id	sid	eid	entity	type
m-1153	1	1	awolowo university	ORG
m-1153	1	2	nigeria	GPE
m-1153	6	1	1	CARDINAL
m-1153	8	1	ijo international journal of mathematics	ORG
m-1153	8	2	2992-4421	DATE
m-1153	8	3	08	CARDINAL
m-1153	9	1	9 | september 2025	TIME
m-1153	9	2	23 1	CARDINAL
m-1153	9	3	ali et al.	PERSON
m-1153	9	4	2015	DATE
m-1153	9	5	2023	CARDINAL
m-1153	10	1	2004	DATE
m-1153	11	1	africa	LOC
m-1153	11	2	asia	LOC
m-1153	11	3	latin america	LOC
m-1153	11	4	2011	DATE
m-1153	11	5	2001	DATE
m-1153	12	1	anderson	PERSON
m-1153	12	2	1991	DATE
m-1153	12	3	capasso	PERSON
m-1153	12	4	paveri-fontana	ORG
m-1153	12	5	1979	DATE
m-1153	12	6	hartley et al.	PERSON
m-1153	12	7	2006	DATE
m-1153	14	1	2001	DATE
m-1153	14	2	tien	PERSON
m-1153	14	3	2010	DATE
m-1153	15	1	leung et al.	PERSON
m-1153	15	2	2012	DATE
m-1153	15	3	2023	CARDINAL
m-1153	16	1	2020	DATE
m-1153	17	1	2007	DATE
m-1153	17	2	chao et al.	PERSON
m-1153	17	3	2011	DATE
m-1153	19	1	van den driessche	PERSON
m-1153	19	2	watmough	GPE
m-1153	19	3	2002	DATE
m-1153	20	1	cholera ijo international journal of mathematics	ORG
m-1153	20	2	2992-4421	DATE
m-1153	20	3	08	CARDINAL
m-1153	21	1	9 | september 2025	TIME
m-1153	21	2	24	CARDINAL
m-1153	22	1	castillo-chavez	PERSON
m-1153	22	2	feng	PERSON
m-1153	22	3	1997	DATE
m-1153	22	4	2011	DATE
m-1153	23	1	paveri-fontana	ORG
m-1153	23	2	1979	DATE
m-1153	23	3	1973	DATE
m-1153	23	4	the mediterranean region	LOC
m-1153	24	1	2001	DATE
m-1153	27	1	hartley et al	PERSON
m-1153	27	2	2006	DATE
m-1153	28	1	tien	PERSON
m-1153	28	2	2010	DATE
m-1153	29	1	bertuzzo et al	PERSON
m-1153	29	2	2011	DATE
m-1153	29	3	haiti	GPE
m-1153	31	1	van den driessche	PERSON
m-1153	31	2	watmough	GPE
m-1153	31	3	2002	DATE
m-1153	32	1	2011	DATE
m-1153	32	2	eisenberg et al.	PERSON
m-1153	32	3	2013	DATE
m-1153	35	1	2007	DATE
m-1153	35	2	chao et al	PERSON
m-1153	36	1	2011	DATE
m-1153	37	1	leung et al.	PERSON
m-1153	37	2	2012	DATE
m-1153	37	3	qadri ijo international journal of mathematics	ORG
m-1153	37	4	2992-4421	DATE
m-1153	37	5	08	CARDINAL
m-1153	38	1	9 | september 2025	TIME
m-1153	39	1	25 et	QUANTITY
m-1153	39	2	2020	DATE
m-1153	40	1	anderson	PERSON
m-1153	40	2	1991	DATE
m-1153	40	3	2000	DATE
m-1153	41	1	el niño	ORG
m-1153	42	1	2000	DATE
m-1153	42	2	2004	DATE
m-1153	44	1	al	ORG
m-1153	45	1	2018	DATE
m-1153	45	2	2023	CARDINAL
m-1153	49	1	2	CARDINAL
m-1153	49	2	four	CARDINAL
m-1153	51	1	+ i(t	PERSON
m-1153	53	1	2992-4421	DATE
m-1153	54	1	08	CARDINAL
m-1153	55	1	9 | september 2025	TIME
m-1153	55	2	26	CARDINAL
m-1153	55	3	1	CARDINAL
m-1153	57	1	2	CARDINAL
m-1153	59	1	4	CARDINAL
m-1153	59	2	5	CARDINAL
m-1153	59	3	•	CARDINAL
m-1153	59	4	•	CARDINAL
m-1153	59	5	•	CARDINAL
m-1153	59	6	•	CARDINAL
m-1153	59	7	•	CARDINAL
m-1153	59	8	•	CARDINAL
m-1153	59	9	•	CARDINAL
m-1153	59	10	•	CARDINAL
m-1153	59	11	•	CARDINAL
m-1153	59	12	•	CARDINAL
m-1153	60	1	ijo international journal of mathematics	ORG
m-1153	60	2	2992-4421	DATE
m-1153	60	3	08	CARDINAL
m-1153	61	1	9 | september 2025	TIME
m-1153	62	1	27 3	CARDINAL
m-1153	62	2	3.1	CARDINAL
m-1153	64	1	3.2	CARDINAL
m-1153	64	2	0	CARDINAL
m-1153	65	1	1	CARDINAL
m-1153	65	2	0	CARDINAL
m-1153	66	1	3	CARDINAL
m-1153	66	2	0	CARDINAL
m-1153	67	1	0	DATE
m-1153	68	1	0	CARDINAL
m-1153	68	2	2	CARDINAL
m-1153	68	3	0	CARDINAL
m-1153	70	1	0	DATE
m-1153	70	2	ν	NORP
m-1153	71	1	ijo international journal of mathematics	ORG
m-1153	71	2	2992-4421	DATE
m-1153	71	3	08	CARDINAL
m-1153	72	1	9 | september 2025	TIME
m-1153	73	1	28 3.3	CARDINAL
m-1153	73	2	0	CARDINAL
m-1153	73	3	1	CARDINAL
m-1153	73	4	0	CARDINAL
m-1153	75	1	τ i∗.	ORG
m-1153	75	2	2	CARDINAL
m-1153	76	1	0	CARDINAL
m-1153	77	1	0	CARDINAL
m-1153	77	2	ν	NORP
m-1153	78	1	3	CARDINAL
m-1153	79	1	− s∗ (βpi ∗ + βbb	ORG
m-1153	79	2	ρs∗.	GPE
m-1153	80	1	− ρs∗.	PERSON
m-1153	81	1	0	CARDINAL
m-1153	81	2	4	CARDINAL
m-1153	82	1	0	CARDINAL
m-1153	83	1	ijo international journal of mathematics	ORG
m-1153	83	2	2992-4421	DATE
m-1153	83	3	08	CARDINAL
m-1153	84	1	9 | september 2025	TIME
m-1153	85	1	29	CARDINAL
m-1153	85	2	5	CARDINAL
m-1153	86	1	2	CARDINAL
m-1153	86	2	4a(µ+	CARDINAL
m-1153	87	1	σ	MONEY
m-1153	87	2	b∗	ORG
m-1153	87	3	γ +	ORG
m-1153	87	4	3.4	CARDINAL
m-1153	88	1	2	CARDINAL
m-1153	88	2	0	CARDINAL
m-1153	91	1	1− 1 r0	LAW
m-1153	91	2	b∗	ORG
m-1153	92	1	1	CARDINAL
m-1153	92	2	4	CARDINAL
m-1153	92	3	4.1	CARDINAL
m-1153	93	1	ijo international journal of mathematics	ORG
m-1153	93	2	2992-4421	DATE
m-1153	93	3	08	CARDINAL
m-1153	94	1	9 | september 2025	TIME
m-1153	94	2	30	CARDINAL
m-1153	95	1	dfe	ORG
m-1153	95	2	r∗ =	PERSON
m-1153	95	3	0	CARDINAL
m-1153	95	4	+ η	PERSON
m-1153	95	5	1	CARDINAL
m-1153	96	1	b)⊤.	PERSON
m-1153	98	1	2)–(4	CARDINAL
m-1153	98	2	0	CARDINAL
m-1153	99	1	2	CARDINAL
m-1153	99	2	jacobians	NORP
m-1153	100	1	σ 0	PERSON
m-1153	101	1	3	CARDINAL
m-1153	102	1	σ	ORG
m-1153	102	2	0	CARDINAL
m-1153	103	1	−1	CARDINAL
m-1153	103	2	1	CARDINAL
m-1153	104	1	k = fv	PERSON
m-1153	105	1	∗	CARDINAL
m-1153	105	2	0	CARDINAL
m-1153	106	1	ijo international journal of mathematics	ORG
m-1153	106	2	2992-4421	DATE
m-1153	106	3	08	CARDINAL
m-1153	107	1	9 | september 2025	TIME
m-1153	107	2	31	CARDINAL
m-1153	107	3	4	CARDINAL
m-1153	108	1	1	CARDINAL
m-1153	108	2	1	CARDINAL
m-1153	111	1	1	CARDINAL
m-1153	112	1	+ η	PERSON
m-1153	113	1	4.2	CARDINAL
m-1153	113	2	∗ σ︸	DATE
m-1153	116	1	1	CARDINAL
m-1153	116	2	5	CARDINAL
m-1153	116	3	5.1	CARDINAL
m-1153	120	1	ijo international journal of mathematics	ORG
m-1153	120	2	2992-4421	DATE
m-1153	120	3	08	CARDINAL
m-1153	121	1	9 | september 2025	TIME
m-1153	122	1	32	DATE
m-1153	123	1	1	CARDINAL
m-1153	124	1	+ η	PERSON
m-1153	125	1	6	CARDINAL
m-1153	126	1	1	CARDINAL
m-1153	126	2	1	CARDINAL
m-1153	127	1	1	CARDINAL
m-1153	130	1	2	CARDINAL
m-1153	131	1	+ η	PERSON
m-1153	132	1	3	CARDINAL
m-1153	135	1	4.	CARDINAL
m-1153	136	1	1	CARDINAL
m-1153	138	1	ijo international journal of mathematics	ORG
m-1153	138	2	2992-4421	DATE
m-1153	138	3	08	CARDINAL
m-1153	139	1	9 | september 2025	TIME
m-1153	139	2	33	CARDINAL
m-1153	139	3	•	CARDINAL
m-1153	142	1	•	CARDINAL
m-1153	144	1	•	CARDINAL
m-1153	146	1	•	CARDINAL
m-1153	149	1	•	CARDINAL
m-1153	155	1	ijo international journal of mathematics	ORG
m-1153	155	2	2992-4421	DATE
m-1153	155	3	08	CARDINAL
m-1153	156	1	9 | september 2025	TIME
m-1153	156	2	34	CARDINAL
m-1153	156	3	ali	PERSON
m-1153	156	4	m., nelson	PERSON
m-1153	156	5	a. r.	PERSON
m-1153	156	6	a. l.	PERSON
m-1153	156	7	d. a.	PERSON
m-1153	156	8	2015	CARDINAL
m-1153	158	1	plos	PERSON
m-1153	159	1	anderson	PERSON
m-1153	159	2	r. m.	PERSON
m-1153	159	3	r. m.	PERSON
m-1153	159	4	1991	DATE
m-1153	161	1	oxford university	ORG
m-1153	162	1	bertuzzo	PERSON
m-1153	162	2	e.	PERSON
m-1153	162	3	mari	PERSON
m-1153	162	4	l.	PERSON
m-1153	162	5	r.	NORP
m-1153	162	6	blokesch	GPE
m-1153	162	7	m.	PERSON
m-1153	162	8	rinaldo, a. (	PERSON
m-1153	162	9	2011	DATE
m-1153	164	1	38(6	CARDINAL
m-1153	165	1	capasso	PERSON
m-1153	165	2	paveri-fontana	ORG
m-1153	165	3	s. l. (	PERSON
m-1153	165	4	1979	DATE
m-1153	166	1	1973	DATE
m-1153	166	2	european	NORP
m-1153	166	3	mediterranean	LOC
m-1153	167	1	d’épidémiologie et de santé publique	PERSON
m-1153	167	2	27(2):121–132	DATE
m-1153	168	1	castillo-chavez	PERSON
m-1153	168	2	1997	DATE
m-1153	170	1	35(6):629–656	ORG
m-1153	171	1	chao	PERSON
m-1153	171	2	d. l.	PERSON
m-1153	171	3	halloran	GPE
m-1153	171	4	m. e.	PERSON
m-1153	171	5	i. m.	PERSON
m-1153	171	6	2011	DATE
m-1153	172	1	haiti	GPE
m-1153	173	1	the national academy of sciences	ORG
m-1153	173	2	108(17):7081–7085	CARDINAL
m-1153	173	3	c. t.	PERSON
m-1153	173	4	2001	DATE
m-1153	175	1	1:1	CARDINAL
m-1153	176	1	eisenberg	PERSON
m-1153	176	2	m. c.	PERSON
m-1153	176	3	shuai	PERSON
m-1153	176	4	z.	PERSON
m-1153	176	5	tien	PERSON
m-1153	176	6	j. h.	PERSON
m-1153	176	7	van den driessche	PERSON
m-1153	176	8	2013	DATE
m-1153	178	1	246(1):105–112	CARDINAL
m-1153	179	1	hartley	ORG
m-1153	179	2	d. m.	PERSON
m-1153	179	3	j. g.	PERSON
m-1153	179	4	d. l.	PERSON
m-1153	179	5	2006	DATE
m-1153	181	1	plos medicine	PERSON
m-1153	181	2	3(1):e7	CARDINAL
m-1153	182	1	h. w.	PERSON
m-1153	182	2	2000	DATE
m-1153	184	1	siam	GPE
m-1153	184	2	42(4):599	CARDINAL
m-1153	184	3	653	CARDINAL
m-1153	185	1	ijo international journal of mathematics	ORG
m-1153	185	2	2992-4421	DATE
m-1153	185	3	08	CARDINAL
m-1153	186	1	9 | september 2025	TIME
m-1153	186	2	35 koelle	QUANTITY
m-1153	186	3	k.	PERSON
m-1153	186	4	m. (	PERSON
m-1153	186	5	2004	DATE
m-1153	188	1	american	NORP
m-1153	188	2	163(6):901–913	CARDINAL
m-1153	188	3	leung	PERSON
m-1153	188	4	d. t.	PERSON
m-1153	188	5	rahman	PERSON
m-1153	188	6	m. a.	PERSON
m-1153	188	7	mohasin	GPE
m-1153	188	8	m., riyadh	PERSON
m-1153	188	9	m. a.	PERSON
m-1153	188	10	patel	PERSON
m-1153	188	11	s. m.	PERSON
m-1153	188	12	qadri, f. (	ORG
m-1153	188	13	2012	DATE
m-1153	190	1	30(4):594–599	CARDINAL
m-1153	191	1	i. m.	PERSON
m-1153	191	2	nizam, a., ali, m., yunus	PERSON
m-1153	191	3	m.	PERSON
m-1153	191	4	j. d.	PERSON
m-1153	191	5	2007	DATE
m-1153	193	1	plos medicine	PERSON
m-1153	193	2	4(11):e336	CARDINAL
m-1153	193	3	mukandavire	PERSON
m-1153	193	4	z.	PERSON
m-1153	193	5	s.	PERSON
m-1153	193	6	wang	PERSON
m-1153	193	7	j.	PERSON
m-1153	193	8	smith	GPE
m-1153	193	9	d. l.	PERSON
m-1153	193	10	j. g.	PERSON
m-1153	193	11	2011	DATE
m-1153	194	1	2008–2009	CARDINAL
m-1153	194	2	zimbabwe	GPE
m-1153	195	1	the national academy of sciences	ORG
m-1153	195	2	108(21):8767–8772	CARDINAL
m-1153	196	1	m.	PERSON
m-1153	196	2	x.	GPE
m-1153	196	3	ellner	PERSON
m-1153	196	4	s. p.	PERSON
m-1153	196	5	colwell	PERSON
m-1153	196	6	r.	NORP
m-1153	196	7	m. j.	PERSON
m-1153	196	8	2000	DATE
m-1153	197	1	el niño	GPE
m-1153	198	1	289(5485):1766–1769	CARDINAL
m-1153	199	1	qadri	ORG
m-1153	199	2	f.	PERSON
m-1153	199	3	t. f., ali	PERSON
m-1153	199	4	m.	PERSON
m-1153	199	5	j. d.	PERSON
m-1153	199	6	2020	DATE
m-1153	200	1	yemen	GPE
m-1153	201	1	new england journal of medicine	ORG
m-1153	201	2	382(6):568–571	DATE
m-1153	202	1	tien	PERSON
m-1153	202	2	j. h.	PERSON
m-1153	202	3	d. j. d.	PERSON
m-1153	202	4	2010	DATE
m-1153	204	1	72(6):1506	CARDINAL
m-1153	204	2	1533	DATE
m-1153	205	1	b. f.	PERSON
m-1153	205	2	khalil	GPE
m-1153	205	3	i. a.	PERSON
m-1153	205	4	rao	ORG
m-1153	205	5	p. c.	PERSON
m-1153	205	6	j.	PERSON
m-1153	205	7	s. r.	PERSON
m-1153	205	8	r. c.	PERSON
m-1153	205	9	2018	DATE
m-1153	206	1	195	CARDINAL
m-1153	206	2	2016	DATE
m-1153	207	1	18(11):1211–1228	DATE
m-1153	208	1	van den driessche	PERSON
m-1153	208	2	watmough	GPE
m-1153	208	3	j. (	PERSON
m-1153	208	4	2002	DATE
m-1153	210	1	180(1–2):29–48	CARDINAL
m-1153	211	1	ijo international journal of mathematics	ORG
m-1153	211	2	2992-4421	DATE
m-1153	211	3	08	CARDINAL
m-1153	212	1	9 | september 2025	TIME
m-1153	212	2	36	CARDINAL
m-1153	212	3	2023	CARDINAL
m-1153	215	1	2025	CARDINAL
m-1153	216	1	ijo international journal of mathematics	ORG
m-1153	216	2	2992-4421	DATE
m-1153	216	3	08	CARDINAL
m-1153	217	1	9 | september 2025	TIME
m-1153	217	2	37	CARDINAL
m-1153	217	3	i*>0	DATE