Controlling imported malaria cases in the United States of America

Bassidy Dembele; Abdul-Aziz Yakubu

doi:10.3934/mbe.2017007

Article Contents

2017, Volume 14, Issue 1: 95-109. Doi: 10.3934/mbe.2017007

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Controlling imported malaria cases in the United States of America

Bassidy Dembele^1, and
Abdul-Aziz Yakubu^2, ,

1.
Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USA
2.
Department of Mathematics, Howard University, Washington, DC 20059, USA

* Corresponding author: Abdul-Aziz Yakubu
* Corresponding author: Abdul-Aziz Yakubu

Received: November 23, 2015

Accepted: July 2016

Published: September 2017

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Abstract

We extend the mathematical malaria epidemic model framework of Dembele et al. and use it to “capture” the 2013 Centers for Disease Control and Prevention (CDC) reported data on the 2011 number of imported malaria cases in the USA. Furthermore, we use our “fitted” malaria models for the top 20 countries of malaria acquisition by USA residents to study the impact of protecting USA residents from malaria infection when they travel to malaria endemic areas, the impact of protecting residents of malaria endemic regions from mosquito bites and the impact of killing mosquitoes in those endemic areas on the CDC number of imported malaria cases in USA. To significantly reduce the number of imported malaria cases in USA, for each top 20 country of malaria acquisition by USA travelers, we compute the optimal proportion of USA international travelers that must be protected against malaria infection and the optimal proportion of mosquitoes that must be killed.

Keywords:

Mathematics Subject Classification: 92B05.

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Table 1. Model Parameters and Descriptions.

Parameter	Description
α_hm	Human infectivity rate
α_mh	Mosquito infectivity rate
b_m	Mosquito biting rate
λ_h	Human birth rate
λ_m	Mosquito birth rate
β_h	Human loss of immunity rate
α_h	Human recovery rate
μ_d	Malaria induced death rate
μ_h, μ_m	Human, mosquito death rates
θ_m	Mosquito loss of incubation rate
c_h	Proportion of humans using bed net
c_m	Proportion of mosquitoes killed
c_u	Proportion of USA travellers to endemic countries
$\gamma =\frac{\alpha _{hm}b_{m}N_{m}}{N_{h}}$	Infection rate of humans in endemic countries
γ_u	Infection rate of USA travellers to endemic countries

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Table 2. 2011 CDC Data: Number of Imported Malaria Cases and Country Of Acquisition.

Malaria Acquisition Country	2011 CDC Data
Afghanistan	60
Cameroon	62
Cote D'Ivoire	28
Ethiopia	55
Ghana	156
Guinea	40
Guyana	19
Haiti	72
Honduras	21
India	223
Kenya	37
Liberia	90
Nigeria	213
Pakistan	39
Sierra Leone	116
Sudan	32
Uganda	61
Senegal	17
Eritrea	18
Gambia	21
Other	540

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Table 3. Estimates of Model Parameters Per Day.

Country	α_mh	α_hm	u	λ_h	β_h	α_h	μ_h	μ_m	θ_m	μ_d
Afghanistan	0.014	0.014	0.020845	0.000124	0.03	0.25	0.0000219	0.033	0.1	3.1144*10^-9
Cameroon	0.096	0.096	0.0043860	0.000094	0.03	0.25	0.0000329	0.033	0.1	6.9372*10^-7
Cote D'Ivoire	0.088	0.088	0.002231	0.00009	0.03	0.25	0.0000411	0.033	0.1	2.3603*10^-6
Ethiopia	0.037	0.037	0.010205	0.000098	0.03	0.25	0.0000219	0.033	0.1	3.7081*10^-8
Ghana	0.080	0.080	0.013519	0.00008	0.03	0.25	0.0000247	0.033	0.1	3.8825*10^-7
Guinea	0.081	0.081	0.00343	0.000102	0.03	0.25	0.0000329	0.033	0.1	1.5945*10^-7
Guyana	0.018	0.018	0.005986	0.000045	0.03	0.25	0.0000192	0.033	0.1	3.01337*10^-7
Haiti	0.005	0.005	0.02941	0.000071	0.03	0.25	0.0000247	0.033	0.1	2.4658*10^-7
Honduras	0.001	0.001	0.008831	0.000075	0.03	0.25	0.000037	0.033	0.1	3.6696*10^-10
India	0.001	0.001	0.09373	0.00006	0.03	0.25	0.0000219	0.033	0.1	2.5911*10^-9
Kenya	0.204	0.204	0.001605	0.000099	0.03	0.25	0.0000247	0.033	0.1	1.8904*10^-6
Liberia	0.220	0.220	0.0037256	0.000099	0.03	0.25	0.0000247	0.033	0.1	1.1818*10^-6
Nigeria	0.028	0.028	0.0506	0.0001	0.03	0.25	0.0000384	0.033	0.1	1.3319*10^-7
Pakistan	0.023	0.023	0.010676	0.000075	0.03	0.25	0.0000192	0.033	0.1	1.5343*10^-6
Sierra Leone	0.114	0.114	0.0074855	0.0001	0.03	0.25	0.0000493	0.033	0.1	8.3397*10^-7
Sudan	0.064	0.064	0.0034228	0.000089	0.03	0.25	0.0000247	0.033	0.1	9.05*10^-8
Uganda	0.3	0.3	0.0021354	0.000121	0.03	0.25	0.0000193	0.033	0.1	5.2734*10^-7
Senegal	0.01773	0.01773	0.005383	0.0001	0.03	0.25	0.0000219	0.033	0.1	1.2547*10^-7
Eritrea	0.0042	0.0042	0.007413	0.000092	0.03	0.25	0.0000192	0.033	0.1	1.2421*10^-8
Gambia	0.28	0.28	0.0007616	0.000094	0.03	0.25	0.0000274	0.033	0.1	3.86*10^-7
Other	0.005	0.005	0.220536	0.00009	0.03	0.25	0.00006	0.033	0.1	1.4227*10^-5

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Table 4. 2011 CDC Data Versus Model Results: Number of Imported Malaria Cases and Country Of Acquisition.

Malaria Country	CDC Data	Model Result
Afghanistan	60	60.02
Cameroon	62	62.04
Cote D'Ivoire	28	28.02
Ethiopia	55	55.01
Ghana	156	156.06
Guinea	40	40.04
Guyana	19	19.06
Haiti	72	72.04
Honduras	21	21.02
India	223	223.03
Kenya	37	37.09
Liberia	90	90.04
Nigeria	213	213.03
Pakistan	39	39.02
Sierra Leone	116	116.05
Sudan	32	32.06
Uganda	61	61.01
Senegal	17	17.02
Eritrea	18	18.01
Gambia	21	21.02
Other	540	540.03

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Table 5. Policy 1: Percentage of USA Protection and Optimal Number of Imported Malaria Cases.

Country	10%	20%	30%	40%	50%	60%	70%	80%	90%
Afghanistan	54.03	48.04	42.05	36.03	30.04	24.02	18.02	12.02	6.01
Cameroon	55.84	49.65	43.46	37.25	31.05	24.83	18.62	12.02	6.21
Cote D'Ivoire	25.23	22.43	19.63	16.82	14.02	11.22	8.41	5.61	2.8
Ethiopia	49.52	44.03	38.54	33.03	27.53	22.02	16.51	11.01	5.5
Ghana	140.49	124.91	109.34	93.7	78.11	62.48	46.85	31.25	15.62
Guinea	36.04	32.05	28.05	24.04	20.04	16.03	12.02	8.02	4.01
Guyana	17.16	15.26	13.36	11.45	9.54	7.63	5.72	3.82	1.91
Haiti	64.85	57.66	50.47	43.26	36.06	28.84	21.63	14.42	7.21
Honduras	18.92	16.82	14.73	12.63	10.52	8.41	6.31	4.21	2.1
India	200.78	178.53	156.27	133.92	111.64	89.3	66.96	44.66	22.32
Kenya	33.39	26.69	25.99	22.27	18.57	14.85	11.13	7.43	3.71
Liberia	81.05	72.07	63.08	54.06	45.06	36.04	27.03	18.03	9.01
Nigeria	191.77	170.52	149.26	127.92	106.63	85.29	63.96	42.66	21.32
Pakistan	35.12	31.23	27.34	23.43	19.53	15.62	11.71	7.81	3.9
Sierra Leone	104.47	92.89	81.31	69.68	58.09	46.46	34.84	23.24	11.61
Sudan	28.86	25.66	22.46	19.25	16.04	12.83	9.62	6.42	3.21
Uganda	54.92	48.83	42.74	36.63	30.54	24.42	18.31	12.21	6.1
Senegal	15.32	13.62	11.93	10.22	8.52	6.81	5.11	3.41	1.7
Eritrea	16.21	14.41	12.61	10.81	9.01	7.21	5.4	3.6	1.8
Gambia	18.92	16.82	14.73	12.62	10.52	8.41	6.31	4.21	2.1
Other	486.17	432.30	378.42	324.33	270.38	216.27	162.19	108.18	54.07
Total	1,729.06	1,537.42	1,345.77	1,153.35	961.44	768.99	576.66	384.64	192.22

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Table 6. Policy 3: Percentage of Mosquitoes Killed in Endemic Regions and Optimal Number of Imported Malaria Cases.

Country	10%	20%	30%	40%	50%	60%	70%	80%	90%
Afghanistan	58.12	56.16	54.14	51.87	49.37	46.42	42.75	37.73	30.16
Cameroon	55.81	49.43	42.91	36.34	29.79	23.42	17.45	12.14	7.66
Cote D'Ivoire	25.18	22.27	19.32	16.36	13.44	10.63	8.01	5.67	3.66
Ethiopia	50.15	45.46	40.95	36.63	32.46	28.41	24.37	20.12	15.22
Ghana	140.02	123.75	107.33	91.00	75.05	59.78	45.64	32.99	21.83
Guinea	35.93	31.75	27.54	23.34	19.24	15.31	11.66	8.41	5.55
Guyana	18.25	17.43	16.60	15.74	14.81	13.78	12.55	10.98	8.71
Haiti	71.15	70.1	68.84	67.26	65.21	62.43	58.44	52.38	42.38
Honduras	20.84	20.61	20.31	19.91	19.37	18.61	17.48	15.71	12.74
India	221.1	218.65	215.49	211.32	205.58	197.49	185.47	166.69	135.18
Kenya	33.91	30.51	26.90	23.70	19.04	14.88	10.67	6.66	3.35
Liberia	82.45	74.33	65.67	56.43	46.67p>	36.51	26.19	16.28	8.01
Nigeria	198.11	183.65	169.59	155.75	142.02	128.04	113.13	96.19	74.54
Pakistan	36.80	34.62	32.47	30.30	28.07	25.72	23.10	19.92	15.63
Sierra Leone	104.75	93.06	80.98	68.66	56.19	43.87	32.13	21.61	12.96
Sudan	28.71	25.38	22.08	18.86	15.78	12.87	10.17	7.70	5.35
Uganda	56.29	51.16	45.59	39.53	33.00	26.03	18.76	11.55	5.31
Senegal	16.31	15.59	14.86	14.10	13.28	12.36	11.27	9.86	7.83
Eritrea	17.80	17.56	17.26	16.88	16.38	15.7	14.71	13.19	10.68
Gambia	19.36	17.56	15.62	13.52	11.26	8.86	6.38	3.93	1.83
Other	533.34	525.49	516.02	504.20	488.82	468.03	438.16	392.72	317.79
Total	1,824.38	1,724.52	1,620.43	1,511.7	1,394.83	1,269.15	1,128.49	962.43	746.37

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Table 7. Policy 4: Percentage of Protected USA Residents Plus Percentage of Mosquitoes Killed and the Resulting Number of Imported Malaria Cases.

Country	USA Protected	Mosquitoes Killed	Malaria cases
Afghanistan	90%	70%	4.27
Cameroon	90%	70%	1.75
Cote D'Ivoire	90%	70%	0.80
Ethiopia	90%	70%	2.44
Ghana	90%	70%	4.56
Guinea	90%	70%	1.17
Guyana	90%	70%	1.26
Haiti	90%	70%	5.85
Honduras	90%	70%	1.75
India	90%	70%	18.56
Kenya	90%	70%	1.07
Liberia	90%	70%	2.62
Nigeria	90%	70%	11.32
Pakistan	90%	70%	2.31
Sierra Leone	90%	70%	3.21
Sudan	90%	70%	1.02
Uganda	90%	70%	1.88
Senegal	90%	70%	1.13
Eritrea	90%	70%	1.47
Gambia	90%	60%	0.64
Other	90%	70%	43.85

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