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Stochastic Dynamics of an SIRS Epidemic Model with Ratio‐Dependent Incidence Rate

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  • Yongli Cai
  • Xixi Wang
  • Weiming Wang
  • Min Zhao

Abstract

We investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. We first deal with the boundedness, dissipation, persistence, and the stability of the disease‐free and endemic points of the deterministic model. And then we prove the existence and uniqueness of the global positive solutions, stochastic boundedness, and permanence for the stochastic epidemic model. Furthermore, we perform some numerical examples to validate the analytical findings. Needless to say, both deterministic and stochastic epidemic models have their important roles.

Suggested Citation

  • Yongli Cai & Xixi Wang & Weiming Wang & Min Zhao, 2013. "Stochastic Dynamics of an SIRS Epidemic Model with Ratio‐Dependent Incidence Rate," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:172631
    DOI: 10.1155/2013/172631
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    References listed on IDEAS

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    1. Xixi Wang & Huilin Huang & Yongli Cai & Weiming Wang, 2012. "The Complex Dynamics of a Stochastic Predator-Prey Model," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-24, September.
    2. Xixi Wang & Huilin Huang & Yongli Cai & Weiming Wang, 2012. "The Complex Dynamics of a Stochastic Predator‐Prey Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Liu, Meng & Wang, Ke, 2009. "Survival analysis of stochastic single-species population models in polluted environments," Ecological Modelling, Elsevier, vol. 220(9), pages 1347-1357.
    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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    Cited by:

    1. Wenbin Liu, 2013. "A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Feng Rao, 2014. "Dynamics Analysis of a Stochastic SIR Epidemic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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