-6776	370	9	(	(	PUNCT
ejpam-6776	370	10	lim	lim	PROPN
ejpam-6776	370	11	sup	sup	NOUN
ejpam-6776	370	12	t→∞	t→∞	NUM
ejpam-6776	370	13	∥x	∥x	PROPN
ejpam-6776	370	14	x0(t)−	x0(t)−	PROPN
ejpam-6776	370	15	e0∥	e0∥	PROPN
ejpam-6776	370	16	>	>	X
ejpam-6776	370	17	0	0	NUM
ejpam-6776	370	18	)	)	PUNCT
ejpam-6776	371	1	=	=	SYM
ejpam-6776	371	2	0	0	NUM
ejpam-6776	371	3	,	,	PUNCT
ejpam-6776	371	4	implying	imply	VERB
ejpam-6776	371	5	:	:	PUNCT
ejpam-6776	371	6	p	p	X
ejpam-6776	371	7	(	(	PUNCT
ejpam-6776	371	8	lim	lim	PROPN
ejpam-6776	371	9	t→∞	t→∞	NUM
ejpam-6776	371	10	x	x	PROPN
ejpam-6776	371	11	x0(t	x0(t	PROPN
ejpam-6776	371	12	)	)	PUNCT
ejpam-6776	371	13	=	=	SYM
ejpam-6776	371	14	e0	e0	PROPN
ejpam-6776	371	15	)	)	PUNCT
ejpam-6776	372	1	=	=	PUNCT
ejpam-6776	372	2	1	1	X
ejpam-6776	372	3	.	.	PUNCT
ejpam-6776	373	1	this	this	PRON
ejpam-6776	373	2	completes	complete	VERB
ejpam-6776	373	3	the	the	DET
ejpam-6776	373	4	proof	proof	NOUN
ejpam-6776	373	5	.	.	PUNCT
ejpam-6776	374	1	4	4	X
ejpam-6776	374	2	.	.	NOUN
ejpam-6776	374	3	numerical	numerical	ADJ
ejpam-6776	374	4	analysis	analysis	NOUN
ejpam-6776	374	5	and	and	CCONJ
ejpam-6776	374	6	dynamics	dynamic	NOUN
ejpam-6776	374	7	to	to	PART
ejpam-6776	374	8	elucidate	elucidate	VERB
ejpam-6776	374	9	the	the	DET
ejpam-6776	374	10	impact	impact	NOUN
ejpam-6776	374	11	of	of	ADP
ejpam-6776	374	12	stochastic	stochastic	ADJ
ejpam-6776	374	13	perturbations	perturbation	NOUN
ejpam-6776	374	14	on	on	ADP
ejpam-6776	374	15	epidemic	epidemic	NOUN
ejpam-6776	374	16	dynamics	dynamic	NOUN
ejpam-6776	374	17	,	,	PUNCT
ejpam-6776	374	18	we	we	PRON
ejpam-6776	374	19	compare	compare	VERB
ejpam-6776	374	20	our	our	PRON
ejpam-6776	374	21	findings	finding	NOUN
ejpam-6776	374	22	with	with	ADP
ejpam-6776	374	23	a	a	DET
ejpam-6776	374	24	deterministic	deterministic	ADJ
ejpam-6776	374	25	model	model	NOUN
ejpam-6776	374	26	analyzed	analyze	VERB
ejpam-6776	374	27	in	in	ADP
ejpam-6776	374	28	prior	prior	ADJ
ejpam-6776	374	29	work	work	NOUN
ejpam-6776	374	30	[	[	X
ejpam-6776	374	31	40–43	40–43	NUM
ejpam-6776	374	32	]	]	X
ejpam-6776	374	33	.	.	PUNCT
ejpam-6776	375	1	that	that	DET
ejpam-6776	375	2	study	study	NOUN
ejpam-6776	375	3	explored	explore	VERB
ejpam-6776	375	4	the	the	DET
ejpam-6776	375	5	global	global	ADJ
ejpam-6776	375	6	behavior	behavior	NOUN
ejpam-6776	375	7	of	of	ADP
ejpam-6776	375	8	the	the	DET
ejpam-6776	375	9	deterministic	deterministic	ADJ
ejpam-6776	375	10	system	system	NOUN
ejpam-6776	375	11	(	(	PUNCT
ejpam-6776	375	12	denoted	denote	VERB
ejpam-6776	375	13	as	as	ADP
ejpam-6776	375	14	equation	equation	NOUN
ejpam-6776	375	15	(	(	PUNCT
ejpam-6776	375	16	1.1	1.1	NUM
ejpam-6776	375	17	)	)	PUNCT
ejpam-6776	375	18	)	)	PUNCT
ejpam-6776	375	19	across	across	ADP
ejpam-6776	375	20	three	three	NUM
ejpam-6776	375	21	parameter	parameter	NOUN
ejpam-6776	375	22	regions	region	NOUN
ejpam-6776	375	23	defined	define	VERB
ejpam-6776	375	24	by	by	ADP
ejpam-6776	375	25	λ	λ	PROPN
ejpam-6776	375	26	and	and	CCONJ
ejpam-6776	375	27	α	α	NOUN
ejpam-6776	375	28	:	:	PUNCT
ejpam-6776	375	29	o1	o1	NOUN
ejpam-6776	375	30	=	=	SYM
ejpam-6776	375	31	{	{	PUNCT
ejpam-6776	375	32	(	(	PUNCT
ejpam-6776	375	33	λ	λ	PROPN
ejpam-6776	375	34	,	,	PUNCT
ejpam-6776	375	35	α	α	NOUN
ejpam-6776	375	36	)	)	PUNCT
ejpam-6776	375	37	:	:	PUNCT
ejpam-6776	376	1	λ	λ	X
ejpam-6776	376	2	≥	≥	NUM
ejpam-6776	376	3	δ	δ	X
ejpam-6776	376	4	β	β	X
ejpam-6776	377	1	+	+	X
ejpam-6776	377	2	δk	δk	INTJ
ejpam-6776	377	3	,	,	PUNCT
ejpam-6776	377	4	α	α	X
ejpam-6776	377	5	>	>	X
ejpam-6776	377	6	0	0	NUM
ejpam-6776	377	7	}	}	PUNCT
ejpam-6776	377	8	,	,	PUNCT
ejpam-6776	377	9	o2	o2	PROPN
ejpam-6776	377	10	=	=	SYM
ejpam-6776	377	11	{	{	PUNCT
ejpam-6776	377	12	(	(	PUNCT
ejpam-6776	377	13	λ	λ	PROPN
ejpam-6776	377	14	,	,	PUNCT
ejpam-6776	377	15	α	α	NOUN
ejpam-6776	377	16	)	)	PUNCT
ejpam-6776	377	17	:	:	PUNCT
ejpam-6776	378	1	0	0	PUNCT
ejpam-6776	378	2	<	<	X
ejpam-6776	378	3	λ	λ	X
ejpam-6776	378	4	<	<	X
ejpam-6776	378	5	δ	δ	X
ejpam-6776	378	6	β	β	X
ejpam-6776	378	7	+	+	X
ejpam-6776	378	8	δk	δk	INTJ
ejpam-6776	378	9	,	,	PUNCT
ejpam-6776	378	10	0	0	NUM
ejpam-6776	378	11	<	<	X
ejpam-6776	378	12	α	α	PROPN
ejpam-6776	378	13	≤	≤	NUM
ejpam-6776	378	14	α0(λ	α0(λ	NUM
ejpam-6776	378	15	)	)	PUNCT
ejpam-6776	378	16	}	}	PUNCT
ejpam-6776	378	17	,	,	PUNCT
ejpam-6776	378	18	j.	j.	PROPN
ejpam-6776	378	19	leo	leo	PROPN
ejpam-6776	378	20	amalraj	amalraj	PROPN
ejpam-6776	378	21	et	et	PROPN
ejpam-6776	378	22	al	al	PROPN
ejpam-6776	378	23	.	.	PUNCT
ejpam-6776	378	24	/	/	SYM
ejpam-6776	378	25	eur	eur	PROPN
ejpam-6776	378	26	.	.	PUNCT
ejpam-6776	379	1	j.	j.	PROPN
ejpam-6776	379	2	pure	pure	PROPN
ejpam-6776	379	3	appl	appl	PROPN
ejpam-6776	379	4	.	.	PROPN
ejpam-6776	379	5	math	math	PROPN
ejpam-6776	379	6	,	,	PUNCT
ejpam-6776	379	7	18	18	NUM
ejpam-6776	379	8	(	(	PUNCT
ejpam-6776	379	9	4	4	NUM
ejpam-6776	379	10	)	)	PUNCT
ejpam-6776	379	11	(	(	PUNCT
ejpam-6776	379	12	2025	2025	NUM
ejpam-6776	379	13	)	)	PUNCT
ejpam-6776	379	14	,	,	PUNCT
ejpam-6776	379	15	6776	6776	NUM
ejpam-6776	379	16	16	16	NUM
ejpam-6776	379	17	of	of	ADP
ejpam-6776	379	18	22	22	NUM
ejpam-6776	379	19	o3	o3	PROPN
ejpam-6776	379	20	=	=	PUNCT
ejpam-6776	379	21	{	{	PUNCT
ejpam-6776	379	22	(	(	PUNCT
ejpam-6776	379	23	λ	λ	PROPN
ejpam-6776	379	24	,	,	PUNCT
ejpam-6776	379	25	α	α	NOUN
ejpam-6776	379	26	)	)	PUNCT
ejpam-6776	379	27	:	:	PUNCT
ejpam-6776	379	28	0	0	PUNCT
ejpam-6776	380	1	<	<	X
ejpam-6776	380	2	λ	λ	X
ejpam-6776	380	3	<	<	X
ejpam-6776	380	4	δ	δ	X
ejpam-6776	380	5	β	β	X
ejpam-6776	380	6	+	+	X
ejpam-6776	380	7	δk	δk	PROPN
ejpam-6776	380	8	,	,	PUNCT
ejpam-6776	380	9	α	α	X
ejpam-6776	380	10	>	>	X
ejpam-6776	380	11	α0(λ	α0(λ	PROPN
ejpam-6776	380	12	)	)	PUNCT
ejpam-6776	380	13	}	}	PUNCT
ejpam-6776	380	14	,	,	PUNCT
ejpam-6776	380	15	where	where	SCONJ
ejpam-6776	380	16	the	the	DET
ejpam-6776	380	17	threshold	threshold	NOUN
ejpam-6776	380	18	is	be	AUX
ejpam-6776	380	19	:	:	PUNCT
ejpam-6776	380	20	α0(λ	α0(λ	X
ejpam-6776	380	21	)	)	PUNCT
ejpam-6776	381	1	=	=	PUNCT
ejpam-6776	381	2	λ2(β	λ2(β	X
ejpam-6776	382	1	+	+	CCONJ
ejpam-6776	382	2	δk)(δ	δk)(δ	PROPN
ejpam-6776	383	1	+	+	CCONJ
ejpam-6776	383	2	γ	γ	X
ejpam-6776	383	3	+	+	SYM
ejpam-6776	383	4	ϵ	ϵ	X
ejpam-6776	383	5	)	)	PUNCT
ejpam-6776	383	6	δ	δ	NOUN
ejpam-6776	383	7	−	−	NOUN
ejpam-6776	384	1	λ(β	λ(β	X
ejpam-6776	384	2	+	+	CCONJ
ejpam-6776	384	3	δk	δk	NOUN
ejpam-6776	384	4	)	)	PUNCT
ejpam-6776	384	5	.	.	PUNCT
ejpam-6776	385	1	the	the	DET
ejpam-6776	385	2	analysis	analysis	NOUN
ejpam-6776	385	3	revealed	reveal	VERB
ejpam-6776	385	4	rich	rich	ADJ
ejpam-6776	385	5	dynamics	dynamic	NOUN
ejpam-6776	385	6	:	:	PUNCT
ejpam-6776	385	7	a	a	DET
ejpam-6776	385	8	forward	forward	ADJ
ejpam-6776	385	9	bifurcation	bifurcation	NOUN
ejpam-6776	385	10	at	at	ADP
ejpam-6776	385	11	r0	r0	NOUN
ejpam-6776	385	12	=	=	SYM
ejpam-6776	385	13	1	1	NUM
ejpam-6776	385	14	for	for	ADP
ejpam-6776	385	15	(	(	PUNCT
ejpam-6776	385	16	λ	λ	PROPN
ejpam-6776	385	17	,	,	PUNCT
ejpam-6776	385	18	α	α	NOUN
ejpam-6776	385	19	)	)	PUNCT
ejpam-6776	385	20	∈	∈	PROPN
ejpam-6776	385	21	o1∪o2	o1∪o2	NOUN
ejpam-6776	385	22	,	,	PUNCT
ejpam-6776	385	23	and	and	CCONJ
ejpam-6776	385	24	a	a	DET
ejpam-6776	385	25	backward	backward	ADJ
ejpam-6776	385	26	bifurcation	bifurcation	NOUN
ejpam-6776	385	27	in	in	ADP
ejpam-6776	385	28	o3	o3	PROPN
ejpam-6776	385	29	when	when	SCONJ
ejpam-6776	385	30	p	p	NOUN
ejpam-6776	385	31	∗	∗	VERB
ejpam-6776	385	32	<	<	X
ejpam-6776	385	33	r0	r0	NOUN
ejpam-6776	385	34	<	<	X
ejpam-6776	385	35	1	1	NUM
ejpam-6776	385	36	,	,	PUNCT
ejpam-6776	385	37	transitioning	transition	VERB
ejpam-6776	385	38	from	from	ADP
ejpam-6776	385	39	the	the	DET
ejpam-6776	385	40	disease	disease	NOUN
ejpam-6776	385	41	-	-	PUNCT
ejpam-6776	385	42	free	free	ADJ
ejpam-6776	385	43	equilibrium	equilibrium	NOUN
ejpam-6776	385	44	to	to	ADP
ejpam-6776	385	45	two	two	NUM
ejpam-6776	385	46	endemic	endemic	ADJ
ejpam-6776	385	47	equilibria	equilibrium	NOUN
ejpam-6776	385	48	,	,	PUNCT
ejpam-6776	385	49	with	with	ADP
ejpam-6776	385	50	p	p	NOUN
ejpam-6776	385	51	∗	∗	NOUN
ejpam-6776	385	52	defined	define	VERB
ejpam-6776	385	53	in	in	ADP
ejpam-6776	385	54	[	[	X
ejpam-6776	385	55	40–43	40–43	NUM
ejpam-6776	385	56	]	]	X
ejpam-6776	385	57	.	.	PUNCT
ejpam-6776	386	1	we	we	PRON
ejpam-6776	386	2	present	present	VERB
ejpam-6776	386	3	three	three	NUM
ejpam-6776	386	4	numerical	numerical	ADJ
ejpam-6776	386	5	examples	example	NOUN
ejpam-6776	386	6	to	to	PART
ejpam-6776	386	7	illustrate	illustrate	VERB
ejpam-6776	386	8	how	how	SCONJ
ejpam-6776	386	9	stochasticity	stochasticity	NOUN
ejpam-6776	386	10	alters	alter	VERB
ejpam-6776	386	11	these	these	DET
ejpam-6776	386	12	dynamics	dynamic	NOUN
ejpam-6776	386	13	,	,	PUNCT
ejpam-6776	386	14	focusing	focus	VERB
ejpam-6776	386	15	on	on	ADP
ejpam-6776	386	16	system	system	NOUN
ejpam-6776	386	17	(	(	PUNCT
ejpam-6776	386	18	1.2	1.2	NUM
ejpam-6776	386	19	)	)	PUNCT
ejpam-6776	386	20	,	,	PUNCT
ejpam-6776	386	21	a	a	DET
ejpam-6776	386	22	stochastic	stochastic	ADJ
ejpam-6776	386	23	extension	extension	NOUN
ejpam-6776	386	24	of	of	ADP
ejpam-6776	386	25	(	(	PUNCT
ejpam-6776	386	26	1.1	1.1	NUM
ejpam-6776	386	27	)	)	PUNCT
ejpam-6776	386	28	.	.	PUNCT
ejpam-6776	387	1	simulations	simulation	NOUN
ejpam-6776	387	2	visualize	visualize	VERB
ejpam-6776	387	3	trajectories	trajectory	NOUN
ejpam-6776	387	4	and	and	CCONJ
ejpam-6776	387	5	bifurcation	bifurcation	NOUN
ejpam-6776	387	6	surfaces	surface	NOUN
ejpam-6776	387	7	,	,	PUNCT
ejpam-6776	387	8	highlighting	highlight	VERB
ejpam-6776	387	9	extinction	extinction	NOUN
ejpam-6776	387	10	,	,	PUNCT
ejpam-6776	387	11	persistence	persistence	NOUN
ejpam-6776	387	12	,	,	PUNCT
ejpam-6776	387	13	and	and	CCONJ
ejpam-6776	387	14	parameterdriven	parameterdriven	ADJ
ejpam-6776	387	15	transitions	transition	NOUN
ejpam-6776	387	16	.	.	PUNCT
ejpam-6776	388	1	4.1	4.1	NUM
ejpam-6776	388	2	.	.	PUNCT
ejpam-6776	388	3	example	example	NOUN
ejpam-6776	388	4	1	1	NUM
ejpam-6776	388	5	:	:	PUNCT
ejpam-6776	388	6	stochastic	stochastic	ADJ
ejpam-6776	388	7	extinction	extinction	NOUN
ejpam-6776	388	8	in	in	ADP
ejpam-6776	388	9	backward	backward	ADJ
ejpam-6776	388	10	bifurcation	bifurcation	NOUN
ejpam-6776	388	11	regime	regime	NOUN
ejpam-6776	388	12	in	in	ADP
ejpam-6776	388	13	the	the	DET
ejpam-6776	388	14	deterministic	deterministic	ADJ
ejpam-6776	388	15	setting	setting	NOUN
ejpam-6776	388	16	,	,	PUNCT
ejpam-6776	388	17	when	when	SCONJ
ejpam-6776	388	18	(	(	PUNCT
ejpam-6776	388	19	λ	λ	NOUN
ejpam-6776	388	20	,	,	PUNCT
ejpam-6776	388	21	α	α	NOUN
ejpam-6776	388	22	)	)	PUNCT
ejpam-6776	388	23	∈	∈	PROPN
ejpam-6776	388	24	o3	o3	PROPN
ejpam-6776	388	25	and	and	CCONJ
ejpam-6776	388	26	p	p	NOUN
ejpam-6776	388	27	∗	∗	NOUN
ejpam-6776	388	28	<	<	X
ejpam-6776	388	29	r0	r0	NOUN
ejpam-6776	388	30	<	<	X
ejpam-6776	388	31	1	1	NUM
ejpam-6776	388	32	,	,	PUNCT
ejpam-6776	388	33	the	the	DET
ejpam-6776	388	34	system	system	NOUN
ejpam-6776	388	35	exhibits	exhibit	VERB
ejpam-6776	388	36	a	a	DET
ejpam-6776	388	37	backward	backward	ADJ
ejpam-6776	388	38	bifurcation	bifurcation	NOUN
ejpam-6776	388	39	,	,	PUNCT
ejpam-6776	388	40	with	with	ADP
ejpam-6776	388	41	a	a	DET
ejpam-6776	388	42	disease	disease	NOUN
ejpam-6776	388	43	-	-	PUNCT
ejpam-6776	388	44	free	free	ADJ
ejpam-6776	388	45	equilibrium	equilibrium	NOUN
ejpam-6776	388	46	e0	e0	PROPN
ejpam-6776	388	47	,	,	PUNCT
ejpam-6776	388	48	a	a	DET
ejpam-6776	388	49	saddle	saddle	NOUN
ejpam-6776	388	50	-	-	PUNCT
ejpam-6776	388	51	point	point	NOUN
ejpam-6776	388	52	endemic	endemic	ADJ
ejpam-6776	388	53	equilibrium	equilibrium	NOUN
ejpam-6776	388	54	e1	e1	NOUN
ejpam-6776	388	55	,	,	PUNCT
ejpam-6776	388	56	and	and	CCONJ
ejpam-6776	388	57	a	a	DET
ejpam-6776	388	58	stable	stable	ADJ
ejpam-6776	388	59	endemic	endemic	ADJ
ejpam-6776	388	60	equilibrium	equilibrium	NOUN
ejpam-6776	388	61	e2	e2	PROPN
ejpam-6776	388	62	.	.	PUNCT
ejpam-6776	389	1	introducing	introduce	VERB
ejpam-6776	389	2	noise	noise	NOUN
ejpam-6776	389	3	can	can	AUX
ejpam-6776	389	4	destabilize	destabilize	VERB
ejpam-6776	389	5	the	the	DET
ejpam-6776	389	6	endemic	endemic	ADJ
ejpam-6776	389	7	state	state	NOUN
ejpam-6776	389	8	,	,	PUNCT
ejpam-6776	389	9	driving	drive	VERB
ejpam-6776	389	10	trajectories	trajectory	NOUN
ejpam-6776	389	11	toward	toward	ADP
ejpam-6776	389	12	extinction	extinction	NOUN
ejpam-6776	389	13	.	.	PUNCT
ejpam-6776	390	1	consider	consider	VERB
ejpam-6776	390	2	the	the	DET
ejpam-6776	390	3	deterministic	deterministic	ADJ
ejpam-6776	390	4	system	system	NOUN
ejpam-6776	390	5	(	(	PUNCT
ejpam-6776	390	6	1.1	1.1	NUM
ejpam-6776	390	7	)	)	PUNCT
ejpam-6776	390	8	with	with	ADP
ejpam-6776	390	9	parameters	parameter	NOUN
ejpam-6776	390	10	:	:	PUNCT
ejpam-6776	390	11	β	β	X
ejpam-6776	390	12	=	=	SYM
ejpam-6776	390	13	0.0048	0.0048	NUM
ejpam-6776	390	14	,	,	PUNCT
ejpam-6776	390	15	λ	λ	X
ejpam-6776	390	16	=	=	SYM
ejpam-6776	390	17	15	15	NUM
ejpam-6776	390	18	,	,	PUNCT
ejpam-6776	390	19	α	α	X
ejpam-6776	390	20	=	=	SYM
ejpam-6776	390	21	6.5	6.5	NUM
ejpam-6776	390	22	,	,	PUNCT
ejpam-6776	390	23	λ	λ	X
ejpam-6776	390	24	=	=	NOUN
ejpam-6776	390	25	6.8	6.8	NUM
ejpam-6776	390	26	,	,	PUNCT
ejpam-6776	390	27	k	k	PROPN
ejpam-6776	390	28	=	=	SYM
ejpam-6776	390	29	0.012	0.012	NUM
ejpam-6776	390	30	,	,	PUNCT
ejpam-6776	390	31	δ	δ	X
ejpam-6776	390	32	=	=	SYM
ejpam-6776	390	33	0.09	0.09	NUM
ejpam-6776	390	34	,	,	PUNCT
ejpam-6776	390	35	γ	γ	X
ejpam-6776	390	36	=	=	SYM
ejpam-6776	390	37	0.015	0.015	NUM
ejpam-6776	390	38	,	,	PUNCT
ejpam-6776	390	39	ϵ	ϵ	X
ejpam-6776	390	40	=	=	PUNCT
ejpam-6776	390	41	0.025	0.025	NUM
ejpam-6776	390	42	.	.	PUNCT
ejpam-6776	391	1	calculating	calculate	VERB
ejpam-6776	391	2	the	the	DET
ejpam-6776	391	3	basic	basic	ADJ
ejpam-6776	391	4	reproduction	reproduction	NOUN
ejpam-6776	391	5	number	number	NOUN
ejpam-6776	391	6	yields	yield	VERB
ejpam-6776	391	7	r0	r0	NOUN
ejpam-6776	391	8	=	=	PUNCT
ejpam-6776	391	9	0.82	0.82	NUM
ejpam-6776	391	10	,	,	PUNCT
ejpam-6776	391	11	and	and	CCONJ
ejpam-6776	391	12	the	the	DET
ejpam-6776	391	13	threshold	threshold	NOUN
ejpam-6776	391	14	p	p	NOUN
ejpam-6776	391	15	∗	∗	NOUN
ejpam-6776	391	16	=	=	SYM
ejpam-6776	391	17	0.78	0.78	NUM
ejpam-6776	391	18	,	,	PUNCT
ejpam-6776	391	19	confirming	confirm	VERB
ejpam-6776	391	20	the	the	DET
ejpam-6776	391	21	presence	presence	NOUN
ejpam-6776	391	22	of	of	ADP
ejpam-6776	391	23	e0	e0	PROPN
ejpam-6776	391	24	,	,	PUNCT
ejpam-6776	391	25	e1	e1	PROPN
ejpam-6776	391	26	,	,	PUNCT
ejpam-6776	391	27	and	and	CCONJ
ejpam-6776	391	28	e2	e2	PROPN
ejpam-6776	391	29	.	.	PUNCT
ejpam-6776	392	1	the	the	DET
ejpam-6776	392	2	threshold	threshold	NOUN
ejpam-6776	392	3	p	p	NOUN
ejpam-6776	392	4	∗	∗	NOUN
ejpam-6776	392	5	=	=	NOUN
ejpam-6776	392	6	0.78	0.78	NUM
ejpam-6776	392	7	represents	represent	VERB
ejpam-6776	392	8	the	the	DET
ejpam-6776	392	9	critical	critical	ADJ
ejpam-6776	392	10	value	value	NOUN
ejpam-6776	392	11	for	for	ADP
ejpam-6776	392	12	backward	backward	ADJ
ejpam-6776	392	13	bifurcation	bifurcation	NOUN
ejpam-6776	392	14	in	in	ADP
ejpam-6776	392	15	the	the	DET
ejpam-6776	392	16	deterministic	deterministic	ADJ
ejpam-6776	392	17	model	model	NOUN
ejpam-6776	392	18	,	,	PUNCT
ejpam-6776	392	19	below	below	ADP
ejpam-6776	392	20	which	which	PRON
ejpam-6776	392	21	multiple	multiple	ADJ
ejpam-6776	392	22	endemic	endemic	ADJ
ejpam-6776	392	23	equilibria	equilibrium	NOUN
ejpam-6776	392	24	exist	exist	VERB
ejpam-6776	392	25	when	when	SCONJ
ejpam-6776	392	26	r0	r0	NOUN
ejpam-6776	392	27	<	<	X
ejpam-6776	392	28	1	1	NUM
ejpam-6776	392	29	,	,	PUNCT
ejpam-6776	392	30	highlighting	highlight	VERB
ejpam-6776	392	31	subcritical	subcritical	ADJ
ejpam-6776	392	32	persistence	persistence	NOUN
ejpam-6776	392	33	.	.	PUNCT
ejpam-6776	393	1	now	now	ADV
ejpam-6776	393	2	,	,	PUNCT
ejpam-6776	393	3	we	we	PRON
ejpam-6776	393	4	simulate	simulate	VERB
ejpam-6776	393	5	the	the	DET
ejpam-6776	393	6	stochastic	stochastic	ADJ
ejpam-6776	393	7	system	system	NOUN
ejpam-6776	393	8	(	(	PUNCT
ejpam-6776	393	9	1.2	1.2	NUM
ejpam-6776	393	10	)	)	PUNCT
ejpam-6776	393	11	with	with	ADP
ejpam-6776	393	12	the	the	DET
ejpam-6776	393	13	same	same	ADJ
ejpam-6776	393	14	parameters	parameter	NOUN
ejpam-6776	393	15	and	and	CCONJ
ejpam-6776	393	16	noise	noise	NOUN
ejpam-6776	393	17	intensity	intensity	NOUN
ejpam-6776	393	18	σ	σ	X
ejpam-6776	393	19	=	=	SYM
ejpam-6776	393	20	0.0018	0.0018	NUM
ejpam-6776	393	21	.	.	PUNCT
ejpam-6776	394	1	this	this	DET
ejpam-6776	394	2	yields	yield	NOUN
ejpam-6776	394	3	:	:	PUNCT
ejpam-6776	394	4	η	η	PROPN
ejpam-6776	394	5	=	=	PROPN
ejpam-6776	394	6	βλ	βλ	PROPN
ejpam-6776	394	7	δ	δ	PROPN
ejpam-6776	394	8	−	−	PROPN
ejpam-6776	395	1	(	(	PUNCT
ejpam-6776	395	2	δ	δ	PROPN
ejpam-6776	395	3	+	+	CCONJ
ejpam-6776	395	4	γ	γ	X
ejpam-6776	395	5	+	+	X
ejpam-6776	395	6	ϵ+	ϵ+	PUNCT
ejpam-6776	395	7	α	α	X
ejpam-6776	395	8	λ	λ	X
ejpam-6776	395	9	+	+	NOUN
ejpam-6776	395	10	1	1	NUM
ejpam-6776	395	11	2	2	NUM
ejpam-6776	395	12	(	(	PUNCT
ejpam-6776	395	13	σλ	σλ	NOUN
ejpam-6776	395	14	δ	δ	PROPN
ejpam-6776	395	15	)	)	PUNCT
ejpam-6776	395	16	2	2	X
ejpam-6776	395	17	)	)	PUNCT
ejpam-6776	396	1	=	=	SYM
ejpam-6776	396	2	−0.22	−0.22	NOUN
ejpam-6776	396	3	<	<	X
ejpam-6776	396	4	0	0	NUM
ejpam-6776	396	5	,	,	PUNCT
ejpam-6776	396	6	satisfying	satisfy	VERB
ejpam-6776	396	7	theorem	theorem	NOUN
ejpam-6776	396	8	4	4	NUM
ejpam-6776	396	9	.	.	PUNCT
ejpam-6776	396	10	figure	figure	NOUN
ejpam-6776	396	11	1	1	NUM
ejpam-6776	396	12	compares	compare	VERB
ejpam-6776	396	13	deterministic	deterministic	ADJ
ejpam-6776	396	14	and	and	CCONJ
ejpam-6776	396	15	stochastic	stochastic	ADJ
ejpam-6776	396	16	trajectories	trajectory	NOUN
ejpam-6776	396	17	,	,	PUNCT
ejpam-6776	396	18	showing	show	VERB
ejpam-6776	396	19	the	the	DET
ejpam-6776	396	20	stochastic	stochastic	ADJ
ejpam-6776	396	21	system	system	NOUN
ejpam-6776	396	22	converging	converge	VERB
ejpam-6776	396	23	to	to	ADP
ejpam-6776	396	24	e0	e0	PROPN
ejpam-6776	396	25	,	,	PUNCT
ejpam-6776	396	26	unlike	unlike	ADP
ejpam-6776	396	27	the	the	DET
ejpam-6776	396	28	deterministic	deterministic	ADJ
ejpam-6776	396	29	case	case	NOUN
ejpam-6776	396	30	,	,	PUNCT
ejpam-6776	396	31	which	which	PRON
ejpam-6776	396	32	stabilizes	stabilize	VERB
ejpam-6776	396	33	at	at	ADP
ejpam-6776	396	34	e2	e2	PROPN
ejpam-6776	396	35	.	.	PUNCT
ejpam-6776	397	1	4.2	4.2	NUM
ejpam-6776	397	2	.	.	PUNCT
ejpam-6776	397	3	example	example	NOUN
ejpam-6776	397	4	2	2	NUM
ejpam-6776	397	5	:	:	PUNCT
ejpam-6776	397	6	bifurcation	bifurcation	NOUN
ejpam-6776	397	7	surfaces	surface	NOUN
ejpam-6776	397	8	under	under	ADP
ejpam-6776	397	9	stochasticity	stochasticity	NOUN
ejpam-6776	397	10	to	to	PART
ejpam-6776	397	11	explore	explore	VERB
ejpam-6776	397	12	the	the	DET
ejpam-6776	397	13	influence	influence	NOUN
ejpam-6776	397	14	of	of	ADP
ejpam-6776	397	15	parameters	parameter	NOUN
ejpam-6776	397	16	λ	λ	PROPN
ejpam-6776	397	17	and	and	CCONJ
ejpam-6776	397	18	α	α	NOUN
ejpam-6776	397	19	on	on	ADP
ejpam-6776	397	20	the	the	DET
ejpam-6776	397	21	infected	infected	ADJ
ejpam-6776	397	22	population	population	NOUN
ejpam-6776	397	23	,	,	PUNCT
ejpam-6776	397	24	we	we	PRON
ejpam-6776	397	25	analyze	analyze	VERB
ejpam-6776	397	26	system	system	NOUN
ejpam-6776	397	27	(	(	PUNCT
ejpam-6776	397	28	1.2	1.2	NUM
ejpam-6776	397	29	)	)	PUNCT
ejpam-6776	397	30	with	with	ADP
ejpam-6776	397	31	:	:	PUNCT
ejpam-6776	397	32	β	β	X
ejpam-6776	397	33	=	=	SYM
ejpam-6776	397	34	0.009	0.009	NUM
ejpam-6776	397	35	,	,	PUNCT
ejpam-6776	397	36	λ	λ	X
ejpam-6776	397	37	=	=	NOUN
ejpam-6776	397	38	15	15	NUM
ejpam-6776	397	39	,	,	PUNCT
ejpam-6776	397	40	k	k	PROPN
ejpam-6776	397	41	=	=	SYM
ejpam-6776	397	42	0.0015	0.0015	PROPN
ejpam-6776	397	43	,	,	PUNCT
ejpam-6776	397	44	δ	δ	X
ejpam-6776	397	45	=	=	SYM
ejpam-6776	397	46	0.095	0.095	NUM
ejpam-6776	397	47	,	,	PUNCT
ejpam-6776	397	48	γ	γ	X
ejpam-6776	397	49	=	=	SYM
ejpam-6776	397	50	0.11	0.11	NUM
ejpam-6776	397	51	,	,	PUNCT
ejpam-6776	397	52	ϵ	ϵ	X
ejpam-6776	397	53	=	=	SYM
ejpam-6776	397	54	0.18	0.18	NUM
ejpam-6776	397	55	,	,	PUNCT
ejpam-6776	397	56	σ	σ	PROPN
ejpam-6776	397	57	=	=	SYM
ejpam-6776	397	58	0.0015	0.0015	PROPN
ejpam-6776	397	59	.	.	PUNCT
ejpam-6776	398	1	j.	j.	PROPN
ejpam-6776	398	2	leo	leo	PROPN
ejpam-6776	398	3	amalraj	amalraj	PROPN
ejpam-6776	398	4	et	et	PROPN
ejpam-6776	398	5	al	al	PROPN
ejpam-6776	398	6	.	.	PUNCT
ejpam-6776	398	7	/	/	SYM
ejpam-6776	398	8	eur	eur	PROPN
ejpam-6776	398	9	.	.	PUNCT
ejpam-6776	399	1	j.	j.	PROPN
ejpam-6776	399	2	pure	pure	PROPN
ejpam-6776	399	3	appl	appl	PROPN
ejpam-6776	399	4	.	.	PROPN
ejpam-6776	399	5	math	math	PROPN
ejpam-6776	399	6	,	,	PUNCT
ejpam-6776	399	7	18	18	NUM
ejpam-6776	399	8	(	(	PUNCT
ejpam-6776	399	9	4	4	NUM
ejpam-6776	399	10	)	)	PUNCT
ejpam-6776	399	11	(	(	PUNCT
ejpam-6776	399	12	2025	2025	NUM
ejpam-6776	399	13	)	)	PUNCT
ejpam-6776	399	14	,	,	PUNCT
ejpam-6776	399	15	6776	6776	NUM
ejpam-6776	399	16	17	17	NUM
ejpam-6776	399	17	of	of	ADP
ejpam-6776	399	18	22	22	NUM
ejpam-6776	399	19	figure	figure	NOUN
ejpam-6776	399	20	1	1	NUM
ejpam-6776	399	21	:	:	PUNCT
ejpam-6776	399	22	comparison	comparison	NOUN
ejpam-6776	399	23	of	of	ADP
ejpam-6776	399	24	deterministic	deterministic	ADJ
ejpam-6776	399	25	and	and	CCONJ
ejpam-6776	399	26	stochastic	stochastic	ADJ
ejpam-6776	399	27	dynamics	dynamic	NOUN
ejpam-6776	399	28	for	for	ADP
ejpam-6776	399	29	example	example	NOUN
ejpam-6776	399	30	1	1	NUM
ejpam-6776	399	31	.	.	PUNCT
ejpam-6776	400	1	the	the	DET
ejpam-6776	400	2	deterministic	deterministic	ADJ
ejpam-6776	400	3	trajectory	trajectory	NOUN
ejpam-6776	400	4	(	(	PUNCT
ejpam-6776	400	5	blue	blue	ADJ
ejpam-6776	400	6	)	)	PUNCT
ejpam-6776	400	7	converges	converge	NOUN
ejpam-6776	400	8	to	to	ADP
ejpam-6776	400	9	the	the	DET
ejpam-6776	400	10	endemic	endemic	ADJ
ejpam-6776	400	11	equilibrium	equilibrium	NOUN
ejpam-6776	400	12	e2	e2	NOUN
ejpam-6776	400	13	,	,	PUNCT
ejpam-6776	400	14	while	while	SCONJ
ejpam-6776	400	15	the	the	DET
ejpam-6776	400	16	stochastic	stochastic	ADJ
ejpam-6776	400	17	trajectory	trajectory	NOUN
ejpam-6776	400	18	(	(	PUNCT
ejpam-6776	400	19	red	red	ADJ
ejpam-6776	400	20	)	)	PUNCT
ejpam-6776	400	21	approaches	approach	VERB
ejpam-6776	400	22	the	the	DET
ejpam-6776	400	23	disease	disease	NOUN
ejpam-6776	400	24	-	-	PUNCT
ejpam-6776	400	25	free	free	ADJ
ejpam-6776	400	26	equilibrium	equilibrium	NOUN
ejpam-6776	400	27	e0	e0	PROPN
ejpam-6776	400	28	,	,	PUNCT
ejpam-6776	400	29	illustrating	illustrate	VERB
ejpam-6776	400	30	theorem	theorem	NOUN
ejpam-6776	400	31	4	4	NUM
ejpam-6776	400	32	with	with	ADP
ejpam-6776	400	33	η	η	PROPN
ejpam-6776	400	34	=	=	PROPN
ejpam-6776	401	1	−0.25	−0.25	PROPN
ejpam-6776	401	2	<	<	X
ejpam-6776	401	3	0	0	X
ejpam-6776	401	4	.	.	PUNCT
ejpam-6776	402	1	bifurcation	bifurcation	NOUN
ejpam-6776	402	2	analysis	analysis	NOUN
ejpam-6776	402	3	reveals	reveal	VERB
ejpam-6776	402	4	how	how	SCONJ
ejpam-6776	402	5	λ	λ	NOUN
ejpam-6776	402	6	and	and	CCONJ
ejpam-6776	402	7	α	α	PRON
ejpam-6776	402	8	shape	shape	NOUN
ejpam-6776	402	9	the	the	DET
ejpam-6776	402	10	long	long	ADJ
ejpam-6776	402	11	-	-	PUNCT
ejpam-6776	402	12	term	term	NOUN
ejpam-6776	402	13	infected	infected	ADJ
ejpam-6776	402	14	population	population	NOUN
ejpam-6776	402	15	size	size	NOUN
ejpam-6776	402	16	.	.	PUNCT
ejpam-6776	403	1	we	we	PRON
ejpam-6776	403	2	generate	generate	VERB
ejpam-6776	403	3	bifurcation	bifurcation	NOUN
ejpam-6776	403	4	surfaces	surface	NOUN
ejpam-6776	403	5	for	for	ADP
ejpam-6776	403	6	both	both	CCONJ
ejpam-6776	403	7	deterministic	deterministic	ADJ
ejpam-6776	403	8	(	(	PUNCT
ejpam-6776	403	9	1.1	1.1	NUM
ejpam-6776	403	10	)	)	PUNCT
ejpam-6776	403	11	and	and	CCONJ
ejpam-6776	403	12	stochastic	stochastic	ADJ
ejpam-6776	403	13	(	(	PUNCT
ejpam-6776	403	14	1.2	1.2	NUM
ejpam-6776	403	15	)	)	PUNCT
ejpam-6776	403	16	systems	system	NOUN
ejpam-6776	403	17	,	,	PUNCT
ejpam-6776	403	18	varying	vary	VERB
ejpam-6776	403	19	λ	λ	PROPN
ejpam-6776	403	20	∈	∈	PROPN
ejpam-6776	404	1	[	[	X
ejpam-6776	404	2	1	1	NUM
ejpam-6776	404	3	,	,	PUNCT
ejpam-6776	404	4	10	10	NUM
ejpam-6776	404	5	]	]	PUNCT
ejpam-6776	404	6	and	and	CCONJ
ejpam-6776	404	7	α	α	PRON
ejpam-6776	404	8	∈	∈	PROPN
ejpam-6776	405	1	[	[	X
ejpam-6776	405	2	0	0	NUM
ejpam-6776	405	3	,	,	PUNCT
ejpam-6776	405	4	10	10	NUM
ejpam-6776	405	5	]	]	PUNCT
ejpam-6776	405	6	.	.	PUNCT
ejpam-6776	406	1	figure	figure	NOUN
ejpam-6776	406	2	2a	2a	PROPN
ejpam-6776	406	3	shows	show	VERB
ejpam-6776	406	4	the	the	DET
ejpam-6776	406	5	deterministic	deterministic	ADJ
ejpam-6776	406	6	bifurcation	bifurcation	NOUN
ejpam-6776	406	7	surface	surface	NOUN
ejpam-6776	406	8	,	,	PUNCT
ejpam-6776	406	9	displaying	display	VERB
ejpam-6776	406	10	regions	region	NOUN
ejpam-6776	406	11	of	of	ADP
ejpam-6776	406	12	extinction	extinction	NOUN
ejpam-6776	406	13	and	and	CCONJ
ejpam-6776	406	14	persistence	persistence	NOUN
ejpam-6776	406	15	,	,	PUNCT
ejpam-6776	406	16	with	with	ADP
ejpam-6776	406	17	transitions	transition	NOUN
ejpam-6776	406	18	corresponding	correspond	VERB
ejpam-6776	406	19	to	to	AUX
ejpam-6776	406	20	r0	r0	VERB
ejpam-6776	406	21	=	=	NOUN
ejpam-6776	406	22	1	1	X
ejpam-6776	406	23	.	.	PUNCT
ejpam-6776	406	24	figure	figure	NOUN
ejpam-6776	406	25	2b	2b	PROPN
ejpam-6776	406	26	presents	present	VERB
ejpam-6776	406	27	the	the	DET
ejpam-6776	406	28	stochastic	stochastic	ADJ
ejpam-6776	406	29	counterpart	counterpart	NOUN
ejpam-6776	406	30	,	,	PUNCT
ejpam-6776	406	31	where	where	SCONJ
ejpam-6776	406	32	noise	noise	NOUN
ejpam-6776	406	33	smooths	smooth	VERB
ejpam-6776	406	34	transitions	transition	NOUN
ejpam-6776	406	35	and	and	CCONJ
ejpam-6776	406	36	expands	expand	VERB
ejpam-6776	406	37	the	the	DET
ejpam-6776	406	38	extinction	extinction	NOUN
ejpam-6776	406	39	region	region	NOUN
ejpam-6776	406	40	,	,	PUNCT
ejpam-6776	406	41	highlighting	highlight	VERB
ejpam-6776	406	42	stochasticity	stochasticity	NOUN
ejpam-6776	406	43	’s	’s	PART
ejpam-6776	406	44	role	role	NOUN
ejpam-6776	406	45	in	in	ADP
ejpam-6776	406	46	epidemic	epidemic	NOUN
ejpam-6776	406	47	control	control	NOUN
ejpam-6776	406	48	.	.	PUNCT
ejpam-6776	407	1	4.3	4.3	NUM
ejpam-6776	407	2	.	.	PUNCT
ejpam-6776	407	3	example	example	NOUN
ejpam-6776	407	4	3	3	NUM
ejpam-6776	407	5	:	:	PUNCT
ejpam-6776	407	6	extinction	extinction	NOUN
ejpam-6776	407	7	vs.	vs.	ADP
ejpam-6776	407	8	persistence	persistence	NOUN
ejpam-6776	407	9	we	we	PRON
ejpam-6776	407	10	demonstrate	demonstrate	VERB
ejpam-6776	407	11	the	the	DET
ejpam-6776	407	12	implications	implication	NOUN
ejpam-6776	407	13	of	of	ADP
ejpam-6776	407	14	theorems	theorem	NOUN
ejpam-6776	407	15	1	1	NUM
ejpam-6776	407	16	and	and	CCONJ
ejpam-6776	407	17	4	4	NUM
ejpam-6776	407	18	by	by	ADP
ejpam-6776	407	19	considering	consider	VERB
ejpam-6776	407	20	the	the	DET
ejpam-6776	407	21	parameters	parameter	NOUN
ejpam-6776	407	22	:	:	PUNCT
ejpam-6776	407	23	λ	λ	X
ejpam-6776	407	24	=	=	SYM
ejpam-6776	407	25	15	15	NUM
ejpam-6776	407	26	,	,	PUNCT
ejpam-6776	407	27	δ	δ	X
ejpam-6776	407	28	=	=	SYM
ejpam-6776	407	29	0.09	0.09	NUM
ejpam-6776	407	30	,	,	PUNCT
ejpam-6776	407	31	γ	γ	X
ejpam-6776	407	32	=	=	SYM
ejpam-6776	407	33	0.015	0.015	NUM
ejpam-6776	407	34	,	,	PUNCT
ejpam-6776	407	35	ϵ	ϵ	X
ejpam-6776	407	36	=	=	PUNCT
ejpam-6776	407	37	0.025	0.025	NUM
ejpam-6776	407	38	,	,	PUNCT
ejpam-6776	407	39	k	k	PROPN
ejpam-6776	407	40	=	=	PUNCT
ejpam-6776	407	41	0.012	0.012	NUM
ejpam-6776	407	42	,	,	PUNCT
ejpam-6776	407	43	β	β	X
ejpam-6776	407	44	=	=	NOUN
ejpam-6776	407	45	0.0028	0.0028	NUM
ejpam-6776	407	46	,	,	PUNCT
ejpam-6776	407	47	with	with	ADP
ejpam-6776	407	48	(	(	PUNCT
ejpam-6776	407	49	α	α	X
ejpam-6776	407	50	,	,	PUNCT
ejpam-6776	407	51	λ	λ	NOUN
ejpam-6776	407	52	)	)	PUNCT
ejpam-6776	407	53	∈	∈	PROPN
ejpam-6776	407	54	o1	o1	NOUN
ejpam-6776	407	55	∪	∪	X
ejpam-6776	407	56	o2	o2	PROPN
ejpam-6776	407	57	,	,	PUNCT
ejpam-6776	407	58	and	and	CCONJ
ejpam-6776	407	59	noise	noise	NOUN
ejpam-6776	407	60	levels	level	NOUN
ejpam-6776	407	61	σ	σ	PROPN
ejpam-6776	407	62	∈	∈	PROPN
ejpam-6776	407	63	{	{	PUNCT
ejpam-6776	407	64	0.001	0.001	NUM
ejpam-6776	407	65	,	,	PUNCT
ejpam-6776	407	66	0.003	0.003	NUM
ejpam-6776	407	67	}	}	PUNCT
ejpam-6776	407	68	.	.	PUNCT
ejpam-6776	408	1	for	for	ADP
ejpam-6776	408	2	σ	σ	PROPN
ejpam-6776	408	3	=	=	SYM
ejpam-6776	408	4	0.001	0.001	NUM
ejpam-6776	408	5	,	,	PUNCT
ejpam-6776	408	6	η	η	PROPN
ejpam-6776	408	7	=	=	PROPN
ejpam-6776	408	8	0.20	0.20	NUM
ejpam-6776	408	9	>	>	X
ejpam-6776	408	10	0	0	NUM
ejpam-6776	408	11	,	,	PUNCT
ejpam-6776	408	12	showing	show	VERB
ejpam-6776	408	13	persistence	persistence	NOUN
ejpam-6776	408	14	(	(	PUNCT
ejpam-6776	408	15	figure	figure	NOUN
ejpam-6776	408	16	3b	3b	NUM
ejpam-6776	408	17	)	)	PUNCT
ejpam-6776	408	18	.	.	PUNCT
ejpam-6776	409	1	for	for	ADP
ejpam-6776	409	2	σ	σ	PROPN
ejpam-6776	409	3	=	=	SYM
ejpam-6776	409	4	0.003	0.003	NUM
ejpam-6776	409	5	,	,	PUNCT
ejpam-6776	409	6	η	η	X
ejpam-6776	409	7	=	=	PROPN
ejpam-6776	409	8	−0.20	−0.20	PROPN
ejpam-6776	409	9	<	<	X
ejpam-6776	409	10	0	0	PROPN
ejpam-6776	409	11	,	,	PUNCT
ejpam-6776	409	12	showing	show	VERB
ejpam-6776	409	13	extinction	extinction	NOUN
ejpam-6776	409	14	(	(	PUNCT
ejpam-6776	409	15	figure	figure	NOUN
ejpam-6776	409	16	3a	3a	NUM
ejpam-6776	409	17	)	)	PUNCT
ejpam-6776	409	18	.	.	PUNCT
ejpam-6776	410	1	j.	j.	PROPN
ejpam-6776	410	2	leo	leo	PROPN
ejpam-6776	410	3	amalraj	amalraj	PROPN
ejpam-6776	410	4	et	et	PROPN
ejpam-6776	410	5	al	al	PROPN
ejpam-6776	410	6	.	.	PUNCT
ejpam-6776	410	7	/	/	SYM
ejpam-6776	410	8	eur	eur	PROPN
ejpam-6776	410	9	.	.	PUNCT
ejpam-6776	411	1	j.	j.	PROPN
ejpam-6776	411	2	pure	pure	PROPN
ejpam-6776	411	3	appl	appl	PROPN
ejpam-6776	411	4	.	.	PROPN
ejpam-6776	411	5	math	math	PROPN
ejpam-6776	411	6	,	,	PUNCT
ejpam-6776	411	7	18	18	NUM
ejpam-6776	411	8	(	(	PUNCT
ejpam-6776	411	9	4	4	NUM
ejpam-6776	411	10	)	)	PUNCT
ejpam-6776	411	11	(	(	PUNCT
ejpam-6776	411	12	2025	2025	NUM
ejpam-6776	411	13	)	)	PUNCT
ejpam-6776	411	14	,	,	PUNCT
ejpam-6776	411	15	6776	6776	NUM
ejpam-6776	411	16	18	18	NUM
ejpam-6776	411	17	of	of	ADP
ejpam-6776	411	18	22	22	NUM
ejpam-6776	411	19	(	(	PUNCT
ejpam-6776	411	20	a	a	NOUN
ejpam-6776	411	21	)	)	PUNCT
ejpam-6776	411	22	deterministic	deterministic	ADJ
ejpam-6776	411	23	bifurcation	bifurcation	NOUN
ejpam-6776	411	24	surface	surface	NOUN
ejpam-6776	411	25	for	for	ADP
ejpam-6776	411	26	the	the	DET
ejpam-6776	411	27	infected	infected	ADJ
ejpam-6776	411	28	population	population	NOUN
ejpam-6776	411	29	as	as	ADP
ejpam-6776	411	30	a	a	DET
ejpam-6776	411	31	function	function	NOUN
ejpam-6776	411	32	of	of	ADP
ejpam-6776	411	33	λ	λ	PROPN
ejpam-6776	411	34	and	and	CCONJ
ejpam-6776	411	35	α	α	NOUN
ejpam-6776	411	36	.	.	PUNCT
ejpam-6776	412	1	sharp	sharp	ADJ
ejpam-6776	412	2	transitions	transition	NOUN
ejpam-6776	412	3	indicate	indicate	VERB
ejpam-6776	412	4	bifurcation	bifurcation	NOUN
ejpam-6776	412	5	boundaries	boundary	NOUN
ejpam-6776	412	6	.	.	PUNCT
ejpam-6776	413	1	(	(	PUNCT
ejpam-6776	413	2	b	b	X
ejpam-6776	413	3	)	)	PUNCT
ejpam-6776	413	4	stochastic	stochastic	ADJ
ejpam-6776	413	5	bifurcation	bifurcation	NOUN
ejpam-6776	413	6	surface	surface	NOUN
ejpam-6776	413	7	,	,	PUNCT
ejpam-6776	413	8	showing	show	VERB
ejpam-6776	413	9	smoothed	smooth	VERB
ejpam-6776	413	10	transitions	transition	NOUN
ejpam-6776	413	11	and	and	CCONJ
ejpam-6776	413	12	an	an	DET
ejpam-6776	413	13	expanded	expand	VERB
ejpam-6776	413	14	extinction	extinction	NOUN
ejpam-6776	413	15	region	region	NOUN
ejpam-6776	413	16	due	due	ADP
ejpam-6776	413	17	to	to	ADP
ejpam-6776	413	18	noise	noise	NOUN
ejpam-6776	413	19	(	(	PUNCT
ejpam-6776	413	20	σ	σ	NOUN
ejpam-6776	413	21	=	=	SYM
ejpam-6776	413	22	0.0015	0.0015	NUM
ejpam-6776	413	23	)	)	PUNCT
ejpam-6776	413	24	.	.	PUNCT
ejpam-6776	414	1	figure	figure	VERB
ejpam-6776	414	2	2	2	NUM
ejpam-6776	414	3	:	:	PUNCT
ejpam-6776	414	4	bifurcation	bifurcation	NOUN
ejpam-6776	414	5	surfaces	surface	NOUN
ejpam-6776	414	6	for	for	ADP
ejpam-6776	414	7	example	example	NOUN
ejpam-6776	414	8	2	2	NUM
ejpam-6776	414	9	,	,	PUNCT
ejpam-6776	414	10	comparing	compare	VERB
ejpam-6776	414	11	deterministic	deterministic	ADJ
ejpam-6776	414	12	and	and	CCONJ
ejpam-6776	414	13	stochastic	stochastic	ADJ
ejpam-6776	414	14	dynamics	dynamic	NOUN
ejpam-6776	414	15	of	of	ADP
ejpam-6776	414	16	system	system	NOUN
ejpam-6776	414	17	(	(	PUNCT
ejpam-6776	414	18	1.2	1.2	NUM
ejpam-6776	414	19	)	)	PUNCT
ejpam-6776	414	20	.	.	PUNCT
ejpam-6776	415	1	(	(	PUNCT
ejpam-6776	415	2	a	a	X
ejpam-6776	415	3	)	)	PUNCT
ejpam-6776	415	4	disease	disease	NOUN
ejpam-6776	415	5	extinction	extinction	NOUN
ejpam-6776	415	6	with	with	ADP
ejpam-6776	415	7	σ	σ	PROPN
ejpam-6776	415	8	=	=	SYM
ejpam-6776	415	9	0.0025	0.0025	NUM
ejpam-6776	415	10	,	,	PUNCT
ejpam-6776	415	11	η	η	X
ejpam-6776	415	12	=	=	PUNCT
ejpam-6776	415	13	−0.18	−0.18	ADP
ejpam-6776	415	14	<	<	X
ejpam-6776	415	15	0	0	NUM
ejpam-6776	415	16	,	,	PUNCT
ejpam-6776	415	17	per	per	ADP
ejpam-6776	415	18	theorem	theorem	NOUN
ejpam-6776	415	19	4	4	NUM
ejpam-6776	415	20	.	.	PUNCT
ejpam-6776	415	21	(	(	PUNCT
ejpam-6776	415	22	b	b	X
ejpam-6776	415	23	)	)	PUNCT
ejpam-6776	415	24	disease	disease	NOUN
ejpam-6776	415	25	persistence	persistence	NOUN
ejpam-6776	415	26	with	with	ADP
ejpam-6776	415	27	σ	σ	PROPN
ejpam-6776	415	28	=	=	SYM
ejpam-6776	415	29	0.0012	0.0012	NUM
ejpam-6776	415	30	,	,	PUNCT
ejpam-6776	415	31	η	η	X
ejpam-6776	415	32	=	=	PROPN
ejpam-6776	415	33	0.15	0.15	NUM
ejpam-6776	415	34	>	>	X
ejpam-6776	415	35	0	0	NUM
ejpam-6776	415	36	,	,	PUNCT
ejpam-6776	415	37	per	per	ADP
ejpam-6776	415	38	theorem	theorem	NOUN
ejpam-6776	415	39	1	1	NUM
ejpam-6776	415	40	.	.	PUNCT
ejpam-6776	415	41	figure	figure	NOUN
ejpam-6776	415	42	3	3	NUM
ejpam-6776	415	43	:	:	PUNCT
ejpam-6776	415	44	stochastic	stochastic	ADJ
ejpam-6776	415	45	trajectories	trajectory	NOUN
ejpam-6776	415	46	for	for	ADP
ejpam-6776	415	47	example	example	NOUN
ejpam-6776	415	48	3	3	NUM
ejpam-6776	415	49	,	,	PUNCT
ejpam-6776	415	50	illustrating	illustrate	VERB
ejpam-6776	415	51	extinction	extinction	NOUN
ejpam-6776	415	52	and	and	CCONJ
ejpam-6776	415	53	persistence	persistence	NOUN
ejpam-6776	415	54	under	under	ADP
ejpam-6776	415	55	different	different	ADJ
ejpam-6776	415	56	noise	noise	NOUN
ejpam-6776	415	57	levels	level	NOUN
ejpam-6776	415	58	.	.	PUNCT
ejpam-6776	416	1	j.	j.	PROPN
ejpam-6776	416	2	leo	leo	PROPN
ejpam-6776	416	3	amalraj	amalraj	PROPN
ejpam-6776	416	4	et	et	PROPN
ejpam-6776	416	5	al	al	PROPN
ejpam-6776	416	6	.	.	PUNCT
ejpam-6776	416	7	/	/	SYM
ejpam-6776	416	8	eur	eur	PROPN
ejpam-6776	416	9	.	.	PUNCT
ejpam-6776	417	1	j.	j.	PROPN
ejpam-6776	417	2	pure	pure	PROPN
ejpam-6776	417	3	appl	appl	PROPN
ejpam-6776	417	4	.	.	PROPN
ejpam-6776	417	5	math	math	PROPN
ejpam-6776	417	6	,	,	PUNCT
ejpam-6776	417	7	18	18	NUM
ejpam-6776	417	8	(	(	PUNCT
ejpam-6776	417	9	4	4	NUM
ejpam-6776	417	10	)	)	PUNCT
ejpam-6776	417	11	(	(	PUNCT
ejpam-6776	417	12	2025	2025	NUM
ejpam-6776	417	13	)	)	PUNCT
ejpam-6776	417	14	,	,	PUNCT
ejpam-6776	417	15	6776	6776	NUM
ejpam-6776	417	16	19	19	NUM
ejpam-6776	417	17	of	of	ADP
ejpam-6776	417	18	22	22	NUM
ejpam-6776	417	19	5	5	NUM
ejpam-6776	417	20	.	.	PUNCT
ejpam-6776	418	1	summary	summary	NOUN
ejpam-6776	418	2	and	and	CCONJ
ejpam-6776	418	3	outlook	outlook	NOUN
ejpam-6776	418	4	this	this	DET
ejpam-6776	418	5	study	study	NOUN
ejpam-6776	418	6	explored	explore	VERB
ejpam-6776	418	7	the	the	DET
ejpam-6776	418	8	dynamics	dynamic	NOUN
ejpam-6776	418	9	of	of	ADP
ejpam-6776	418	10	a	a	DET
ejpam-6776	418	11	stochastic	stochastic	ADJ
ejpam-6776	418	12	sir	sir	NOUN
ejpam-6776	418	13	epidemic	epidemic	NOUN
ejpam-6776	418	14	model	model	NOUN
ejpam-6776	418	15	with	with	ADP
ejpam-6776	418	16	nonlinear	nonlinear	ADJ
ejpam-6776	418	17	incidence	incidence	NOUN
ejpam-6776	418	18	,	,	PUNCT
ejpam-6776	418	19	limited	limited	ADJ
ejpam-6776	418	20	medical	medical	ADJ
ejpam-6776	418	21	resources	resource	NOUN
ejpam-6776	418	22	,	,	PUNCT
ejpam-6776	418	23	and	and	CCONJ
ejpam-6776	418	24	environmental	environmental	ADJ
ejpam-6776	418	25	noise	noise	NOUN
ejpam-6776	418	26	.	.	PUNCT
ejpam-6776	419	1	theoretical	theoretical	ADJ
ejpam-6776	419	2	analysis	analysis	NOUN
ejpam-6776	419	3	established	establish	VERB
ejpam-6776	419	4	conditions	condition	NOUN
ejpam-6776	419	5	for	for	ADP
ejpam-6776	419	6	persistence	persistence	NOUN
ejpam-6776	419	7	,	,	PUNCT
ejpam-6776	419	8	ergodicity	ergodicity	NOUN
ejpam-6776	419	9	,	,	PUNCT
ejpam-6776	419	10	and	and	CCONJ
ejpam-6776	419	11	extinction	extinction	NOUN
ejpam-6776	419	12	,	,	PUNCT
ejpam-6776	419	13	while	while	SCONJ
ejpam-6776	419	14	numerical	numerical	ADJ
ejpam-6776	419	15	simulations	simulation	NOUN
ejpam-6776	419	16	demonstrated	demonstrate	VERB
ejpam-6776	419	17	noise	noise	NOUN
ejpam-6776	419	18	’s	’s	PART
ejpam-6776	419	19	role	role	NOUN
ejpam-6776	419	20	in	in	ADP
ejpam-6776	419	21	eliminating	eliminate	VERB
ejpam-6776	419	22	backward	backward	ADJ
ejpam-6776	419	23	and	and	CCONJ
ejpam-6776	419	24	hopf	hopf	ADJ
ejpam-6776	419	25	bifurcations	bifurcation	NOUN
ejpam-6776	419	26	common	common	ADJ
ejpam-6776	419	27	in	in	ADP
ejpam-6776	419	28	deterministic	deterministic	ADJ
ejpam-6776	419	29	counterparts	counterpart	NOUN
ejpam-6776	419	30	.	.	PUNCT
ejpam-6776	420	1	our	our	PRON
ejpam-6776	420	2	findings	finding	NOUN
ejpam-6776	420	3	underscore	underscore	VERB
ejpam-6776	420	4	how	how	SCONJ
ejpam-6776	420	5	resource	resource	NOUN
ejpam-6776	420	6	constraints	constraint	NOUN
ejpam-6776	420	7	shape	shape	VERB
ejpam-6776	420	8	epidemic	epidemic	NOUN
ejpam-6776	420	9	trajectories	trajectory	NOUN
ejpam-6776	420	10	under	under	ADP
ejpam-6776	420	11	stochasticity	stochasticity	NOUN
ejpam-6776	420	12	,	,	PUNCT
ejpam-6776	420	13	providing	provide	VERB
ejpam-6776	420	14	actionable	actionable	ADJ
ejpam-6776	420	15	insights	insight	NOUN
ejpam-6776	420	16	for	for	ADP
ejpam-6776	420	17	public	public	ADJ
ejpam-6776	420	18	health	health	NOUN
ejpam-6776	420	19	.	.	PUNCT
ejpam-6776	421	1	incorporating	incorporate	VERB
ejpam-6776	421	2	randomness	randomness	NOUN
ejpam-6776	421	3	enhances	enhance	VERB
ejpam-6776	421	4	model	model	NOUN
ejpam-6776	421	5	realism	realism	NOUN
ejpam-6776	421	6	,	,	PUNCT
ejpam-6776	421	7	aiding	aid	VERB
ejpam-6776	421	8	adaptive	adaptive	ADJ
ejpam-6776	421	9	strategies	strategy	NOUN
ejpam-6776	421	10	in	in	ADP
ejpam-6776	421	11	uncertain	uncertain	ADJ
ejpam-6776	421	12	environments	environment	NOUN
ejpam-6776	421	13	.	.	PUNCT
ejpam-6776	422	1	future	future	ADJ
ejpam-6776	422	2	work	work	NOUN
ejpam-6776	422	3	should	should	AUX
ejpam-6776	422	4	extend	extend	VERB
ejpam-6776	422	5	the	the	DET
ejpam-6776	422	6	model	model	NOUN
ejpam-6776	422	7	to	to	PART
ejpam-6776	422	8	include	include	VERB
ejpam-6776	422	9	spatial	spatial	ADJ
ejpam-6776	422	10	diffusion	diffusion	NOUN
ejpam-6776	422	11	,	,	PUNCT
ejpam-6776	422	12	time	time	NOUN
ejpam-6776	422	13	delays	delay	NOUN
ejpam-6776	422	14	,	,	PUNCT
ejpam-6776	422	15	heterogeneous	heterogeneous	ADJ
ejpam-6776	422	16	populations	population	NOUN
ejpam-6776	422	17	,	,	PUNCT
ejpam-6776	422	18	and	and	CCONJ
ejpam-6776	422	19	evolving	evolve	VERB
ejpam-6776	422	20	pathogens	pathogen	NOUN
ejpam-6776	422	21	.	.	PUNCT
ejpam-6776	423	1	empirical	empirical	ADJ
ejpam-6776	423	2	validation	validation	NOUN
ejpam-6776	423	3	with	with	ADP
ejpam-6776	423	4	real	real	ADJ
ejpam-6776	423	5	-	-	PUNCT
ejpam-6776	423	6	world	world	NOUN
ejpam-6776	423	7	data	datum	NOUN
ejpam-6776	423	8	,	,	PUNCT
ejpam-6776	423	9	such	such	ADJ
ejpam-6776	423	10	as	as	ADP
ejpam-6776	423	11	from	from	ADP
ejpam-6776	423	12	recent	recent	ADJ
ejpam-6776	423	13	outbreaks	outbreak	NOUN
ejpam-6776	423	14	,	,	PUNCT
ejpam-6776	423	15	will	will	AUX
ejpam-6776	423	16	refine	refine	VERB
ejpam-6776	423	17	parameters	parameter	NOUN
ejpam-6776	423	18	and	and	CCONJ
ejpam-6776	423	19	align	align	VERB
ejpam-6776	423	20	predictions	prediction	NOUN
ejpam-6776	423	21	with	with	ADP
ejpam-6776	423	22	observed	observed	ADJ
ejpam-6776	423	23	dynamics	dynamic	NOUN
ejpam-6776	423	24	,	,	PUNCT
ejpam-6776	423	25	fostering	foster	VERB
ejpam-6776	423	26	effective	effective	ADJ
ejpam-6776	423	27	interventions	intervention	NOUN
ejpam-6776	423	28	.	.	PUNCT
ejpam-6776	424	1	funding	fund	VERB
ejpam-6776	424	2	this	this	DET
ejpam-6776	424	3	research	research	NOUN
ejpam-6776	424	4	was	be	AUX
ejpam-6776	424	5	supported	support	VERB
ejpam-6776	424	6	by	by	ADP
ejpam-6776	424	7	university	university	NOUN
ejpam-6776	424	8	of	of	ADP
ejpam-6776	424	9	phayao	phayao	NOUN
ejpam-6776	424	10	and	and	CCONJ
ejpam-6776	424	11	thailand	thailand	PROPN
ejpam-6776	424	12	science	science	PROPN
ejpam-6776	424	13	research	research	PROPN
ejpam-6776	424	14	and	and	CCONJ
ejpam-6776	424	15	innovation	innovation	NOUN
ejpam-6776	424	16	fund	fund	NOUN
ejpam-6776	424	17	(	(	PUNCT
ejpam-6776	424	18	fundamental	fundamental	ADJ
ejpam-6776	424	19	fund	fund	NOUN
ejpam-6776	424	20	2026	2026	NUM
ejpam-6776	424	21	,	,	PUNCT
ejpam-6776	424	22	grant	grant	VERB
ejpam-6776	424	23	no	no	NOUN
ejpam-6776	424	24	.	.	PUNCT
ejpam-6776	424	25	xxxx/2568	xxxx/2568	PROPN
ejpam-6776	424	26	)	)	PUNCT
ejpam-6776	424	27	.	.	PUNCT
ejpam-6776	425	1	author	author	NOUN
ejpam-6776	425	2	contributions	contribution	NOUN
ejpam-6776	425	3	:	:	PUNCT
ejpam-6776	425	4	the	the	DET
ejpam-6776	425	5	authors	author	NOUN
ejpam-6776	425	6	equally	equally	ADV
ejpam-6776	425	7	conceived	conceive	VERB
ejpam-6776	425	8	of	of	ADP
ejpam-6776	425	9	the	the	DET
ejpam-6776	425	10	study	study	NOUN
ejpam-6776	425	11	,	,	PUNCT
ejpam-6776	425	12	participated	participate	VERB
ejpam-6776	425	13	in	in	ADP
ejpam-6776	425	14	its	its	PRON
ejpam-6776	425	15	design	design	NOUN
ejpam-6776	425	16	and	and	CCONJ
ejpam-6776	425	17	coordination	coordination	NOUN
ejpam-6776	425	18	,	,	PUNCT
ejpam-6776	425	19	drafted	draft	VERB
ejpam-6776	425	20	the	the	DET
ejpam-6776	425	21	manuscript	manuscript	NOUN
ejpam-6776	425	22	,	,	PUNCT
ejpam-6776	425	23	participated	participate	VERB
ejpam-6776	425	24	in	in	ADP
ejpam-6776	425	25	the	the	DET
ejpam-6776	425	26	sequence	sequence	NOUN
ejpam-6776	425	27	alignment	alignment	NOUN
ejpam-6776	425	28	,	,	PUNCT
ejpam-6776	425	29	and	and	CCONJ
ejpam-6776	425	30	read	read	VERB
ejpam-6776	425	31	and	and	CCONJ
ejpam-6776	425	32	approved	approve	VERB
ejpam-6776	425	33	the	the	DET
ejpam-6776	425	34	final	final	ADJ
ejpam-6776	425	35	manuscript	manuscript	NOUN
ejpam-6776	425	36	.	.	PUNCT
ejpam-6776	426	1	conflicts	conflict	NOUN
ejpam-6776	426	2	of	of	ADP
ejpam-6776	426	3	interest	interest	NOUN
ejpam-6776	426	4	:	:	PUNCT
ejpam-6776	426	5	the	the	DET
ejpam-6776	426	6	authors	author	NOUN
ejpam-6776	426	7	declare	declare	VERB
ejpam-6776	426	8	that	that	SCONJ
ejpam-6776	426	9	they	they	PRON
ejpam-6776	426	10	have	have	VERB
ejpam-6776	426	11	no	no	DET
ejpam-6776	426	12	competing	compete	VERB
ejpam-6776	426	13	interests	interest	NOUN
ejpam-6776	426	14	.	.	PUNCT
ejpam-6776	427	1	references	reference	NOUN
ejpam-6776	427	2	[	[	X
ejpam-6776	427	3	1	1	X
ejpam-6776	427	4	]	]	X
ejpam-6776	427	5	h.w	h.w	PROPN
ejpam-6776	427	6	.	.	PROPN
ejpam-6776	427	7	hethcote	hethcote	PROPN
ejpam-6776	427	8	.	.	PUNCT
ejpam-6776	428	1	qualitative	qualitative	ADJ
ejpam-6776	428	2	analyses	analysis	NOUN
ejpam-6776	428	3	of	of	ADP
ejpam-6776	428	4	communicable	communicable	NOUN
ejpam-6776	428	5	disease	disease	NOUN
ejpam-6776	428	6	models	model	NOUN
ejpam-6776	428	7	.	.	PUNCT
ejpam-6776	429	1	mathematical	mathematical	ADJ
ejpam-6776	429	2	biosciences	bioscience	NOUN
ejpam-6776	429	3	,	,	PUNCT
ejpam-6776	429	4	28(3	28(3	PROPN
ejpam-6776	429	5	-	-	PUNCT
ejpam-6776	429	6	4):335–356	4):335–356	NUM
ejpam-6776	429	7	,	,	PUNCT
ejpam-6776	429	8	1976	1976	NUM
ejpam-6776	429	9	.	.	PUNCT
ejpam-6776	430	1	[	[	X
ejpam-6776	430	2	2	2	NUM
ejpam-6776	430	3	]	]	X
ejpam-6776	430	4	y.	y.	PROPN
ejpam-6776	430	5	cai	cai	PROPN
ejpam-6776	430	6	,	,	PUNCT
ejpam-6776	430	7	j.	j.	PROPN
ejpam-6776	430	8	jiao	jiao	PROPN
ejpam-6776	430	9	,	,	PUNCT
ejpam-6776	430	10	z.	z.	PROPN
ejpam-6776	430	11	gui	gui	PROPN
ejpam-6776	430	12	,	,	PUNCT
ejpam-6776	430	13	y.	y.	PROPN
ejpam-6776	430	14	liu	liu	PROPN
ejpam-6776	430	15	,	,	PUNCT
ejpam-6776	430	16	andw.wang	andw.wang	PROPN
ejpam-6776	430	17	.	.	PUNCT
ejpam-6776	430	18	environmental	environmental	ADJ
ejpam-6776	430	19	variability	variability	NOUN
ejpam-6776	430	20	in	in	ADP
ejpam-6776	430	21	a	a	DET
ejpam-6776	430	22	stochastic	stochastic	ADJ
ejpam-6776	430	23	epidemic	epidemic	NOUN
ejpam-6776	430	24	model	model	NOUN
ejpam-6776	430	25	.	.	PUNCT
ejpam-6776	431	1	applied	apply	VERB
ejpam-6776	431	2	mathematics	mathematic	NOUN
ejpam-6776	431	3	and	and	CCONJ
ejpam-6776	431	4	computation	computation	NOUN
ejpam-6776	431	5	,	,	PUNCT
ejpam-6776	431	6	329:210–226	329:210–226	NUM
ejpam-6776	431	7	,	,	PUNCT
ejpam-6776	431	8	2018	2018	NUM
ejpam-6776	431	9	.	.	PUNCT
ejpam-6776	432	1	[	[	X
ejpam-6776	432	2	3	3	X
ejpam-6776	432	3	]	]	X
ejpam-6776	432	4	j.	j.	PROPN
ejpam-6776	432	5	muhammad	muhammad	PROPN
ejpam-6776	432	6	,	,	PUNCT
ejpam-6776	432	7	u.	u.	PROPN
ejpam-6776	432	8	younas	younas	PROPN
ejpam-6776	432	9	,	,	PUNCT
ejpam-6776	432	10	n.	n.	NOUN
ejpam-6776	432	11	nasreen	nasreen	PROPN
ejpam-6776	432	12	,	,	PUNCT
ejpam-6776	432	13	a.	a.	PROPN
ejpam-6776	432	14	khan	khan	PROPN
ejpam-6776	432	15	,	,	PUNCT
ejpam-6776	432	16	and	and	CCONJ
ejpam-6776	432	17	t.	t.	PROPN
ejpam-6776	432	18	abdeljawad	abdeljawad	NOUN
ejpam-6776	432	19	.	.	PUNCT
ejpam-6776	433	1	multicomponent	multicomponent	PROPN
ejpam-6776	433	2	nonlinear	nonlinear	ADJ
ejpam-6776	433	3	fractional	fractional	ADJ
ejpam-6776	433	4	schrödinger	schrödinger	NOUN
ejpam-6776	433	5	equation	equation	NOUN
ejpam-6776	433	6	:	:	PUNCT
ejpam-6776	433	7	on	on	ADP
ejpam-6776	433	8	the	the	DET
ejpam-6776	433	9	study	study	NOUN
ejpam-6776	433	10	of	of	ADP
ejpam-6776	433	11	optical	optical	ADJ
ejpam-6776	433	12	wave	wave	NOUN
ejpam-6776	433	13	propagation	propagation	NOUN
ejpam-6776	433	14	in	in	ADP
ejpam-6776	433	15	the	the	DET
ejpam-6776	433	16	fiber	fiber	NOUN
ejpam-6776	433	17	optics	optic	NOUN
ejpam-6776	433	18	.	.	PUNCT
ejpam-6776	434	1	partial	partial	ADJ
ejpam-6776	434	2	differential	differential	ADJ
ejpam-6776	434	3	equations	equation	NOUN
ejpam-6776	434	4	in	in	ADP
ejpam-6776	434	5	applied	applied	ADJ
ejpam-6776	434	6	mathematics	mathematic	NOUN
ejpam-6776	434	7	,	,	PUNCT
ejpam-6776	434	8	11:100805	11:100805	NUM
ejpam-6776	434	9	,	,	PUNCT
ejpam-6776	434	10	2024	2024	NUM
ejpam-6776	434	11	.	.	PUNCT
ejpam-6776	435	1	[	[	X
ejpam-6776	435	2	4	4	NUM
ejpam-6776	435	3	]	]	X
ejpam-6776	435	4	f.	f.	PROPN
ejpam-6776	435	5	brauer	brauer	PROPN
ejpam-6776	435	6	,	,	PUNCT
ejpam-6776	435	7	c.	c.	PROPN
ejpam-6776	435	8	castillo	castillo	PROPN
ejpam-6776	435	9	-	-	PUNCT
ejpam-6776	435	10	chavez	chavez	PROPN
ejpam-6776	435	11	,	,	PUNCT
ejpam-6776	435	12	z.	z.	PROPN
ejpam-6776	435	13	feng	feng	PROPN
ejpam-6776	435	14	,	,	PUNCT
ejpam-6776	435	15	f.	f.	PROPN
ejpam-6776	435	16	brauer	brauer	PROPN
ejpam-6776	435	17	,	,	PUNCT
ejpam-6776	435	18	c.	c.	PROPN
ejpam-6776	435	19	castillo	castillo	PROPN
ejpam-6776	435	20	-	-	PUNCT
ejpam-6776	435	21	chavez	chavez	PROPN
ejpam-6776	435	22	,	,	PUNCT
ejpam-6776	435	23	and	and	CCONJ
ejpam-6776	435	24	z.	z.	PROPN
ejpam-6776	435	25	feng	feng	PROPN
ejpam-6776	435	26	.	.	PUNCT
ejpam-6776	436	1	simple	simple	ADJ
ejpam-6776	436	2	compartmental	compartmental	ADJ
ejpam-6776	436	3	models	model	NOUN
ejpam-6776	436	4	for	for	ADP
ejpam-6776	436	5	disease	disease	NOUN
ejpam-6776	436	6	transmission	transmission	NOUN
ejpam-6776	436	7	.	.	PUNCT
ejpam-6776	437	1	in	in	ADP
ejpam-6776	437	2	mathematical	mathematical	ADJ
ejpam-6776	437	3	models	model	NOUN
ejpam-6776	437	4	in	in	ADP
ejpam-6776	437	5	epidemiology	epidemiology	NOUN
ejpam-6776	437	6	,	,	PUNCT
ejpam-6776	437	7	pages	page	NOUN
ejpam-6776	437	8	21–61	21–61	NUM
ejpam-6776	437	9	.	.	PUNCT
ejpam-6776	437	10	springer	springer	NOUN
ejpam-6776	437	11	,	,	PUNCT
ejpam-6776	437	12	2019	2019	NUM
ejpam-6776	437	13	.	.	PUNCT
ejpam-6776	438	1	[	[	X
ejpam-6776	438	2	5	5	X
ejpam-6776	438	3	]	]	PUNCT
ejpam-6776	438	4	s.	s.	PROPN
ejpam-6776	438	5	hottovy	hottovy	PROPN
ejpam-6776	438	6	and	and	CCONJ
ejpam-6776	438	7	s.n	s.n	PROPN
ejpam-6776	438	8	.	.	PROPN
ejpam-6776	438	9	stechmann	stechmann	PROPN
ejpam-6776	438	10	.	.	PUNCT
ejpam-6776	439	1	a	a	DET
ejpam-6776	439	2	spatiotemporal	spatiotemporal	ADJ
ejpam-6776	439	3	stochastic	stochastic	ADJ
ejpam-6776	439	4	model	model	NOUN
ejpam-6776	439	5	for	for	ADP
ejpam-6776	439	6	tropical	tropical	ADJ
ejpam-6776	439	7	precipitation	precipitation	NOUN
ejpam-6776	439	8	and	and	CCONJ
ejpam-6776	439	9	water	water	NOUN
ejpam-6776	439	10	vapor	vapor	NOUN
ejpam-6776	439	11	dynamics	dynamic	NOUN
ejpam-6776	439	12	.	.	PUNCT
ejpam-6776	440	1	journal	journal	NOUN
ejpam-6776	440	2	of	of	ADP
ejpam-6776	440	3	the	the	DET
ejpam-6776	440	4	atmospheric	atmospheric	PROPN
ejpam-6776	440	5	sciences	science	NOUN
ejpam-6776	440	6	,	,	PUNCT
ejpam-6776	440	7	72(12):4721–4738	72(12):4721–4738	NUM
ejpam-6776	440	8	,	,	PUNCT
ejpam-6776	440	9	2015	2015	NUM
ejpam-6776	440	10	.	.	PUNCT
ejpam-6776	441	1	j.	j.	PROPN
ejpam-6776	441	2	leo	leo	PROPN
ejpam-6776	441	3	amalraj	amalraj	PROPN
ejpam-6776	441	4	et	et	PROPN
ejpam-6776	441	5	al	al	PROPN
ejpam-6776	441	6	.	.	PUNCT
ejpam-6776	441	7	/	/	SYM
ejpam-6776	441	8	eur	eur	PROPN
ejpam-6776	441	9	.	.	PUNCT
ejpam-6776	442	1	j.	j.	PROPN
ejpam-6776	442	2	pure	pure	PROPN
ejpam-6776	442	3	appl	appl	PROPN
ejpam-6776	442	4	.	.	PROPN
ejpam-6776	442	5	math	math	PROPN
ejpam-6776	442	6	,	,	PUNCT
ejpam-6776	442	7	18	18	NUM
ejpam-6776	442	8	(	(	PUNCT
ejpam-6776	442	9	4	4	NUM
ejpam-6776	442	10	)	)	PUNCT
ejpam-6776	442	11	(	(	PUNCT
ejpam-6776	442	12	2025	2025	NUM
ejpam-6776	442	13	)	)	PUNCT
ejpam-6776	442	14	,	,	PUNCT
ejpam-6776	442	15	6776	6776	NUM
ejpam-6776	442	16	20	20	NUM
ejpam-6776	442	17	of	of	ADP
ejpam-6776	442	18	22	22	NUM
ejpam-6776	443	1	[	[	X
ejpam-6776	443	2	6	6	NUM
ejpam-6776	443	3	]	]	PUNCT
ejpam-6776	443	4	g.	g.	PROPN
ejpam-6776	443	5	lan	lan	PROPN
ejpam-6776	443	6	,	,	PUNCT
ejpam-6776	443	7	b.	b.	PROPN
ejpam-6776	443	8	song	song	PROPN
ejpam-6776	443	9	,	,	PUNCT
ejpam-6776	443	10	and	and	CCONJ
ejpam-6776	443	11	s.	s.	PROPN
ejpam-6776	443	12	yuan	yuan	PROPN
ejpam-6776	443	13	.	.	PUNCT
ejpam-6776	444	1	epidemic	epidemic	NOUN
ejpam-6776	444	2	threshold	threshold	NOUN
ejpam-6776	444	3	and	and	CCONJ
ejpam-6776	444	4	ergodicity	ergodicity	NOUN
ejpam-6776	444	5	of	of	ADP
ejpam-6776	444	6	an	an	DET
ejpam-6776	444	7	seir	seir	ADJ
ejpam-6776	444	8	model	model	NOUN
ejpam-6776	444	9	with	with	ADP
ejpam-6776	444	10	vertical	vertical	ADJ
ejpam-6776	444	11	transmission	transmission	NOUN
ejpam-6776	444	12	under	under	ADP
ejpam-6776	444	13	the	the	DET
ejpam-6776	444	14	telegraph	telegraph	NOUN
ejpam-6776	444	15	noise	noise	NOUN
ejpam-6776	444	16	.	.	PUNCT
ejpam-6776	445	1	chaos	chaos	NOUN
ejpam-6776	445	2	,	,	PUNCT
ejpam-6776	445	3	solitons	soliton	NOUN
ejpam-6776	445	4	and	and	CCONJ
ejpam-6776	445	5	fractals	fractal	NOUN
ejpam-6776	445	6	,	,	PUNCT
ejpam-6776	445	7	167:113017	167:113017	NUM
ejpam-6776	445	8	,	,	PUNCT
ejpam-6776	445	9	2023	2023	NUM
ejpam-6776	445	10	.	.	PUNCT
ejpam-6776	446	1	[	[	X
ejpam-6776	446	2	7	7	NUM
ejpam-6776	446	3	]	]	X
ejpam-6776	446	4	w.o	w.o	PROPN
ejpam-6776	446	5	.	.	PROPN
ejpam-6776	446	6	kermack	kermack	PROPN
ejpam-6776	446	7	and	and	CCONJ
ejpam-6776	446	8	a.g	a.g	PROPN
ejpam-6776	446	9	.	.	PROPN
ejpam-6776	446	10	mckendrick	mckendrick	PROPN
ejpam-6776	446	11	.	.	PUNCT
ejpam-6776	447	1	a	a	DET
ejpam-6776	447	2	contribution	contribution	NOUN
ejpam-6776	447	3	to	to	ADP
ejpam-6776	447	4	the	the	DET
ejpam-6776	447	5	mathematical	mathematical	ADJ
ejpam-6776	447	6	theory	theory	NOUN
ejpam-6776	447	7	of	of	ADP
ejpam-6776	447	8	epidemics	epidemic	NOUN
ejpam-6776	447	9	.	.	PUNCT
ejpam-6776	448	1	proceedings	proceeding	NOUN
ejpam-6776	448	2	of	of	ADP
ejpam-6776	448	3	the	the	DET
ejpam-6776	448	4	royal	royal	ADJ
ejpam-6776	448	5	society	society	NOUN
ejpam-6776	448	6	of	of	ADP
ejpam-6776	448	7	london	london	PROPN
ejpam-6776	448	8	.	.	PUNCT
ejpam-6776	449	1	series	series	PROPN
ejpam-6776	449	2	a	a	PROPN
ejpam-6776	449	3	,	,	PUNCT
ejpam-6776	449	4	containing	contain	VERB
ejpam-6776	449	5	papers	paper	NOUN
ejpam-6776	449	6	of	of	ADP
ejpam-6776	449	7	a	a	DET
ejpam-6776	449	8	mathematical	mathematical	ADJ
ejpam-6776	449	9	and	and	CCONJ
ejpam-6776	449	10	physical	physical	ADJ
ejpam-6776	449	11	character	character	NOUN
ejpam-6776	449	12	,	,	PUNCT
ejpam-6776	449	13	115(772):700–721	115(772):700–721	NUM
ejpam-6776	449	14	,	,	PUNCT
ejpam-6776	449	15	1927	1927	NUM
ejpam-6776	449	16	.	.	PUNCT
ejpam-6776	450	1	[	[	X
ejpam-6776	450	2	8	8	NUM
ejpam-6776	450	3	]	]	X
ejpam-6776	450	4	a.v	a.v	PROPN
ejpam-6776	450	5	.	.	PROPN
ejpam-6776	450	6	arundel	arundel	PROPN
ejpam-6776	450	7	,	,	PUNCT
ejpam-6776	450	8	e.m	e.m	PROPN
ejpam-6776	450	9	.	.	PROPN
ejpam-6776	450	10	sterling	sterling	PROPN
ejpam-6776	450	11	,	,	PUNCT
ejpam-6776	450	12	j.h	j.h	PROPN
ejpam-6776	450	13	.	.	PROPN
ejpam-6776	450	14	biggin	biggin	PROPN
ejpam-6776	450	15	,	,	PUNCT
ejpam-6776	450	16	and	and	CCONJ
ejpam-6776	450	17	t.d	t.d	PROPN
ejpam-6776	450	18	.	.	PUNCT
ejpam-6776	450	19	sterling	sterling	PROPN
ejpam-6776	450	20	.	.	PUNCT
ejpam-6776	451	1	indirect	indirect	ADJ
ejpam-6776	451	2	health	health	NOUN
ejpam-6776	451	3	effects	effect	NOUN
ejpam-6776	451	4	of	of	ADP
ejpam-6776	451	5	relative	relative	ADJ
ejpam-6776	451	6	humidity	humidity	NOUN
ejpam-6776	451	7	in	in	ADP
ejpam-6776	451	8	indoor	indoor	ADJ
ejpam-6776	451	9	environments	environment	NOUN
ejpam-6776	451	10	.	.	PUNCT
ejpam-6776	452	1	environmental	environmental	ADJ
ejpam-6776	452	2	health	health	NOUN
ejpam-6776	452	3	perspectives	perspective	NOUN
ejpam-6776	452	4	,	,	PUNCT
ejpam-6776	452	5	65:351	65:351	NOUN
ejpam-6776	452	6	–	–	PUNCT
ejpam-6776	452	7	361	361	NUM
ejpam-6776	452	8	,	,	PUNCT
ejpam-6776	452	9	1986	1986	NUM
ejpam-6776	452	10	.	.	PUNCT
ejpam-6776	453	1	[	[	X
ejpam-6776	453	2	9	9	NUM
ejpam-6776	453	3	]	]	SYM
ejpam-6776	453	4	s.m	s.m	PROPN
ejpam-6776	453	5	.	.	PROPN
ejpam-6776	453	6	ud	ud	PROPN
ejpam-6776	453	7	-	-	PUNCT
ejpam-6776	453	8	dean	dean	PROPN
ejpam-6776	453	9	.	.	PUNCT
ejpam-6776	454	1	structural	structural	ADJ
ejpam-6776	454	2	explanation	explanation	NOUN
ejpam-6776	454	3	for	for	ADP
ejpam-6776	454	4	the	the	DET
ejpam-6776	454	5	effect	effect	NOUN
ejpam-6776	454	6	of	of	ADP
ejpam-6776	454	7	humidity	humidity	NOUN
ejpam-6776	454	8	on	on	ADP
ejpam-6776	454	9	persistence	persistence	NOUN
ejpam-6776	454	10	of	of	ADP
ejpam-6776	454	11	airborne	airborne	ADJ
ejpam-6776	454	12	virus	virus	NOUN
ejpam-6776	454	13	:	:	PUNCT
ejpam-6776	454	14	seasonality	seasonality	NOUN
ejpam-6776	454	15	of	of	ADP
ejpam-6776	454	16	influenza	influenza	NOUN
ejpam-6776	454	17	.	.	PUNCT
ejpam-6776	455	1	journal	journal	NOUN
ejpam-6776	455	2	of	of	ADP
ejpam-6776	455	3	theoretical	theoretical	ADJ
ejpam-6776	455	4	biology	biology	NOUN
ejpam-6776	455	5	,	,	PUNCT
ejpam-6776	455	6	264(3):822	264(3):822	NUM
ejpam-6776	455	7	–	–	PUNCT
ejpam-6776	455	8	829	829	NUM
ejpam-6776	455	9	,	,	PUNCT
ejpam-6776	455	10	2010	2010	NUM
ejpam-6776	455	11	.	.	PUNCT
ejpam-6776	456	1	[	[	X
ejpam-6776	456	2	10	10	NUM
ejpam-6776	456	3	]	]	X
ejpam-6776	456	4	m.j	m.j	PROPN
ejpam-6776	456	5	.	.	PROPN
ejpam-6776	456	6	keeling	keeling	PROPN
ejpam-6776	456	7	and	and	CCONJ
ejpam-6776	456	8	p.	p.	PROPN
ejpam-6776	456	9	rohani	rohani	PROPN
ejpam-6776	456	10	.	.	PUNCT
ejpam-6776	457	1	modeling	model	VERB
ejpam-6776	457	2	infectious	infectious	ADJ
ejpam-6776	457	3	diseases	disease	NOUN
ejpam-6776	457	4	in	in	ADP
ejpam-6776	457	5	humans	human	NOUN
ejpam-6776	457	6	and	and	CCONJ
ejpam-6776	457	7	animals	animal	NOUN
ejpam-6776	457	8	.	.	PUNCT
ejpam-6776	458	1	princeton	princeton	PROPN
ejpam-6776	458	2	university	university	PROPN
ejpam-6776	458	3	press	press	NOUN
ejpam-6776	458	4	,	,	PUNCT
ejpam-6776	458	5	2008	2008	NUM
ejpam-6776	458	6	.	.	PUNCT
ejpam-6776	459	1	[	[	X
ejpam-6776	459	2	11	11	NUM
ejpam-6776	459	3	]	]	PUNCT
ejpam-6776	459	4	p.	p.	NOUN
ejpam-6776	459	5	barmpounakis	barmpounakis	PROPN
ejpam-6776	459	6	and	and	CCONJ
ejpam-6776	459	7	n.	n.	PROPN
ejpam-6776	459	8	demiris	demiris	PROPN
ejpam-6776	459	9	.	.	PUNCT
ejpam-6776	460	1	multiphasic	multiphasic	NOUN
ejpam-6776	460	2	stochastic	stochastic	ADJ
ejpam-6776	460	3	epidemic	epidemic	NOUN
ejpam-6776	460	4	models	model	NOUN
ejpam-6776	460	5	.	.	PUNCT
ejpam-6776	461	1	journal	journal	NOUN
ejpam-6776	461	2	of	of	ADP
ejpam-6776	461	3	the	the	DET
ejpam-6776	461	4	royal	royal	ADJ
ejpam-6776	461	5	statistical	statistical	ADJ
ejpam-6776	461	6	society	society	NOUN
ejpam-6776	461	7	series	series	NOUN
ejpam-6776	461	8	c	c	PROPN
ejpam-6776	461	9	:	:	PUNCT
ejpam-6776	461	10	applied	applied	ADJ
ejpam-6776	461	11	statistics	statistic	NOUN
ejpam-6776	461	12	,	,	PUNCT
ejpam-6776	461	13	74(2):491–505	74(2):491–505	NUM
ejpam-6776	461	14	,	,	PUNCT
ejpam-6776	461	15	2025	2025	NUM
ejpam-6776	461	16	.	.	PUNCT
ejpam-6776	462	1	[	[	X
ejpam-6776	462	2	12	12	NUM
ejpam-6776	462	3	]	]	PUNCT
ejpam-6776	462	4	b.	b.	NOUN
ejpam-6776	462	5	boukanjime	boukanjime	NOUN
ejpam-6776	462	6	and	and	CCONJ
ejpam-6776	462	7	m.	m.	NOUN
ejpam-6776	462	8	maama	maama	PROPN
ejpam-6776	462	9	.	.	PUNCT
ejpam-6776	463	1	stochastic	stochastic	ADJ
ejpam-6776	463	2	dynamics	dynamic	NOUN
ejpam-6776	463	3	and	and	CCONJ
ejpam-6776	463	4	probability	probability	NOUN
ejpam-6776	463	5	analysis	analysis	NOUN
ejpam-6776	463	6	for	for	ADP
ejpam-6776	463	7	a	a	DET
ejpam-6776	463	8	generalized	generalized	ADJ
ejpam-6776	463	9	epidemic	epidemic	NOUN
ejpam-6776	463	10	model	model	NOUN
ejpam-6776	463	11	with	with	ADP
ejpam-6776	463	12	environmental	environmental	ADJ
ejpam-6776	463	13	noise	noise	NOUN
ejpam-6776	463	14	.	.	PUNCT
ejpam-6776	464	1	chaos	chaos	NOUN
ejpam-6776	464	2	,	,	PUNCT
ejpam-6776	464	3	solitons	soliton	NOUN
ejpam-6776	464	4	&	&	CCONJ
ejpam-6776	464	5	fractals	fractal	NOUN
ejpam-6776	464	6	,	,	PUNCT
ejpam-6776	464	7	199:116744	199:116744	NUM
ejpam-6776	464	8	,	,	PUNCT
ejpam-6776	464	9	2025	2025	NUM
ejpam-6776	464	10	.	.	PUNCT
ejpam-6776	465	1	[	[	X
ejpam-6776	465	2	13	13	NUM
ejpam-6776	465	3	]	]	PUNCT
ejpam-6776	465	4	j.	j.	PROPN
ejpam-6776	465	5	song	song	PROPN
ejpam-6776	465	6	,	,	PUNCT
ejpam-6776	465	7	w.	w.	PROPN
ejpam-6776	465	8	lv	lv	PROPN
ejpam-6776	465	9	,	,	PUNCT
ejpam-6776	465	10	x.	x.	PROPN
ejpam-6776	465	11	yang	yang	PROPN
ejpam-6776	465	12	,	,	PUNCT
ejpam-6776	465	13	and	and	CCONJ
ejpam-6776	465	14	c.	c.	PROPN
ejpam-6776	465	15	zhang	zhang	PROPN
ejpam-6776	465	16	.	.	PUNCT
ejpam-6776	466	1	a	a	DET
ejpam-6776	466	2	stochastic	stochastic	ADJ
ejpam-6776	466	3	epidemic	epidemic	NOUN
ejpam-6776	466	4	model	model	NOUN
ejpam-6776	466	5	with	with	ADP
ejpam-6776	466	6	individual	individual	ADJ
ejpam-6776	466	7	heterogeneity	heterogeneity	NOUN
ejpam-6776	466	8	and	and	CCONJ
ejpam-6776	466	9	mean	mean	ADJ
ejpam-6776	466	10	-	-	PUNCT
ejpam-6776	466	11	reverting	revert	VERB
ejpam-6776	466	12	ornstein	ornstein	ADJ
ejpam-6776	466	13	–	–	PUNCT
ejpam-6776	466	14	uhlenbeck	uhlenbeck	NOUN
ejpam-6776	466	15	process	process	NOUN
ejpam-6776	466	16	.	.	PUNCT
ejpam-6776	467	1	international	international	ADJ
ejpam-6776	467	2	journal	journal	NOUN
ejpam-6776	467	3	of	of	ADP
ejpam-6776	467	4	biomathematics	biomathematic	NOUN
ejpam-6776	467	5	,	,	PUNCT
ejpam-6776	467	6	page	page	NOUN
ejpam-6776	467	7	2450035	2450035	NUM
ejpam-6776	467	8	,	,	PUNCT
ejpam-6776	467	9	2024	2024	NUM
ejpam-6776	467	10	.	.	PUNCT
ejpam-6776	468	1	[	[	X
ejpam-6776	468	2	14	14	NUM
ejpam-6776	468	3	]	]	X
ejpam-6776	468	4	l.	l.	PROPN
ejpam-6776	468	5	liu	liu	PROPN
ejpam-6776	468	6	,	,	PUNCT
ejpam-6776	468	7	y.	y.	PROPN
ejpam-6776	468	8	zhang	zhang	PROPN
ejpam-6776	468	9	,	,	PUNCT
ejpam-6776	468	10	y.	y.	PROPN
ejpam-6776	468	11	tian	tian	PROPN
ejpam-6776	468	12	,	,	PUNCT
ejpam-6776	468	13	d.	d.	PROPN
ejpam-6776	468	14	wei	wei	PROPN
ejpam-6776	468	15	,	,	PUNCT
ejpam-6776	468	16	and	and	CCONJ
ejpam-6776	468	17	z.	z.	PROPN
ejpam-6776	468	18	huang	huang	PROPN
ejpam-6776	468	19	.	.	PUNCT
ejpam-6776	469	1	sliding	slide	VERB
ejpam-6776	469	2	mode	mode	NOUN
ejpam-6776	469	3	control	control	NOUN
ejpam-6776	469	4	for	for	ADP
ejpam-6776	469	5	stochastic	stochastic	ADJ
ejpam-6776	469	6	sir	sir	NOUN
ejpam-6776	469	7	models	model	NOUN
ejpam-6776	469	8	with	with	ADP
ejpam-6776	469	9	telegraph	telegraph	NOUN
ejpam-6776	469	10	and	and	CCONJ
ejpam-6776	469	11	lévy	lévy	PRON
ejpam-6776	469	12	noise	noise	NOUN
ejpam-6776	469	13	:	:	PUNCT
ejpam-6776	469	14	theory	theory	NOUN
ejpam-6776	469	15	and	and	CCONJ
ejpam-6776	469	16	applications	application	NOUN
ejpam-6776	469	17	.	.	PUNCT
ejpam-6776	469	18	symmetry	symmetry	NOUN
ejpam-6776	469	19	,	,	PUNCT
ejpam-6776	469	20	17(6):963	17(6):963	NUM
ejpam-6776	469	21	,	,	PUNCT
ejpam-6776	469	22	2025	2025	NUM
ejpam-6776	469	23	.	.	PUNCT
ejpam-6776	470	1	[	[	X
ejpam-6776	470	2	15	15	NUM
ejpam-6776	470	3	]	]	X
ejpam-6776	470	4	p.j	p.j	PROPN
ejpam-6776	470	5	.	.	PROPN
ejpam-6776	470	6	landrigan	landrigan	PROPN
ejpam-6776	470	7	.	.	PUNCT
ejpam-6776	471	1	air	air	NOUN
ejpam-6776	471	2	pollution	pollution	PROPN
ejpam-6776	471	3	and	and	CCONJ
ejpam-6776	471	4	health	health	NOUN
ejpam-6776	471	5	.	.	PUNCT
ejpam-6776	472	1	the	the	DET
ejpam-6776	472	2	lancet	lancet	PROPN
ejpam-6776	472	3	public	public	PROPN
ejpam-6776	472	4	health	health	NOUN
ejpam-6776	472	5	,	,	PUNCT
ejpam-6776	472	6	2(1):e4	2(1):e4	NUM
ejpam-6776	472	7	–	–	PUNCT
ejpam-6776	472	8	e5	e5	PROPN
ejpam-6776	472	9	,	,	PUNCT
ejpam-6776	472	10	2017	2017	NUM
ejpam-6776	472	11	.	.	PUNCT
ejpam-6776	473	1	[	[	X
ejpam-6776	473	2	16	16	NUM
ejpam-6776	473	3	]	]	X
ejpam-6776	473	4	s.g	s.g	PROPN
ejpam-6776	473	5	.	.	PROPN
ejpam-6776	473	6	al	al	PROPN
ejpam-6776	473	7	-	-	PUNCT
ejpam-6776	473	8	kindi	kindi	NOUN
ejpam-6776	473	9	,	,	PUNCT
ejpam-6776	473	10	r.d	r.d	PROPN
ejpam-6776	473	11	.	.	PROPN
ejpam-6776	473	12	brook	brook	PROPN
ejpam-6776	473	13	,	,	PUNCT
ejpam-6776	473	14	s.	s.	PROPN
ejpam-6776	473	15	biswal	biswal	PROPN
ejpam-6776	473	16	,	,	PUNCT
ejpam-6776	473	17	and	and	CCONJ
ejpam-6776	473	18	s.	s.	PROPN
ejpam-6776	473	19	rajagopalan	rajagopalan	PROPN
ejpam-6776	473	20	.	.	PUNCT
ejpam-6776	474	1	environmental	environmental	ADJ
ejpam-6776	474	2	determinants	determinant	NOUN
ejpam-6776	474	3	of	of	ADP
ejpam-6776	474	4	cardiovascular	cardiovascular	ADJ
ejpam-6776	474	5	disease	disease	NOUN
ejpam-6776	474	6	:	:	PUNCT
ejpam-6776	474	7	lessons	lesson	NOUN
ejpam-6776	474	8	learned	learn	VERB
ejpam-6776	474	9	from	from	ADP
ejpam-6776	474	10	air	air	NOUN
ejpam-6776	474	11	pollution	pollution	NOUN
ejpam-6776	474	12	.	.	PUNCT
ejpam-6776	475	1	nature	nature	NOUN
ejpam-6776	475	2	reviews	review	VERB
ejpam-6776	475	3	cardiology	cardiology	NOUN
ejpam-6776	475	4	,	,	PUNCT
ejpam-6776	475	5	17(10):656–672	17(10):656–672	NUM
ejpam-6776	475	6	,	,	PUNCT
ejpam-6776	475	7	2020	2020	NUM
ejpam-6776	475	8	.	.	PUNCT
ejpam-6776	476	1	[	[	X
ejpam-6776	476	2	17	17	NUM
ejpam-6776	476	3	]	]	X
ejpam-6776	476	4	b.g	b.g	PROPN
ejpam-6776	476	5	.	.	PROPN
ejpam-6776	476	6	armstrong	armstrong	PROPN
ejpam-6776	476	7	.	.	PROPN
ejpam-6776	476	8	effect	effect	NOUN
ejpam-6776	476	9	of	of	ADP
ejpam-6776	476	10	measurement	measurement	NOUN
ejpam-6776	476	11	error	error	NOUN
ejpam-6776	476	12	on	on	ADP
ejpam-6776	476	13	epidemiological	epidemiological	ADJ
ejpam-6776	476	14	studies	study	NOUN
ejpam-6776	476	15	of	of	ADP
ejpam-6776	476	16	environmental	environmental	ADJ
ejpam-6776	476	17	and	and	CCONJ
ejpam-6776	476	18	occupational	occupational	ADJ
ejpam-6776	476	19	exposures	exposure	NOUN
ejpam-6776	476	20	.	.	PUNCT
ejpam-6776	477	1	occupational	occupational	ADJ
ejpam-6776	477	2	and	and	CCONJ
ejpam-6776	477	3	environmental	environmental	ADJ
ejpam-6776	477	4	medicine	medicine	NOUN
ejpam-6776	477	5	,	,	PUNCT
ejpam-6776	477	6	55(10):651–656	55(10):651–656	NUM
ejpam-6776	477	7	,	,	PUNCT
ejpam-6776	477	8	1998	1998	NUM
ejpam-6776	477	9	.	.	PUNCT
ejpam-6776	478	1	[	[	X
ejpam-6776	478	2	18	18	NUM
ejpam-6776	478	3	]	]	X
ejpam-6776	478	4	c.	c.	PROPN
ejpam-6776	478	5	asbach	asbach	PROPN
ejpam-6776	478	6	,	,	PUNCT
ejpam-6776	478	7	h.	h.	PROPN
ejpam-6776	478	8	kaminski	kaminski	PROPN
ejpam-6776	478	9	,	,	PUNCT
ejpam-6776	478	10	d.	d.	PROPN
ejpam-6776	478	11	von	von	PROPN
ejpam-6776	478	12	barany	barany	PROPN
ejpam-6776	478	13	,	,	PUNCT
ejpam-6776	478	14	t.a	t.a	PROPN
ejpam-6776	478	15	.	.	PROPN
ejpam-6776	478	16	kuhlbusch	kuhlbusch	PROPN
ejpam-6776	478	17	,	,	PUNCT
ejpam-6776	478	18	c.	c.	PROPN
ejpam-6776	478	19	monz	monz	PROPN
ejpam-6776	478	20	,	,	PUNCT
ejpam-6776	478	21	n.	n.	PROPN
ejpam-6776	478	22	dziurowitz	dziurowitz	PROPN
ejpam-6776	478	23	,	,	PUNCT
ejpam-6776	478	24	j.	j.	PROPN
ejpam-6776	478	25	pelzer	pelzer	PROPN
ejpam-6776	478	26	,	,	PUNCT
ejpam-6776	478	27	k.	k.	PROPN
ejpam-6776	478	28	vossen	vossen	PROPN
ejpam-6776	478	29	,	,	PUNCT
ejpam-6776	478	30	k.	k.	PROPN
ejpam-6776	478	31	berlin	berlin	PROPN
ejpam-6776	478	32	,	,	PUNCT
ejpam-6776	478	33	s.	s.	PROPN
ejpam-6776	478	34	dietrich	dietrich	PROPN
ejpam-6776	478	35	,	,	PUNCT
ejpam-6776	478	36	and	and	CCONJ
ejpam-6776	478	37	u.w.e	u.w.e	NOUN
ejpam-6776	478	38	.	.	PUNCT
ejpam-6776	479	1	götz	götz	PROPN
ejpam-6776	479	2	.	.	PUNCT
ejpam-6776	480	1	comparability	comparability	NOUN
ejpam-6776	480	2	of	of	ADP
ejpam-6776	480	3	portable	portable	ADJ
ejpam-6776	480	4	nanoparticle	nanoparticle	NOUN
ejpam-6776	480	5	exposure	exposure	NOUN
ejpam-6776	480	6	monitors	monitor	NOUN
ejpam-6776	480	7	.	.	PUNCT
ejpam-6776	481	1	annals	annal	NOUN
ejpam-6776	481	2	of	of	ADP
ejpam-6776	481	3	occupational	occupational	ADJ
ejpam-6776	481	4	hygiene	hygiene	NOUN
ejpam-6776	481	5	,	,	PUNCT
ejpam-6776	481	6	56(5):606	56(5):606	NUM
ejpam-6776	481	7	–	–	PUNCT
ejpam-6776	481	8	621	621	NUM
ejpam-6776	481	9	,	,	PUNCT
ejpam-6776	481	10	2012	2012	NUM
ejpam-6776	481	11	.	.	PUNCT
ejpam-6776	482	1	[	[	X
ejpam-6776	482	2	19	19	NUM
ejpam-6776	482	3	]	]	X
ejpam-6776	482	4	e.	e.	PROPN
ejpam-6776	482	5	van	van	PROPN
ejpam-6776	482	6	de	de	PROPN
ejpam-6776	482	7	beek	beek	PROPN
ejpam-6776	482	8	,	,	PUNCT
ejpam-6776	482	9	j.	j.	PROPN
ejpam-6776	482	10	kerckhoffs	kerckhoffs	PROPN
ejpam-6776	482	11	,	,	PUNCT
ejpam-6776	482	12	g.	g.	PROPN
ejpam-6776	482	13	hoek	hoek	PROPN
ejpam-6776	482	14	,	,	PUNCT
ejpam-6776	482	15	g.	g.	PROPN
ejpam-6776	482	16	sterk	sterk	PROPN
ejpam-6776	482	17	,	,	PUNCT
ejpam-6776	482	18	k.	k.	PROPN
ejpam-6776	482	19	meliefste	meliefste	PROPN
ejpam-6776	482	20	,	,	PUNCT
ejpam-6776	482	21	u.	u.	PROPN
ejpam-6776	482	22	gehring	gehring	PROPN
ejpam-6776	482	23	,	,	PUNCT
ejpam-6776	482	24	and	and	CCONJ
ejpam-6776	482	25	r.	r.	PROPN
ejpam-6776	482	26	vermeulen	vermeulen	PROPN
ejpam-6776	482	27	.	.	PUNCT
ejpam-6776	483	1	spatial	spatial	ADJ
ejpam-6776	483	2	and	and	CCONJ
ejpam-6776	483	3	spatiotemporal	spatiotemporal	ADJ
ejpam-6776	483	4	variability	variability	NOUN
ejpam-6776	483	5	of	of	ADP
ejpam-6776	483	6	regional	regional	ADJ
ejpam-6776	483	7	background	background	NOUN
ejpam-6776	483	8	ultrafine	ultrafine	NOUN
ejpam-6776	483	9	particle	particle	NOUN
ejpam-6776	483	10	concentrations	concentration	NOUN
ejpam-6776	483	11	in	in	ADP
ejpam-6776	483	12	the	the	DET
ejpam-6776	483	13	netherlands	netherlands	PROPN
ejpam-6776	483	14	.	.	PUNCT
ejpam-6776	484	1	environmental	environmental	ADJ
ejpam-6776	484	2	science	science	NOUN
ejpam-6776	484	3	and	and	CCONJ
ejpam-6776	484	4	technology	technology	NOUN
ejpam-6776	484	5	,	,	PUNCT
ejpam-6776	484	6	55(2):1067–105	55(2):1067–105	NUM
ejpam-6776	484	7	,	,	PUNCT
ejpam-6776	484	8	2020	2020	NUM
ejpam-6776	484	9	.	.	PUNCT
ejpam-6776	485	1	[	[	X
ejpam-6776	485	2	20	20	NUM
ejpam-6776	485	3	]	]	X
ejpam-6776	485	4	v.	v.	CCONJ
ejpam-6776	485	5	capasso	capasso	PROPN
ejpam-6776	485	6	.	.	PUNCT
ejpam-6776	486	1	mathematical	mathematical	ADJ
ejpam-6776	486	2	structures	structure	NOUN
ejpam-6776	486	3	of	of	ADP
ejpam-6776	486	4	epidemic	epidemic	NOUN
ejpam-6776	486	5	systems	system	NOUN
ejpam-6776	486	6	.	.	PUNCT
ejpam-6776	487	1	springer	springer	NOUN
ejpam-6776	487	2	-	-	PUNCT
ejpam-6776	487	3	verlag	verlag	PROPN
ejpam-6776	487	4	berlin	berlin	PROPN
ejpam-6776	487	5	heidelberg	heidelberg	PROPN
ejpam-6776	487	6	,	,	PUNCT
ejpam-6776	487	7	2008	2008	NUM
ejpam-6776	487	8	.	.	PUNCT
ejpam-6776	488	1	[	[	X
ejpam-6776	488	2	21	21	NUM
ejpam-6776	488	3	]	]	X
ejpam-6776	488	4	f.	f.	PROPN
ejpam-6776	488	5	brauer	brauer	PROPN
ejpam-6776	488	6	,	,	PUNCT
ejpam-6776	488	7	c.	c.	PROPN
ejpam-6776	488	8	castillo	castillo	PROPN
ejpam-6776	488	9	-	-	PUNCT
ejpam-6776	488	10	chavez	chavez	PROPN
ejpam-6776	488	11	,	,	PUNCT
ejpam-6776	488	12	and	and	CCONJ
ejpam-6776	488	13	c.	c.	PROPN
ejpam-6776	488	14	castillo	castillo	PROPN
ejpam-6776	488	15	-	-	PUNCT
ejpam-6776	488	16	chavez	chavez	PROPN
ejpam-6776	488	17	.	.	PUNCT
ejpam-6776	489	1	mathematical	mathematical	ADJ
ejpam-6776	489	2	models	model	NOUN
ejpam-6776	489	3	in	in	ADP
ejpam-6776	489	4	popj	popj	NOUN
ejpam-6776	489	5	.	.	PUNCT
ejpam-6776	490	1	leo	leo	PROPN
ejpam-6776	490	2	amalraj	amalraj	PROPN
ejpam-6776	490	3	et	et	PROPN
ejpam-6776	490	4	al	al	PROPN
ejpam-6776	490	5	.	.	PUNCT
ejpam-6776	490	6	/	/	SYM
ejpam-6776	490	7	eur	eur	PROPN
ejpam-6776	490	8	.	.	PUNCT
ejpam-6776	491	1	j.	j.	PROPN
ejpam-6776	491	2	pure	pure	PROPN
ejpam-6776	491	3	appl	appl	PROPN
ejpam-6776	491	4	.	.	PROPN
ejpam-6776	491	5	math	math	PROPN
ejpam-6776	491	6	,	,	PUNCT
ejpam-6776	491	7	18	18	NUM
ejpam-6776	491	8	(	(	PUNCT
ejpam-6776	491	9	4	4	NUM
ejpam-6776	491	10	)	)	PUNCT
ejpam-6776	491	11	(	(	PUNCT
ejpam-6776	491	12	2025	2025	NUM
ejpam-6776	491	13	)	)	PUNCT
ejpam-6776	491	14	,	,	PUNCT
ejpam-6776	491	15	6776	6776	NUM
ejpam-6776	491	16	21	21	NUM
ejpam-6776	491	17	of	of	ADP
ejpam-6776	491	18	22	22	NUM
ejpam-6776	491	19	ulation	ulation	NOUN
ejpam-6776	491	20	biology	biology	NOUN
ejpam-6776	491	21	and	and	CCONJ
ejpam-6776	491	22	epidemiology	epidemiology	NOUN
ejpam-6776	491	23	,	,	PUNCT
ejpam-6776	491	24	volume	volume	NOUN
ejpam-6776	491	25	2	2	NUM
ejpam-6776	491	26	.	.	PUNCT
ejpam-6776	491	27	springer	springer	PROPN
ejpam-6776	491	28	new	new	PROPN
ejpam-6776	491	29	york	york	PROPN
ejpam-6776	491	30	,	,	PUNCT
ejpam-6776	491	31	2012	2012	NUM
ejpam-6776	491	32	.	.	PUNCT
ejpam-6776	492	1	[	[	X
ejpam-6776	492	2	22	22	NUM
ejpam-6776	492	3	]	]	PUNCT
ejpam-6776	492	4	m.	m.	NOUN
ejpam-6776	492	5	lipsitch	lipsitch	PROPN
ejpam-6776	492	6	,	,	PUNCT
ejpam-6776	492	7	y.h	y.h	PROPN
ejpam-6776	492	8	.	.	PROPN
ejpam-6776	492	9	grad	grad	PROPN
ejpam-6776	492	10	,	,	PUNCT
ejpam-6776	492	11	a.	a.	NOUN
ejpam-6776	492	12	sette	sette	PROPN
ejpam-6776	492	13	,	,	PUNCT
ejpam-6776	492	14	and	and	CCONJ
ejpam-6776	492	15	s.	s.	PROPN
ejpam-6776	492	16	crotty	crotty	PROPN
ejpam-6776	492	17	.	.	PUNCT
ejpam-6776	492	18	cross	cross	ADJ
ejpam-6776	492	19	-	-	ADJ
ejpam-6776	492	20	reactive	reactive	ADJ
ejpam-6776	492	21	memory	memory	NOUN
ejpam-6776	492	22	t	t	NOUN
ejpam-6776	492	23	cells	cell	NOUN
ejpam-6776	492	24	and	and	CCONJ
ejpam-6776	492	25	herd	herd	NOUN
ejpam-6776	492	26	immunity	immunity	NOUN
ejpam-6776	492	27	to	to	ADP
ejpam-6776	492	28	sars	sar	NOUN
ejpam-6776	492	29	-	-	PUNCT
ejpam-6776	492	30	cov-2	cov-2	NOUN
ejpam-6776	492	31	.	.	PUNCT
ejpam-6776	492	32	nature	nature	NOUN
ejpam-6776	492	33	reviews	review	VERB
ejpam-6776	492	34	immunology	immunology	NOUN
ejpam-6776	492	35	,	,	PUNCT
ejpam-6776	492	36	20(11):709–713	20(11):709–713	NUM
ejpam-6776	492	37	,	,	PUNCT
ejpam-6776	492	38	2020	2020	NUM
ejpam-6776	492	39	.	.	PUNCT
ejpam-6776	493	1	[	[	X
ejpam-6776	493	2	23	23	NUM
ejpam-6776	493	3	]	]	X
ejpam-6776	493	4	j.m	j.m	PROPN
ejpam-6776	493	5	.	.	PROPN
ejpam-6776	493	6	dan	dan	PROPN
ejpam-6776	493	7	,	,	PUNCT
ejpam-6776	493	8	j.	j.	PROPN
ejpam-6776	493	9	mateus	mateus	PROPN
ejpam-6776	493	10	,	,	PUNCT
ejpam-6776	493	11	y.	y.	PROPN
ejpam-6776	493	12	kato	kato	PROPN
ejpam-6776	493	13	,	,	PUNCT
ejpam-6776	493	14	k.m	k.m	PROPN
ejpam-6776	493	15	.	.	PROPN
ejpam-6776	493	16	hastie	hastie	PROPN
ejpam-6776	493	17	,	,	PUNCT
ejpam-6776	493	18	e.d	e.d	PROPN
ejpam-6776	493	19	.	.	PROPN
ejpam-6776	493	20	yu	yu	PROPN
ejpam-6776	493	21	,	,	PUNCT
ejpam-6776	493	22	c.e	c.e	PROPN
ejpam-6776	493	23	.	.	PROPN
ejpam-6776	493	24	faliti	faliti	PROPN
ejpam-6776	493	25	,	,	PUNCT
ejpam-6776	493	26	a.	a.	NOUN
ejpam-6776	493	27	grifoni	grifoni	PROPN
ejpam-6776	493	28	,	,	PUNCT
ejpam-6776	493	29	s.i	s.i	PROPN
ejpam-6776	493	30	.	.	PROPN
ejpam-6776	493	31	ramirez	ramirez	PROPN
ejpam-6776	493	32	,	,	PUNCT
ejpam-6776	493	33	s.	s.	PROPN
ejpam-6776	493	34	haupt	haupt	PROPN
ejpam-6776	493	35	,	,	PUNCT
ejpam-6776	493	36	a.	a.	PROPN
ejpam-6776	493	37	frazier	frazier	PROPN
ejpam-6776	493	38	,	,	PUNCT
ejpam-6776	493	39	and	and	CCONJ
ejpam-6776	493	40	c.	c.	PROPN
ejpam-6776	493	41	nakao	nakao	PROPN
ejpam-6776	493	42	.	.	PUNCT
ejpam-6776	494	1	immunological	immunological	ADJ
ejpam-6776	494	2	memory	memory	NOUN
ejpam-6776	494	3	to	to	ADP
ejpam-6776	494	4	sars	sar	NOUN
ejpam-6776	494	5	-	-	PUNCT
ejpam-6776	494	6	cov-2	cov-2	NOUN
ejpam-6776	494	7	assessed	assess	VERB
ejpam-6776	494	8	for	for	ADP
ejpam-6776	494	9	up	up	ADP
ejpam-6776	494	10	to	to	PART
ejpam-6776	494	11	8	8	NUM
ejpam-6776	494	12	months	month	NOUN
ejpam-6776	494	13	after	after	ADP
ejpam-6776	494	14	infection	infection	NOUN
ejpam-6776	494	15	.	.	PUNCT
ejpam-6776	495	1	science	science	NOUN
ejpam-6776	495	2	,	,	PUNCT
ejpam-6776	495	3	371(6529):eabf4063	371(6529):eabf4063	PROPN
ejpam-6776	495	4	,	,	PUNCT
ejpam-6776	495	5	2021	2021	NUM
ejpam-6776	495	6	.	.	PUNCT
ejpam-6776	496	1	[	[	X
ejpam-6776	496	2	24	24	NUM
ejpam-6776	496	3	]	]	X
ejpam-6776	496	4	b.s	b.s	PROPN
ejpam-6776	496	5	.	.	PROPN
ejpam-6776	496	6	graham	graham	PROPN
ejpam-6776	496	7	,	,	PUNCT
ejpam-6776	496	8	j.r	j.r	PROPN
ejpam-6776	496	9	.	.	PROPN
ejpam-6776	496	10	mascola	mascola	PROPN
ejpam-6776	496	11	,	,	PUNCT
ejpam-6776	496	12	and	and	CCONJ
ejpam-6776	496	13	a.s	a.s	PROPN
ejpam-6776	496	14	.	.	PROPN
ejpam-6776	496	15	fauci	fauci	PROPN
ejpam-6776	496	16	.	.	PUNCT
ejpam-6776	497	1	novel	novel	ADJ
ejpam-6776	497	2	vaccine	vaccine	NOUN
ejpam-6776	497	3	technologies	technology	NOUN
ejpam-6776	497	4	:	:	PUNCT
ejpam-6776	497	5	essential	essential	ADJ
ejpam-6776	497	6	components	component	NOUN
ejpam-6776	497	7	of	of	ADP
ejpam-6776	497	8	an	an	DET
ejpam-6776	497	9	adequate	adequate	ADJ
ejpam-6776	497	10	response	response	NOUN
ejpam-6776	497	11	to	to	ADP
ejpam-6776	497	12	emerging	emerge	VERB
ejpam-6776	497	13	viral	viral	ADJ
ejpam-6776	497	14	diseases	disease	NOUN
ejpam-6776	497	15	.	.	PUNCT
ejpam-6776	498	1	jama	jama	PROPN
ejpam-6776	498	2	,	,	PUNCT
ejpam-6776	498	3	319(14):1431	319(14):1431	PROPN
ejpam-6776	498	4	–	–	PUNCT
ejpam-6776	498	5	1432	1432	NUM
ejpam-6776	498	6	,	,	PUNCT
ejpam-6776	498	7	2018	2018	NUM
ejpam-6776	498	8	.	.	PUNCT
ejpam-6776	499	1	[	[	X
ejpam-6776	499	2	25	25	NUM
ejpam-6776	499	3	]	]	PUNCT
ejpam-6776	499	4	j.	j.	PROPN
ejpam-6776	499	5	yang	yang	PROPN
ejpam-6776	499	6	,	,	PUNCT
ejpam-6776	499	7	m.	m.	NOUN
ejpam-6776	499	8	zhou	zhou	PROPN
ejpam-6776	499	9	,	,	PUNCT
ejpam-6776	499	10	and	and	CCONJ
ejpam-6776	499	11	x.	x.	PROPN
ejpam-6776	499	12	li	li	PROPN
ejpam-6776	499	13	.	.	PROPN
ejpam-6776	499	14	backward	backward	ADJ
ejpam-6776	499	15	bifurcation	bifurcation	NOUN
ejpam-6776	499	16	of	of	ADP
ejpam-6776	499	17	an	an	DET
ejpam-6776	499	18	age	age	NOUN
ejpam-6776	499	19	-	-	PUNCT
ejpam-6776	499	20	structured	structure	VERB
ejpam-6776	499	21	epidemic	epidemic	NOUN
ejpam-6776	499	22	model	model	NOUN
ejpam-6776	499	23	with	with	ADP
ejpam-6776	499	24	partial	partial	ADJ
ejpam-6776	499	25	immunity	immunity	NOUN
ejpam-6776	499	26	:	:	PUNCT
ejpam-6776	499	27	the	the	DET
ejpam-6776	499	28	lyapunov	lyapunov	PROPN
ejpam-6776	499	29	–	–	PUNCT
ejpam-6776	499	30	schmidt	schmidt	PROPN
ejpam-6776	499	31	approach	approach	NOUN
ejpam-6776	499	32	.	.	PUNCT
ejpam-6776	500	1	applied	apply	VERB
ejpam-6776	500	2	mathematics	mathematics	NOUN
ejpam-6776	500	3	letters	letter	NOUN
ejpam-6776	500	4	,	,	PUNCT
ejpam-6776	500	5	133:108292	133:108292	NUM
ejpam-6776	500	6	,	,	PUNCT
ejpam-6776	500	7	2022	2022	NUM
ejpam-6776	500	8	.	.	PUNCT
ejpam-6776	501	1	[	[	X
ejpam-6776	501	2	26	26	NUM
ejpam-6776	501	3	]	]	X
ejpam-6776	501	4	m.r	m.r	PROPN
ejpam-6776	501	5	.	.	PROPN
ejpam-6776	501	6	boyce	boyce	PROPN
ejpam-6776	501	7	and	and	CCONJ
ejpam-6776	501	8	r.	r.	PROPN
ejpam-6776	501	9	katz	katz	PROPN
ejpam-6776	501	10	.	.	PUNCT
ejpam-6776	502	1	community	community	NOUN
ejpam-6776	502	2	health	health	NOUN
ejpam-6776	502	3	workers	worker	NOUN
ejpam-6776	502	4	and	and	CCONJ
ejpam-6776	502	5	pandemic	pandemic	ADJ
ejpam-6776	502	6	preparedness	preparedness	NOUN
ejpam-6776	502	7	:	:	PUNCT
ejpam-6776	502	8	current	current	ADJ
ejpam-6776	502	9	and	and	CCONJ
ejpam-6776	502	10	prospective	prospective	ADJ
ejpam-6776	502	11	roles	role	NOUN
ejpam-6776	502	12	.	.	PUNCT
ejpam-6776	503	1	frontiers	frontier	NOUN
ejpam-6776	503	2	in	in	ADP
ejpam-6776	503	3	public	public	ADJ
ejpam-6776	503	4	health	health	NOUN
ejpam-6776	503	5	,	,	PUNCT
ejpam-6776	503	6	7:62	7:62	NUM
ejpam-6776	503	7	,	,	PUNCT
ejpam-6776	503	8	2019	2019	NUM
ejpam-6776	503	9	.	.	PUNCT
ejpam-6776	504	1	[	[	X
ejpam-6776	504	2	27	27	NUM
ejpam-6776	504	3	]	]	PUNCT
ejpam-6776	504	4	m.	m.	NOUN
ejpam-6776	504	5	shammi	shammi	PROPN
ejpam-6776	504	6	,	,	PUNCT
ejpam-6776	504	7	m.	m.	NOUN
ejpam-6776	504	8	bodrud	bodrud	PROPN
ejpam-6776	504	9	-	-	PUNCT
ejpam-6776	504	10	doza	doza	PROPN
ejpam-6776	504	11	,	,	PUNCT
ejpam-6776	504	12	a.r.m.t	a.r.m.t	PROPN
ejpam-6776	504	13	.	.	PROPN
ejpam-6776	504	14	islam	islam	PROPN
ejpam-6776	504	15	,	,	PUNCT
ejpam-6776	504	16	and	and	CCONJ
ejpam-6776	504	17	m.m	m.m	PROPN
ejpam-6776	504	18	.	.	PROPN
ejpam-6776	504	19	rahman	rahman	PROPN
ejpam-6776	504	20	.	.	PUNCT
ejpam-6776	505	1	strategic	strategic	ADJ
ejpam-6776	505	2	assessment	assessment	NOUN
ejpam-6776	505	3	of	of	ADP
ejpam-6776	505	4	covid-19	covid-19	PROPN
ejpam-6776	505	5	pandemic	pandemic	ADJ
ejpam-6776	505	6	in	in	ADP
ejpam-6776	505	7	bangladesh	bangladesh	NOUN
ejpam-6776	505	8	:	:	PUNCT
ejpam-6776	505	9	comparative	comparative	ADJ
ejpam-6776	505	10	lockdown	lockdown	NOUN
ejpam-6776	505	11	scenario	scenario	NOUN
ejpam-6776	505	12	analysis	analysis	NOUN
ejpam-6776	505	13	,	,	PUNCT
ejpam-6776	505	14	public	public	ADJ
ejpam-6776	505	15	perception	perception	NOUN
ejpam-6776	505	16	,	,	PUNCT
ejpam-6776	505	17	and	and	CCONJ
ejpam-6776	505	18	management	management	NOUN
ejpam-6776	505	19	for	for	ADP
ejpam-6776	505	20	sustainability	sustainability	NOUN
ejpam-6776	505	21	.	.	PUNCT
ejpam-6776	506	1	environment	environment	NOUN
ejpam-6776	506	2	,	,	PUNCT
ejpam-6776	506	3	development	development	NOUN
ejpam-6776	506	4	and	and	CCONJ
ejpam-6776	506	5	sustainability	sustainability	NOUN
ejpam-6776	506	6	,	,	PUNCT
ejpam-6776	506	7	23:6148–6191	23:6148–6191	NUM
ejpam-6776	506	8	,	,	PUNCT
ejpam-6776	506	9	2021	2021	NUM
ejpam-6776	506	10	.	.	PUNCT
ejpam-6776	507	1	[	[	X
ejpam-6776	507	2	28	28	NUM
ejpam-6776	507	3	]	]	X
ejpam-6776	507	4	f.	f.	PROPN
ejpam-6776	507	5	carinci	carinci	PROPN
ejpam-6776	507	6	.	.	PUNCT
ejpam-6776	508	1	covid-19	covid-19	PROPN
ejpam-6776	508	2	:	:	PUNCT
ejpam-6776	508	3	preparedness	preparedness	NOUN
ejpam-6776	508	4	,	,	PUNCT
ejpam-6776	508	5	decentralisation	decentralisation	NOUN
ejpam-6776	508	6	,	,	PUNCT
ejpam-6776	508	7	and	and	CCONJ
ejpam-6776	508	8	the	the	DET
ejpam-6776	508	9	hunt	hunt	NOUN
ejpam-6776	508	10	for	for	ADP
ejpam-6776	508	11	patient	patient	ADJ
ejpam-6776	508	12	zero	zero	NUM
ejpam-6776	508	13	.	.	PUNCT
ejpam-6776	509	1	bmj	bmj	PROPN
ejpam-6776	509	2	,	,	PUNCT
ejpam-6776	509	3	368	368	NUM
ejpam-6776	509	4	,	,	PUNCT
ejpam-6776	509	5	2020	2020	NUM
ejpam-6776	509	6	.	.	PUNCT
ejpam-6776	510	1	[	[	X
ejpam-6776	510	2	29	29	NUM
ejpam-6776	510	3	]	]	X
ejpam-6776	510	4	d.r	d.r	PROPN
ejpam-6776	510	5	.	.	PROPN
ejpam-6776	510	6	chaudhury	chaudhury	PROPN
ejpam-6776	510	7	.	.	PUNCT
ejpam-6776	511	1	at	at	ADP
ejpam-6776	511	2	current	current	ADJ
ejpam-6776	511	3	pace	pace	NOUN
ejpam-6776	511	4	,	,	PUNCT
ejpam-6776	511	5	bangladesh	bangladesh	NOUN
ejpam-6776	511	6	to	to	PART
ejpam-6776	511	7	end	end	VERB
ejpam-6776	511	8	extreme	extreme	ADJ
ejpam-6776	511	9	poverty	poverty	NOUN
ejpam-6776	511	10	by	by	ADP
ejpam-6776	511	11	2021	2021	NUM
ejpam-6776	511	12	.	.	PUNCT
ejpam-6776	512	1	the	the	DET
ejpam-6776	512	2	economic	economic	PROPN
ejpam-6776	512	3	times	time	NOUN
ejpam-6776	512	4	,	,	PUNCT
ejpam-6776	512	5	2018	2018	NUM
ejpam-6776	512	6	.	.	PUNCT
ejpam-6776	513	1	[	[	X
ejpam-6776	513	2	30	30	NUM
ejpam-6776	513	3	]	]	X
ejpam-6776	513	4	j.p	j.p	PROPN
ejpam-6776	513	5	.	.	PROPN
ejpam-6776	513	6	aparicio	aparicio	PROPN
ejpam-6776	513	7	,	,	PUNCT
ejpam-6776	513	8	a.f	a.f	PROPN
ejpam-6776	513	9	.	.	PROPN
ejpam-6776	513	10	capurro	capurro	PROPN
ejpam-6776	513	11	,	,	PUNCT
ejpam-6776	513	12	and	and	CCONJ
ejpam-6776	513	13	c.	c.	PROPN
ejpam-6776	513	14	castillo	castillo	PROPN
ejpam-6776	513	15	-	-	PUNCT
ejpam-6776	513	16	chavez	chavez	PROPN
ejpam-6776	513	17	.	.	PUNCT
ejpam-6776	514	1	transmission	transmission	NOUN
ejpam-6776	514	2	and	and	CCONJ
ejpam-6776	514	3	dynamics	dynamic	NOUN
ejpam-6776	514	4	of	of	ADP
ejpam-6776	514	5	tuberculosis	tuberculosis	NOUN
ejpam-6776	514	6	on	on	ADP
ejpam-6776	514	7	generalized	generalized	ADJ
ejpam-6776	514	8	households	household	NOUN
ejpam-6776	514	9	.	.	PUNCT
ejpam-6776	515	1	journal	journal	NOUN
ejpam-6776	515	2	of	of	ADP
ejpam-6776	515	3	theoretical	theoretical	ADJ
ejpam-6776	515	4	biology	biology	NOUN
ejpam-6776	515	5	,	,	PUNCT
ejpam-6776	515	6	206(3):327–341	206(3):327–341	NUM
ejpam-6776	515	7	,	,	PUNCT
ejpam-6776	515	8	2000	2000	NUM
ejpam-6776	515	9	.	.	PUNCT
ejpam-6776	516	1	[	[	X
ejpam-6776	516	2	31	31	NUM
ejpam-6776	516	3	]	]	PUNCT
ejpam-6776	516	4	w.	w.	PROPN
ejpam-6776	516	5	miller	miller	PROPN
ejpam-6776	516	6	,	,	PUNCT
ejpam-6776	516	7	c.	c.	PROPN
ejpam-6776	516	8	castillo	castillo	PROPN
ejpam-6776	516	9	-	-	PUNCT
ejpam-6776	516	10	chavez	chavez	PROPN
ejpam-6776	516	11	,	,	PUNCT
ejpam-6776	516	12	s.	s.	PROPN
ejpam-6776	516	13	blower	blower	PROPN
ejpam-6776	516	14	,	,	PUNCT
ejpam-6776	516	15	d.	d.	PROPN
ejpam-6776	516	16	kirschner	kirschner	PROPN
ejpam-6776	516	17	,	,	PUNCT
ejpam-6776	516	18	and	and	CCONJ
ejpam-6776	516	19	a.a	a.a	PROPN
ejpam-6776	516	20	.	.	PROPN
ejpam-6776	516	21	yakubu	yakubu	PROPN
ejpam-6776	516	22	.	.	PROPN
ejpam-6776	516	23	mathematical	mathematical	PROPN
ejpam-6776	516	24	approaches	approach	NOUN
ejpam-6776	516	25	for	for	ADP
ejpam-6776	516	26	emerging	emerge	VERB
ejpam-6776	516	27	and	and	CCONJ
ejpam-6776	516	28	reemerging	reemerging	ADJ
ejpam-6776	516	29	infectious	infectious	ADJ
ejpam-6776	516	30	diseases	disease	NOUN
ejpam-6776	516	31	:	:	PUNCT
ejpam-6776	516	32	models	model	NOUN
ejpam-6776	516	33	,	,	PUNCT
ejpam-6776	516	34	methods	method	NOUN
ejpam-6776	516	35	,	,	PUNCT
ejpam-6776	516	36	and	and	CCONJ
ejpam-6776	516	37	theory	theory	NOUN
ejpam-6776	516	38	.	.	PUNCT
ejpam-6776	517	1	springer	springer	PROPN
ejpam-6776	517	2	new	new	PROPN
ejpam-6776	517	3	york	york	PROPN
ejpam-6776	517	4	,	,	PUNCT
ejpam-6776	517	5	2002	2002	NUM
ejpam-6776	517	6	.	.	PUNCT
ejpam-6776	518	1	[	[	X
ejpam-6776	518	2	32	32	NUM
ejpam-6776	518	3	]	]	X
ejpam-6776	518	4	j.p	j.p	PROPN
ejpam-6776	518	5	.	.	PROPN
ejpam-6776	518	6	aparicio	aparicio	PROPN
ejpam-6776	518	7	,	,	PUNCT
ejpam-6776	518	8	a.f	a.f	PROPN
ejpam-6776	518	9	.	.	PROPN
ejpam-6776	518	10	capurro	capurro	PROPN
ejpam-6776	518	11	,	,	PUNCT
ejpam-6776	518	12	and	and	CCONJ
ejpam-6776	518	13	c.	c.	PROPN
ejpam-6776	518	14	castillo	castillo	PROPN
ejpam-6776	518	15	-	-	PUNCT
ejpam-6776	518	16	chavez	chavez	PROPN
ejpam-6776	518	17	.	.	PUNCT
ejpam-6776	519	1	markers	marker	NOUN
ejpam-6776	519	2	of	of	ADP
ejpam-6776	519	3	disease	disease	NOUN
ejpam-6776	519	4	evolution	evolution	NOUN
ejpam-6776	519	5	:	:	PUNCT
ejpam-6776	519	6	the	the	DET
ejpam-6776	519	7	case	case	NOUN
ejpam-6776	519	8	of	of	ADP
ejpam-6776	519	9	tuberculosis	tuberculosis	NOUN
ejpam-6776	519	10	.	.	PUNCT
ejpam-6776	520	1	journal	journal	NOUN
ejpam-6776	520	2	of	of	ADP
ejpam-6776	520	3	theoretical	theoretical	ADJ
ejpam-6776	520	4	biology	biology	NOUN
ejpam-6776	520	5	,	,	PUNCT
ejpam-6776	520	6	215(2):227–237	215(2):227–237	NUM
ejpam-6776	520	7	,	,	PUNCT
ejpam-6776	520	8	2002	2002	NUM
ejpam-6776	520	9	.	.	PUNCT
ejpam-6776	521	1	[	[	X
ejpam-6776	521	2	33	33	NUM
ejpam-6776	521	3	]	]	X
ejpam-6776	521	4	s.j	s.j	PROPN
ejpam-6776	521	5	.	.	PROPN
ejpam-6776	521	6	aston	aston	PROPN
ejpam-6776	521	7	.	.	PUNCT
ejpam-6776	522	1	pneumonia	pneumonia	NOUN
ejpam-6776	522	2	in	in	ADP
ejpam-6776	522	3	the	the	DET
ejpam-6776	522	4	developing	develop	VERB
ejpam-6776	522	5	world	world	NOUN
ejpam-6776	522	6	:	:	PUNCT
ejpam-6776	522	7	characteristic	characteristic	ADJ
ejpam-6776	522	8	features	feature	NOUN
ejpam-6776	522	9	and	and	CCONJ
ejpam-6776	522	10	approach	approach	NOUN
ejpam-6776	522	11	to	to	ADP
ejpam-6776	522	12	management	management	NOUN
ejpam-6776	522	13	.	.	PUNCT
ejpam-6776	523	1	respirology	respirology	NOUN
ejpam-6776	523	2	,	,	PUNCT
ejpam-6776	523	3	22(7):1276–1287	22(7):1276–1287	NUM
ejpam-6776	523	4	,	,	PUNCT
ejpam-6776	523	5	2017	2017	NUM
ejpam-6776	523	6	.	.	PUNCT
ejpam-6776	524	1	[	[	X
ejpam-6776	524	2	34	34	NUM
ejpam-6776	524	3	]	]	X
ejpam-6776	524	4	national	national	ADJ
ejpam-6776	524	5	academies	academy	NOUN
ejpam-6776	524	6	of	of	ADP
ejpam-6776	524	7	sciences	science	NOUN
ejpam-6776	524	8	,	,	PUNCT
ejpam-6776	524	9	engineering	engineering	NOUN
ejpam-6776	524	10	,	,	PUNCT
ejpam-6776	524	11	and	and	CCONJ
ejpam-6776	524	12	medicine	medicine	NOUN
ejpam-6776	524	13	.	.	PUNCT
ejpam-6776	525	1	quality	quality	NOUN
ejpam-6776	525	2	measurement	measurement	NOUN
ejpam-6776	525	3	and	and	CCONJ
ejpam-6776	525	4	quality	quality	NOUN
ejpam-6776	525	5	improvement	improvement	NOUN
ejpam-6776	525	6	.	.	PUNCT
ejpam-6776	526	1	national	national	PROPN
ejpam-6776	526	2	academies	academies	PROPN
ejpam-6776	526	3	press	press	PROPN
ejpam-6776	526	4	(	(	PUNCT
ejpam-6776	526	5	us	us	PROPN
ejpam-6776	526	6	)	)	PUNCT
ejpam-6776	526	7	,	,	PUNCT
ejpam-6776	526	8	2022	2022	NUM
ejpam-6776	526	9	.	.	PUNCT
ejpam-6776	527	1	[	[	X
ejpam-6776	527	2	35	35	NUM
ejpam-6776	527	3	]	]	X
ejpam-6776	527	4	l.	l.	PROPN
ejpam-6776	527	5	hörmander	hörmander	PROPN
ejpam-6776	527	6	.	.	PUNCT
ejpam-6776	528	1	hypoelliptic	hypoelliptic	ADJ
ejpam-6776	528	2	second	second	ADJ
ejpam-6776	528	3	order	order	NOUN
ejpam-6776	528	4	differential	differential	NOUN
ejpam-6776	528	5	operators	operator	NOUN
ejpam-6776	528	6	.	.	PUNCT
ejpam-6776	529	1	acta	acta	PROPN
ejpam-6776	529	2	mathematica	mathematica	PROPN
ejpam-6776	529	3	,	,	PUNCT
ejpam-6776	529	4	119(1):147–171	119(1):147–171	NUM
ejpam-6776	529	5	,	,	PUNCT
ejpam-6776	529	6	1967	1967	NUM
ejpam-6776	529	7	.	.	PUNCT
ejpam-6776	530	1	[	[	X
ejpam-6776	530	2	36	36	NUM
ejpam-6776	530	3	]	]	X
ejpam-6776	530	4	a.	a.	PROPN
ejpam-6776	530	5	khan	khan	PROPN
ejpam-6776	530	6	and	and	CCONJ
ejpam-6776	530	7	r.	r.	PROPN
ejpam-6776	530	8	zarin	zarin	PROPN
ejpam-6776	530	9	.	.	PUNCT
ejpam-6776	531	1	a	a	DET
ejpam-6776	531	2	stochastic	stochastic	ADJ
ejpam-6776	531	3	epidemic	epidemic	NOUN
ejpam-6776	531	4	model	model	NOUN
ejpam-6776	531	5	with	with	ADP
ejpam-6776	531	6	time	time	NOUN
ejpam-6776	531	7	delays	delay	NOUN
ejpam-6776	531	8	and	and	CCONJ
ejpam-6776	531	9	unreported	unreported	ADJ
ejpam-6776	531	10	cases	case	NOUN
ejpam-6776	531	11	:	:	PUNCT
ejpam-6776	531	12	uncertainty	uncertainty	NOUN
ejpam-6776	531	13	and	and	CCONJ
ejpam-6776	531	14	sensitivity	sensitivity	NOUN
ejpam-6776	531	15	analyses	analysis	NOUN
ejpam-6776	531	16	.	.	PUNCT
ejpam-6776	532	1	results	result	NOUN
ejpam-6776	532	2	in	in	ADP
ejpam-6776	532	3	control	control	NOUN
ejpam-6776	532	4	and	and	CCONJ
ejpam-6776	532	5	optimization	optimization	NOUN
ejpam-6776	532	6	,	,	PUNCT
ejpam-6776	532	7	15:100475	15:100475	NUM
ejpam-6776	532	8	,	,	PUNCT
ejpam-6776	532	9	2024	2024	NUM
ejpam-6776	532	10	.	.	PUNCT
ejpam-6776	533	1	[	[	X
ejpam-6776	533	2	37	37	NUM
ejpam-6776	533	3	]	]	PUNCT
ejpam-6776	533	4	x.	x.	PROPN
ejpam-6776	533	5	liu	liu	PROPN
ejpam-6776	533	6	,	,	PUNCT
ejpam-6776	533	7	y.	y.	PROPN
ejpam-6776	533	8	takeuchi	takeuchi	PROPN
ejpam-6776	533	9	,	,	PUNCT
ejpam-6776	533	10	and	and	CCONJ
ejpam-6776	533	11	s.	s.	PROPN
ejpam-6776	533	12	iwami	iwami	PROPN
ejpam-6776	533	13	.	.	PUNCT
ejpam-6776	534	1	svir	svir	NOUN
ejpam-6776	534	2	epidemic	epidemic	NOUN
ejpam-6776	534	3	models	model	NOUN
ejpam-6776	534	4	with	with	ADP
ejpam-6776	534	5	vaccination	vaccination	NOUN
ejpam-6776	534	6	strategies	strategy	NOUN
ejpam-6776	534	7	.	.	PUNCT
ejpam-6776	535	1	journal	journal	NOUN
ejpam-6776	535	2	of	of	ADP
ejpam-6776	535	3	theoretical	theoretical	ADJ
ejpam-6776	535	4	biology	biology	NOUN
ejpam-6776	535	5	,	,	PUNCT
ejpam-6776	535	6	253(1):1–11	253(1):1–11	PROPN
ejpam-6776	535	7	,	,	PUNCT
ejpam-6776	535	8	2008	2008	NUM
ejpam-6776	535	9	.	.	PUNCT
ejpam-6776	536	1	[	[	X
ejpam-6776	536	2	38	38	NUM
ejpam-6776	536	3	]	]	PUNCT
ejpam-6776	536	4	b.	b.	NOUN
ejpam-6776	536	5	øksendal	øksendal	NOUN
ejpam-6776	536	6	.	.	PUNCT
ejpam-6776	537	1	stochastic	stochastic	ADJ
ejpam-6776	537	2	differential	differential	ADJ
ejpam-6776	537	3	equations	equation	NOUN
ejpam-6776	537	4	:	:	PUNCT
ejpam-6776	537	5	an	an	DET
ejpam-6776	537	6	introduction	introduction	NOUN
ejpam-6776	537	7	with	with	ADP
ejpam-6776	537	8	applications	application	NOUN
ejpam-6776	537	9	.	.	PUNCT
ejpam-6776	538	1	springer	springer	PROPN
ejpam-6776	538	2	berlin	berlin	PROPN
ejpam-6776	538	3	,	,	PUNCT
ejpam-6776	538	4	6th	6th	ADJ
ejpam-6776	538	5	edition	edition	NOUN
ejpam-6776	538	6	,	,	PUNCT
ejpam-6776	538	7	2003	2003	NUM
ejpam-6776	538	8	.	.	PUNCT
ejpam-6776	539	1	j.	j.	PROPN
ejpam-6776	539	2	leo	leo	PROPN
ejpam-6776	539	3	amalraj	amalraj	PROPN
ejpam-6776	539	4	et	et	PROPN
ejpam-6776	539	5	al	al	PROPN
ejpam-6776	539	6	.	.	PUNCT
ejpam-6776	539	7	/	/	SYM
ejpam-6776	539	8	eur	eur	PROPN
ejpam-6776	539	9	.	.	PUNCT
ejpam-6776	540	1	j.	j.	PROPN
ejpam-6776	540	2	pure	pure	PROPN
ejpam-6776	540	3	appl	appl	PROPN
ejpam-6776	540	4	.	.	PROPN
ejpam-6776	540	5	math	math	PROPN
ejpam-6776	540	6	,	,	PUNCT
ejpam-6776	540	7	18	18	NUM
ejpam-6776	540	8	(	(	PUNCT
ejpam-6776	540	9	4	4	NUM
ejpam-6776	540	10	)	)	PUNCT
ejpam-6776	540	11	(	(	PUNCT
ejpam-6776	540	12	2025	2025	NUM
ejpam-6776	540	13	)	)	PUNCT
ejpam-6776	540	14	,	,	PUNCT
ejpam-6776	540	15	6776	6776	NUM
ejpam-6776	540	16	22	22	NUM
ejpam-6776	540	17	of	of	ADP
ejpam-6776	540	18	22	22	NUM
ejpam-6776	541	1	[	[	X
ejpam-6776	541	2	39	39	NUM
ejpam-6776	541	3	]	]	PUNCT
ejpam-6776	541	4	x.	x.	NOUN
ejpam-6776	541	5	mao	mao	PROPN
ejpam-6776	541	6	.	.	PUNCT
ejpam-6776	542	1	stochastic	stochastic	ADJ
ejpam-6776	542	2	differential	differential	ADJ
ejpam-6776	542	3	equations	equation	NOUN
ejpam-6776	542	4	and	and	CCONJ
ejpam-6776	542	5	applications	application	NOUN
ejpam-6776	542	6	.	.	PUNCT
ejpam-6776	543	1	horwood	horwood	PROPN
ejpam-6776	543	2	publishing	publishing	PROPN
ejpam-6776	543	3	chichester	chichester	PROPN
ejpam-6776	543	4	,	,	PUNCT
ejpam-6776	543	5	1997	1997	NUM
ejpam-6776	543	6	.	.	PUNCT
ejpam-6776	544	1	[	[	X
ejpam-6776	544	2	40	40	NUM
ejpam-6776	544	3	]	]	PUNCT
ejpam-6776	544	4	q.	q.	PROPN
ejpam-6776	544	5	liu	liu	PROPN
ejpam-6776	544	6	,	,	PUNCT
ejpam-6776	544	7	d.	d.	PROPN
ejpam-6776	544	8	jiang	jiang	PROPN
ejpam-6776	544	9	,	,	PUNCT
ejpam-6776	544	10	n.	n.	PROPN
ejpam-6776	544	11	shi	shi	PROPN
ejpam-6776	544	12	,	,	PUNCT
ejpam-6776	544	13	and	and	CCONJ
ejpam-6776	544	14	t.	t.	PROPN
ejpam-6776	544	15	hayat	hayat	PROPN
ejpam-6776	544	16	.	.	PUNCT
ejpam-6776	544	17	dynamics	dynamic	NOUN
ejpam-6776	544	18	of	of	ADP
ejpam-6776	544	19	a	a	DET
ejpam-6776	544	20	stochastic	stochastic	ADJ
ejpam-6776	544	21	sir	sir	NOUN
ejpam-6776	544	22	epidemic	epidemic	NOUN
ejpam-6776	544	23	model	model	NOUN
ejpam-6776	544	24	with	with	ADP
ejpam-6776	544	25	saturated	saturate	VERB
ejpam-6776	544	26	incidence	incidence	NOUN
ejpam-6776	544	27	and	and	CCONJ
ejpam-6776	544	28	vaccination	vaccination	NOUN
ejpam-6776	544	29	.	.	PUNCT
ejpam-6776	545	1	mathematics	mathematic	NOUN
ejpam-6776	545	2	and	and	CCONJ
ejpam-6776	545	3	computers	computer	NOUN
ejpam-6776	545	4	in	in	ADP
ejpam-6776	545	5	simulation	simulation	NOUN
ejpam-6776	545	6	,	,	PUNCT
ejpam-6776	545	7	205:1–26	205:1–26	NUM
ejpam-6776	545	8	,	,	PUNCT
ejpam-6776	545	9	2023	2023	NUM
ejpam-6776	545	10	.	.	PUNCT
ejpam-6776	546	1	[	[	X
ejpam-6776	546	2	41	41	NUM
ejpam-6776	546	3	]	]	X
ejpam-6776	546	4	y.	y.	PROPN
ejpam-6776	546	5	zhou	zhou	PROPN
ejpam-6776	546	6	and	and	CCONJ
ejpam-6776	546	7	w.	w.	PROPN
ejpam-6776	546	8	zhang	zhang	PROPN
ejpam-6776	546	9	.	.	PUNCT
ejpam-6776	547	1	threshold	threshold	PROPN
ejpam-6776	547	2	dynamics	dynamic	NOUN
ejpam-6776	547	3	of	of	ADP
ejpam-6776	547	4	a	a	DET
ejpam-6776	547	5	stochastic	stochastic	ADJ
ejpam-6776	547	6	sir	sir	NOUN
ejpam-6776	547	7	model	model	NOUN
ejpam-6776	547	8	with	with	ADP
ejpam-6776	547	9	vertical	vertical	ADJ
ejpam-6776	547	10	transmission	transmission	NOUN
ejpam-6776	547	11	and	and	CCONJ
ejpam-6776	547	12	vaccination	vaccination	NOUN
ejpam-6776	547	13	.	.	PUNCT
ejpam-6776	548	1	chaos	chaos	NOUN
ejpam-6776	548	2	,	,	PUNCT
ejpam-6776	548	3	solitons	soliton	NOUN
ejpam-6776	548	4	&	&	CCONJ
ejpam-6776	548	5	fractals	fractal	NOUN
ejpam-6776	548	6	,	,	PUNCT
ejpam-6776	548	7	139:110027	139:110027	NUM
ejpam-6776	548	8	,	,	PUNCT
ejpam-6776	548	9	2020	2020	NUM
ejpam-6776	548	10	.	.	PUNCT
ejpam-6776	549	1	[	[	X
ejpam-6776	549	2	42	42	NUM
ejpam-6776	549	3	]	]	X
ejpam-6776	549	4	o.	o.	NOUN
ejpam-6776	549	5	sharomi	sharomi	PROPN
ejpam-6776	549	6	and	and	CCONJ
ejpam-6776	549	7	t.	t.	PROPN
ejpam-6776	549	8	malik	malik	PROPN
ejpam-6776	549	9	.	.	PUNCT
ejpam-6776	550	1	optimal	optimal	ADJ
ejpam-6776	550	2	control	control	NOUN
ejpam-6776	550	3	in	in	ADP
ejpam-6776	550	4	epidemiology	epidemiology	NOUN
ejpam-6776	550	5	.	.	PUNCT
ejpam-6776	551	1	annals	annal	NOUN
ejpam-6776	551	2	of	of	ADP
ejpam-6776	551	3	operations	operation	NOUN
ejpam-6776	551	4	research	research	NOUN
ejpam-6776	551	5	,	,	PUNCT
ejpam-6776	551	6	251(1–2):55–71	251(1–2):55–71	NUM
ejpam-6776	551	7	,	,	PUNCT
ejpam-6776	551	8	2017	2017	NUM
ejpam-6776	551	9	.	.	PUNCT
ejpam-6776	552	1	[	[	X
ejpam-6776	552	2	43	43	NUM
ejpam-6776	552	3	]	]	PUNCT
ejpam-6776	552	4	z.	z.	PROPN
ejpam-6776	552	5	feng	feng	PROPN
ejpam-6776	552	6	,	,	PUNCT
ejpam-6776	552	7	s.	s.	PROPN
ejpam-6776	552	8	towers	towers	PROPN
ejpam-6776	552	9	,	,	PUNCT
ejpam-6776	552	10	and	and	CCONJ
ejpam-6776	552	11	y.	y.	PROPN
ejpam-6776	552	12	yang	yang	PROPN
ejpam-6776	552	13	.	.	PUNCT
ejpam-6776	553	1	modeling	model	VERB
ejpam-6776	553	2	the	the	DET
ejpam-6776	553	3	effects	effect	NOUN
ejpam-6776	553	4	of	of	ADP
ejpam-6776	553	5	vaccination	vaccination	NOUN
ejpam-6776	553	6	and	and	CCONJ
ejpam-6776	553	7	treatment	treatment	NOUN
ejpam-6776	553	8	on	on	ADP
ejpam-6776	553	9	pandemic	pandemic	ADJ
ejpam-6776	553	10	influenza	influenza	NOUN
ejpam-6776	553	11	.	.	PUNCT
ejpam-6776	554	1	mathematical	mathematical	ADJ
ejpam-6776	554	2	biosciences	bioscience	NOUN
ejpam-6776	554	3	,	,	PUNCT
ejpam-6776	554	4	234(1):1–9	234(1):1–9	NUM
ejpam-6776	554	5	,	,	PUNCT
ejpam-6776	554	6	2011	2011	NUM
ejpam-6776	554	7	.	.	PUNCT