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Global Stability of Multigroup SIRS Epidemic Model with Varying Population Sizes and Stochastic Perturbation around Equilibrium

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  • Xiaoming Fan

Abstract

We discuss multigroup SIRS (susceptible, infectious, and recovered) epidemic models with random perturbations. We carry out a detailed analysis on the asymptotic behavior of the stochastic model; when reproduction number ℛ0 > 1, we deduce the globally asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time average. Numerical methods are employed to illustrate the dynamic behavior of the model and simulate the system of equations developed. The effect of the rate of immunity loss on susceptible and recovered individuals is also analyzed in the deterministic model.

Suggested Citation

  • Xiaoming Fan, 2014. "Global Stability of Multigroup SIRS Epidemic Model with Varying Population Sizes and Stochastic Perturbation around Equilibrium," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:154725
    DOI: 10.1155/2014/154725
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    References listed on IDEAS

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    1. Xiaoming Fan & Zhigang Wang & Xuelian Xu, 2012. "Global Stability of Two‐Group Epidemic Models with Distributed Delays and Random Perturbation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Xiaoming Fan & Zhigang Wang & Xuelian Xu, 2012. "Global Stability of Two-Group Epidemic Models with Distributed Delays and Random Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, March.
    3. Ji, Chunyan & Jiang, Daqing & Shi, Ningzhong, 2011. "Multigroup SIR epidemic model with stochastic perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1747-1762.
    4. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
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