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Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage

Author

Listed:
  • Liyan Wang
  • Huilin Huang
  • Ancha Xu
  • Weiming Wang

Abstract

We extend the classical SIRS epidemic model incorporating media coverage from a deterministic framework to a stochastic differential equation (SDE) and focus on how environmental fluctuations of the contact coefficient affect the extinction of the disease. We give the conditions of existence of unique positive solution and the stochastic extinction of the SDE model and discuss the exponential p‐stability and global stability of the SDE model. One of the most interesting findings is that if the intensity of noise is large, then the disease is prone to extinction, which can provide us with some useful control strategies to regulate disease dynamics.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:891765
    DOI: 10.1155/2013/891765
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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. Wenbin Liu, 2013. "A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    4. Wenbin Liu, 2013. "A SIRS Epidemic Model Incorporating Media Coverage with Random Perturbation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, November.
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    Cited by:

    1. 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).
    2. Sibaliwe Maku Vyambwera & Peter Witbooi, 2018. "A Stochastic TB Model for a Crowded Environment," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    3. 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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