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Controlling imported malaria cases in the United States of America

  • * Corresponding author: Abdul-Aziz Yakubu

    * Corresponding author: Abdul-Aziz Yakubu
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  • 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.

    Mathematics Subject Classification: 92B05.

    Citation:

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  • Table 1.  Model Parameters and Descriptions.

    Parameter Description
    αhm Human infectivity rate
    αmh Mosquito infectivity rate
    bm Mosquito biting rate
    λh Human birth rate
    λm Mosquito birth rate
    βh Human loss of immunity rate
    αh Human recovery rate
    μd Malaria induced death rate
    μh, μm Human, mosquito death rates
    θm Mosquito loss of incubation rate
    ch Proportion of humans using bed net
    cm Proportion of mosquitoes killed
    cu Proportion of USA travellers to endemic countries
    $\gamma =\frac{\alpha _{hm}b_{m}N_{m}}{N_{h}}$ Infection rate of humans in endemic countries
    γu Infection rate of USA travellers to endemic countries
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    Table 3.  Estimates of Model Parameters Per Day.

    Country αmh αhm u λh βh αh μh μm θm μd
    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
     | Show Table
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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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV

    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
     | Show Table
    DownLoad: CSV
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