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Modeling and control of mosquito-borne diseases with Wolbachia and insecticides

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  • Li, Yazhi
  • Liu, Xianning

Abstract

Mosquitoes cause more human suffering than any other organism. It is estimated that over one million people worldwide die from mosquito-borne diseases every year. With the continuous efforts of many researchers, Wolbachia gets more and more attention due to its characteristics of maternal transmission in mosquito population and it may cause cytoplasmic incompatibility (CI) which makes healthy females cannot fertilize normally after mating with infected males. In this paper, mathematical models are established to study Wolbachia transmission in mosquito population, and integrated mosquito control strategies are explored. Firstly, a classical ordinary differential system with general birth and death rate functions is established to describe the maternal transmission and CI effect. It is shown that the replacement strategy that the Wolbachia-uninfected mosquitoes are replaced by the infected ones is determined by the initial infection frequency. And Wolbachia spreads more easily for greater maternal transmission and CI rate. Moreover, all the wild mosquitoes will eventually be infected with Wolbachia if the maternal transmission is complete. Secondly, an impulsive state feedback control model is constructed to describe the integrated mosquito control. Besides Wolbachia, insecticides are sprayed when the quantity of mosquitoes reaches some Economic Threshold. The existence and stability of Wolbachia replacement periodic solution are discussed. Finally, some discussions are done and the future research directions are prospected.

Suggested Citation

  • Li, Yazhi & Liu, Xianning, 2020. "Modeling and control of mosquito-borne diseases with Wolbachia and insecticides," Theoretical Population Biology, Elsevier, vol. 132(C), pages 82-91.
    • Handle: RePEc:eee:thpobi:v:132:y:2020:i:c:p:82-91
    DOI: 10.1016/j.tpb.2019.12.007
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    References listed on IDEAS

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    1. Suandi, Dani & Wijaya, Karunia Putra & Apri, Mochamad & Sidarto, Kuntjoro Adji & Syafruddin, Din & Götz, Thomas & Soewono, Edy, 2019. "A one-locus model describing the evolutionary dynamics of resistance against insecticide in Anopheles mosquitoes," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 90-106.
    2. Hu, Linchao & Huang, Mugen & Tang, Moxun & Yu, Jianshe & Zheng, Bo, 2015. "Wolbachia spread dynamics in stochastic environments," Theoretical Population Biology, Elsevier, vol. 106(C), pages 32-44.
    3. Ndii, Meksianis Z. & Allingham, David & Hickson, R.I. & Glass, Kathryn, 2016. "The effect of Wolbachia on dengue outbreaks when dengue is repeatedly introduced," Theoretical Population Biology, Elsevier, vol. 111(C), pages 9-15.
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    Cited by:

    1. Pérez-Estigarribia, Pastor E. & Bliman, Pierre-Alexandre & Schaerer, Christian E., 2020. "A class of fast–slow models for adaptive resistance evolution," Theoretical Population Biology, Elsevier, vol. 135(C), pages 32-48.
    2. Li, Yazhi & Wang, Yan & Liu, Lili, 2023. "Optimal control of dengue vector based on a reaction–diffusion model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 250-270.
    3. Jabili Angina & Anish Bachhu & Eesha Talati & Rishi Talati & Jan Rychtář & Dewey Taylor, 2022. "Game-Theoretical Model of the Voluntary Use of Insect Repellents to Prevent Zika Fever," Dynamic Games and Applications, Springer, vol. 12(1), pages 133-146, March.

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