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Dynamical Analysis of a Stochastic Cholera Epidemic Model

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  • Xueyong Zhou

    (School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China)

Abstract

Environmental disturbances have a strong impact on cholera transmission. Stochastic differential equations are an effective tool for characterizing environmental perturbations. In this paper, a stochastic infectious disease model for cholera is established and investigated. The dynamics of the stochastic cholera model are discussed. Firstly, the existence and uniqueness of the positive solution are proven. Then, the asymptotical stability of the disease-free equilibrium of the system is investigated. Furthermore, the asymptotical stability of the endemic equilibrium of the deterministic system corresponding to the stochastic system is obtained. Then, the theoretical results are verified by some numerical simulations. Finally, the optimal problem is considered as the theoretical basis for the control of cholera. Both theoretical and numerical results indicate that the random perturbations may make the model more realistic, which provides theoretical assessment for the control of cholera transmission.

Suggested Citation

  • Xueyong Zhou, 2022. "Dynamical Analysis of a Stochastic Cholera Epidemic Model," Mathematics, MDPI, vol. 10(16), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2830-:d:883924
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    References listed on IDEAS

    as
    1. Jing'an Cui & Zhanmin Wu & Xueyong Zhou, 2014. "Mathematical Analysis of a Cholera Model with Vaccination," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-16, February.
    2. Zhou, Xueyong & Shi, Xiangyun & Wei, Ming, 2022. "Dynamical behavior and optimal control of a stochastic mathematical model for cholera," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Liao, Shu & Wang, Jin, 2012. "Global stability analysis of epidemiological models based on Volterra–Lyapunov stable matrices," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 966-977.
    4. El Fatini, Mohamed & Sekkak, Idriss, 2020. "Lévy noise impact on a stochastic delayed epidemic model with Crowly–Martin incidence and crowding effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    Full references (including those not matched with items on IDEAS)

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