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A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality

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  • Bakary Traoré
  • Boureima Sangaré
  • Sado Traoré

Abstract

In this paper, we formulate a mathematical model of nonautonomous ordinary differential equations describing the dynamics of malaria transmission with age structure for the vector population. The biting rate of mosquitoes is considered as a positive periodic function which depends on climatic factors. The basic reproduction ratio of the model is obtained and we show that it is the threshold parameter between the extinction and the persistence of the disease. Thus, by applying the theorem of comparison and the theory of uniform persistence, we prove that if the basic reproduction ratio is less than 1, then the disease‐free equilibrium is globally asymptotically stable and if it is greater than 1, then there exists at least one positive periodic solution. Finally, numerical simulations are carried out to illustrate our analytical results.

Suggested Citation

  • Bakary Traoré & Boureima Sangaré & Sado Traoré, 2017. "A Mathematical Model of Malaria Transmission with Structured Vector Population and Seasonality," Journal of Applied Mathematics, John Wiley & Sons, vol. 2017(1).
    • Handle: RePEc:wly:jnljam:v:2017:y:2017:i:1:n:6754097
    DOI: 10.1155/2017/6754097
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    References listed on IDEAS

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    1. Jianping Wang & Shujing Gao & Yueli Luo & Dehui Xie, 2014. "Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Jianping Wang & Shujing Gao & Yueli Luo & Dehui Xie, 2014. "Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, March.
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    Cited by:

    1. Agnes Adom-Konadu & Ernest Yankson & Samuel M. Naandam & Duah Dwomoh, 2022. "A Mathematical Model for Effective Control and Possible Eradication of Malaria," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Seck, Rama & Ngom, Diene & Ivorra, Benjamin & Ramos, Angel M., 2025. "An age-structured mathematical model for studying Malaria transmission dynamics: Applications to some areas of Senegal," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 392-408.

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