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A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation

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  • Wenbin Liu

Abstract

We investigate the complex dynamics of a SIRS epidemic model incorporating media coverage with random perturbation. We first deal with the boundedness and the stability of the disease—free and endemic equilibria of the deterministic model. And for the corresponding stochastic epidemic model, we prove that the endemic equilibrium of the stochastic model is asymptotically stable in the large. Furthermore, we perform some numerical examples to validate the analytical finding, and find that if the conditions of stochastic stability are not satisfied, the solution for the stochastic model will oscillate strongly around the endemic equilibrium.

Suggested Citation

  • Wenbin Liu, 2013. "A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:792308
    DOI: 10.1155/2013/792308
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. repec:plo:pone00:0020891 is not listed on IDEAS
    4. 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, Hindawi, vol. 2013, pages 1-11, June.
    5. 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).
    6. 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).
    7. 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. Maoxing Liu & Yuting Chang & Lixia Zuo, 2016. "Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    2. Lixia Zuo & Maoxing Liu, 2014. "Effect of Awareness Programs on the Epidemic Outbreaks with Time Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Liyan Wang & Huilin Huang & Ancha Xu & Weiming Wang, 2013. "Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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