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The Behavior of an SVIR Epidemic Model with Stochastic Perturbation

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  • Yanan Zhao
  • Daqing Jiang

Abstract

We discuss a stochastic SIR epidemic model with vaccination. We investigate the asymptotic behavior according to the perturbation and the reproduction number . We deduce the globally asymptotic stability of the disease-free equilibrium when and the perturbation is small, which means that the disease will die out. When , we derive that the disease will prevail, which is measured through the difference between the solution and the endemic equilibrium of the deterministic model in time average. The key to our analysis is choosing appropriate Lyapunov functions.

Suggested Citation

  • Yanan Zhao & Daqing Jiang, 2014. "The Behavior of an SVIR Epidemic Model with Stochastic Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, June.
    • Handle: RePEc:hin:jnlaaa:742730
    DOI: 10.1155/2014/742730
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    Cited by:

    1. Yassine Sabbar & Mohammad Izadi & Aeshah A. Raezah & Waleed Adel, 2024. "Nonlinear Dynamics of a General Stochastic SIR Model with Behavioral and Physical Changes: Analysis and Application to Zoonotic Tuberculosis," Mathematics, MDPI, vol. 12(13), pages 1-17, June.
    2. Sabbar, Yassine & Din, Anwarud & Kiouach, Driss, 2023. "Influence of fractal–fractional differentiation and independent quadratic Lévy jumps on the dynamics of a general epidemic model with vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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