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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 R0. We deduce the globally asymptotic stability of the disease‐free equilibrium when R0 ≤ 1 and the perturbation is small, which means that the disease will die out. When R0 > 1, 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, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:742730
    DOI: 10.1155/2014/742730
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    References listed on IDEAS

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    1. Yanan Zhao & Daqing Jiang, 2013. "Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, September.
    2. Yanan Zhao & Daqing Jiang, 2013. "Dynamics of Stochastically Perturbed SIS Epidemic Model with Vaccination," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Zeng, Guang Zhao & Chen, Lan Sun & Sun, Li Hua, 2005. "Complexity of an SIR epidemic dynamics model with impulsive vaccination control," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 495-505.
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