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Dynamic Behavior of an Interactive Mosquito Model under Stochastic Interference

Author

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  • Xingtong Liu

    (Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China)

  • Yuanshun Tan

    (Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China)

  • Bo Zheng

    (College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China)

Abstract

For decades, mosquito-borne diseases such as dengue fever and Zika have posed serious threats to human health. Diverse mosquito vector control strategies with different advantages have been proposed by the researchers to solve the problem. However, due to the extremely complex living environment of mosquitoes, environmental changes bring significant differences to the mortality of mosquitoes. This dynamic behavior requires stochastic differential equations to characterize the fate of mosquitoes, which has rarely been considered before. Therefore, in this article, we establish a stochastic interactive wild and sterile mosquito model by introducing the white noise to represent the interference of the environment on the survival of mosquitoes. After obtaining the existence and uniqueness of the global positive solution and the stochastically ultimate boundedness of the stochastic system, we study the dynamic behavior of the stochastic model by constructing a series of suitable Lyapunov functions. Our results show that appropriate stochastic environmental fluctuations can effectively inhibit the reproduction of wild mosquitoes. Numerical simulations are provided to numerically verify our conclusions: the intensity of the white noise has an effect on the extinction and persistence of both wild and sterile mosquitoes.

Suggested Citation

  • Xingtong Liu & Yuanshun Tan & Bo Zheng, 2022. "Dynamic Behavior of an Interactive Mosquito Model under Stochastic Interference," Mathematics, MDPI, vol. 10(13), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2284-:d:851742
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    References listed on IDEAS

    as
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    Cited by:

    1. Konstantin Rybakov, 2023. "Spectral Representations of Iterated Stochastic Integrals and Their Application for Modeling Nonlinear Stochastic Dynamics," Mathematics, MDPI, vol. 11(19), pages 1-23, September.

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