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The Time Distribution of Sulfadoxine-Pyrimethamine Protection from Malaria

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Abstract

Sulfadoxine-pyrimethamine (SP) has been one of the most widely used antimalarial treatments world-wide, and is also used prophylactically in vulnerable populations. In this paper, we develop a mathematical model which allows us to infer the time distribution of SP protection from drug-trial data. Fitting our model to data from a controlled field study in Mali, we find that SP provided protection from malaria for an average of 37.9 days in this pediatric population. We demonstrate that the duration of SP protection is not well described by an exponential distribution, and in fact has a much narrower dispersal about the mean; the best-fit standard deviation predicted by our model was only 17.0 days, as opposed to 41.8 days for the exponential model. We estimate the monthly entomological inoculation rate and the basic reproductive number for malaria in this population, and demonstrate that extremely high SP treatment rates would be necessary to maintain an effective reproductive number below one throughout a single rainy season. These results have implications for further efforts to model the impact of SP treatment, or for investigations of the optimal timing of prophylactic SP.

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References

  • Aguas, R., White, L. J., Snow, R. W., & Gomes, M. G. M. (2008). Prospects for malaria eradication in Sub-Saharan Africa. PLoS ONE, 3, 1–6.

    Article  Google Scholar 

  • Anderson, R. M., & May, R. M. (1991). Infectious diseases of humans: dynamics and control. Oxford: Oxford University Press.

    Google Scholar 

  • Arino, J., Ducrot, A., & Zongo, P. (2012). A metapopulation model for malaria with transmission-blocking partial immunity in hosts. J. Math. Biol., 64, 423–448.

    Article  MathSciNet  MATH  Google Scholar 

  • Auger, P., Kouokam, E., Sallet, G., Tchuente, M., & Tsanou, B. (2008). The Ross–Macdonald model in a patchy environment. Math. Biosci., 216, 123–131.

    Article  MathSciNet  MATH  Google Scholar 

  • Barnes, K. I., Little, F., Smith, P. J., Evans, A., Watkins, W. M., & White, N. J. (2006). Sulfadoxine-pyrimethamine pharmacokinetics in malaria: pediatric dosing implications. Clin. Pharmacol. Ther., 67, 582–596.

    Article  Google Scholar 

  • Beier, J. C. (1998). Malaria parasite development in mosquitoes. Annu. Rev. Entomol., 43, 519–543.

    Article  Google Scholar 

  • Bell, D. J., Nyirongo, S. K., Mukaka, M., Zijlstra, E. E., Plowe, C. V., Molyneux, M. E., Ward, S. A., & Winstanley, P. A. (2008). Sulfadoxine-pyrimethamine-based combinations for malaria: a randomised blinded trial to compare efficacy, safety and selection of resistance in Malawi. PLoS ONE, 3, e1578.

    Article  Google Scholar 

  • Burkot, T. R., & Graves, P. M. (1995). The value of vector-based estimates of malaria transmission. Ann. Trop. Med. Parasitol., 89, 125–134.

    Google Scholar 

  • Centers for Disease Control and Prevention (2010). Malaria fact sheets. http://www.cdc.gov/malaria/about/facts.html.

  • Centers for Disease Control and Prevention (2012). CDC health information for international travel 2012: the yellow book. Oxford: Oxford University Press.

    Google Scholar 

  • Chitnis, N., Cushing, J. M., & Hyman, J. M. (2006). Bifurcation analysis of a mathematical model for malaria transmission. SIAM J. Appl. Math., 67, 24–45.

    Article  MathSciNet  MATH  Google Scholar 

  • Chitnis, N., Smith, T., & Steketee, R. (2008). A mathematical model for the dynamics of malaria in mosquitoes feeding on a heterogeneous host population. J. Biol. Dyn., 2, 259–285.

    Article  MathSciNet  MATH  Google Scholar 

  • Chitnis, N., Hardy, D., & Smith, T. (2012). A periodically-forced mathematical model for the seasonal dynamics of malaria in mosquitoes. Bull. Math. Biol., 74, 1098–1124. doi:10.1007/s11538-011-9710-0.

    Article  MathSciNet  MATH  Google Scholar 

  • Cintron-Arias, A., Castillo-Chavez, C., Bettencourt, L. M. A., Lloyd, A. L., & Banks, H. T. (2009). The estimation of the effective reproductive number from disease outbreak data. Math. Biosci. Eng., 6, 261–282.

    Article  MathSciNet  MATH  Google Scholar 

  • Coulibaly, D., Diallo, D. A., Thera, M. A., Dicko, A., Guindo, A. B., Kone, A. K., Cissoko, Y., Coulibaly, S., Djimde, A., Lyke, K., Doumbo, O. K., & Plowe, C. V. (2002). Impact of preseason treatment on incidence of falciparum malaria and parasite density at a site for testing malaria vaccines in Bandiagara, Mali. Am. J. Trop. Med. Hyg., 67, 604–610.

    Google Scholar 

  • Dembele, B., Friedman, A., & Yakubu, A. (2010). Mathematical model for optimal use of sulfadoxine-pyrimethamine as a temporary malaria vaccine. Bull. Math. Biol., 72, 914–930.

    Article  MATH  Google Scholar 

  • Dicko, A., Toure, S. O., Traore, M., Sagara, I., Toure, O. B., Sissoko, M. S., Diallo, A. T., Rogier, C., Salomon, R., de Sousa, A., & Doumbo, O. K. (2011). Increase in epi vaccines coverage after implementation of intermittent preventive treatment of malaria in infant with sulfadoxine-parimethamine in the district of Kolokani, Mali: results from a cluster randomized control trial. BMC Public Health, 11, 1–7.

    Article  Google Scholar 

  • Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. J. (1990). On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol., 28, 365–382.

    Article  MathSciNet  MATH  Google Scholar 

  • Dietz, K., Molineaux, L., & Thomas, A. A. (1974). Malaria model tested in the African Savannah. Bull. World Health Organ., 50, 347–357.

    Google Scholar 

  • Drakeley, C., Schellenberg, D., Kihonda, J., Sousa, C. A., Arez, A. P., Lopes, D., Lines, J., Mshinda, H., Lengeler, C., Schellenberg, J. A., Tanner, M., & Alonso, P. (2003). An estimation of the entomological inoculation rate for Ifakara: a semi-urban area in a region of intense malaria transmission in Tanzania. Trop. Med. Int. Health, 8, 767–774.

    Article  Google Scholar 

  • Ducrot, A., Sirima, S. B., Somé, B., & Zongo, P. (2009). A mathematical model for malaria involving differential susceptibility, exposedness and infectivity of human host. J. Biol. Dyn., 3, 574–598.

    Article  MathSciNet  Google Scholar 

  • Egan, A., Crawley, J., & Schellenberg, D. (2005). Ipti consortium. Intermittent preventive treatment for malaria control in infants: moving towards evidence-based policy and public health action. Trop. Med. Int. Health, 10, 815–817.

    Article  Google Scholar 

  • Farrington, C. P., & Whitaker, H. J. (2003). Estimation of effective reproduction numbers for infectious diseases using serological survey data. Biostatistics, 4, 626–632.

    Google Scholar 

  • Filipe, J. A. N., Riley, E. M., Drakeley, C. J., Sutherland, C. J., & Ghani, A. C. (2007). Determination of the processes driving the acquisition of immunity to malaria using a mathematical transmission model. PLoS Comput. Biol., 3, e255.

    Article  MathSciNet  Google Scholar 

  • Griffin, J. T., Hollingsworth, T. D., Okell, L. C., Churcher, T. S., White, M., Hinsley, W., Bousema, T., Drakely, C. J., Ferguson, N. M., Basáñez, M. G., & Ghani, A. C. (2010). Reducing Plasmodium falciparum malaria transmission in Africa: a model-based evaluation of intervention strategies. PLoS Med., 7, e1000324.

    Article  Google Scholar 

  • De Groote, H., Douro-Kpindou, O., & Togo, T. (2003). Biological control of locusts and grasshoppers in the Dogon area: a participatory rural appraisal. LUBILOSA Socioecon. Working Paper, 98, 1–17.

    Google Scholar 

  • Kelly-Hope, L. A., & Mckenzie, F. (2009). The multiplicity of malaria transmission: a review of entomological inoculation rate measurements and methods across Sub-Saharan Africa. Malar. J., 8, 1–16.

    Article  Google Scholar 

  • Koella, J. C., & Antia, R. (2003). Epidemiological models for the spread of anti-malarial resistance. Malar. J., 2, 1–11.

    Article  Google Scholar 

  • Lou, Y., & Zhao, X. Q. (2010). A climate-based malaria transmission model with structured vector population. SIAM J. Appl. Math., 70, 2023–2044.

    Article  MathSciNet  MATH  Google Scholar 

  • Lyke, K. E., Dicko, A., Kone, A., Coulibaly, D., Guindo, A., Cissoko, Y., Traoré, K., Plowe, C. V., & Doumbo, O. K. (2004). Incidence of severe Plasmodium falciparum malaria as a primary endpoint for vaccine efficacy trials in Bandiagara, Mali. Vaccine, 22, 3169–3174.

    Article  Google Scholar 

  • Macdonald, G. (1957). The epidemiology and control of malaria. London: Oxford University Press.

    Google Scholar 

  • Maire, N., Smith, T., Ross, A., Owusu-Agyei, S., Dietz, K., & Molineaux, L. (2006). A model for natural immunity to asexual blood stages of Plasmodium falciparum malaria in endemic areas. Am. J. Trop. Med. Hyg., 75, 19–31.

    Google Scholar 

  • Ruan, S., Xiaob, D., & Beier, J. C. (2008). On the delayed Ross–Macdonald model for malaria transmission. Bull. Math. Biol., 70, 1089–1114.

    Article  Google Scholar 

  • Shaukat, A. M., Breman, J. G., & Mackenzie, F. E. (2010). Using the entomological inoculation rate to assess the impact of vector control on malaria parasite transmission and elimination. Malar. J., 9, 122.

    Article  Google Scholar 

  • Smith, D. L., Dushoff, J., Snow, R. W., & Hay, S. I. (2005a). The entomological inoculation rate and Plasmodium falciparum infection in African children. Nature, 438, 492–495.

    Article  Google Scholar 

  • Smith, D. L., Dushoff, J., & Mckenzie, F. E. (2005b). The risk of a mosquito-borne infection in a heterogeneous environment. PLoS Biol., 2, 1957–1964.

    Google Scholar 

  • Smith, D. L., Mckenzie, F. E., Snow, R. W., & Hay, S. I. (2007). Revisiting the basic reproductive number for malaria and its implications for malaria control. PLoS Biol., 5, 531–542.

    Google Scholar 

  • Smith, D. L., Drakeley, C. J., Chiyaka, C., & Hay, S. I. (2010). A quantitative analysis of transmission efficiency versus intensity for malaria. Nat. Commun., 1, 108. doi:10.1038/ncomms1107.

    Article  Google Scholar 

  • Sogoba, N., Doumbia, S., Vounatsou, P., Baber, I., Keita, M., Maiga, M., Traore, S. F., Toure, A., Dolo, G., Smith, T., & Ribeiro, J. M. C. (2007). Monitoring of larval habitats and mosquito densities in the Sudan Savanna of Mali: implications for malaria vector control. Am. J. Trop. Med. Hyg., 72, 82–88.

    Google Scholar 

  • ter Kuile, F. O., van Eijk, A. M., & Filler, S. J. (2007). Effect of sulfadoxine-pyrimethamine resistance on the efficacy of intermittent preventive therapy for malaria control during pregnancy. J. Am. Med. Assoc., 297, 2603–2616.

    Article  Google Scholar 

  • van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci., 180, 29–48.

    Article  MathSciNet  MATH  Google Scholar 

  • World Health Organization (2010). WHO policy recommendation on intermittent preventive treatment during infancy with sulphadoxine pyrimethamine (SP-IPTi) for Plasmodium falciparum malaria control in Africa. http://www.who.int/malaria/news/WHO_policy_recommendation_IPTi_032010.pdf.

  • Wyse, A. P. P., Bevilacqua, L., & Rafikov, M. (2007). Simulating malaria model for different treatment intensities in a variable environment. Ecol. Model., 206, 322–330.

    Article  Google Scholar 

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Acknowledgements

The authors are grateful to two referees for their insightful comments, and to the Natural Sciences and Engineering Research Council of Canada for funding.

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Authors and Affiliations

  1. University of Western Ontario, London, Ontario, Canada

    Samira Akbari, Naveen K. Vaidya & Lindi M. Wahl

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  1. Samira Akbari
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  2. Naveen K. Vaidya
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  3. Lindi M. Wahl
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Correspondence to Lindi M. Wahl.

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Akbari, S., Vaidya, N.K. & Wahl, L.M. The Time Distribution of Sulfadoxine-Pyrimethamine Protection from Malaria. Bull Math Biol 74, 2733–2751 (2012). https://doi.org/10.1007/s11538-012-9775-4

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