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Dynamics Analysis of a Stochastic SIR Epidemic Model

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  • Feng Rao

Abstract

We investigate an SIR epidemic model with stochastic perturbations. We assume that stochastic perturbations are of a white noise type which is directly proportional to the distances of three variables from the steady‐state values, respectively. By constructing suitable Lyapunov functions and applying Itô’s formula, some qualitative properties are obtained, such as the existence of global positive solutions, stochastic boundedness, and permanence. A series of numerical simulations to illustrate these mathematical findings are presented.

Suggested Citation

  • Feng Rao, 2014. "Dynamics Analysis of a Stochastic SIR Epidemic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:356013
    DOI: 10.1155/2014/356013
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    References listed on IDEAS

    as
    1. Feng Rao & Shunjun Jiang & Yanqiu Li & Hao Liu, 2013. "Stochastic Analysis of a Hassell‐Varley Type Predation Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    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. 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).
    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. Ming Liu & Yihong Xiao, 2012. "Modeling and Analysis of Epidemic Diffusion within Small-World Network," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-14, June.
    6. 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).
    7. Fathalla A. Rihan & M. Naim Anwar, 2012. "Qualitative Analysis of Delayed SIR Epidemic Model with a Saturated Incidence Rate," International Journal of Differential Equations, Hindawi, vol. 2012, pages 1-13, December.
    8. 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).
    9. Feng Rao & Shunjun Jiang & Yanqiu Li & Hao Liu, 2013. "Stochastic Analysis of a Hassell-Varley Type Predation Model," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, December.
    10. Liyan Wang & Huilin Huang & Ancha Xu & Weiming Wang, 2013. "Stochastic Extinction in an SIRS Epidemic Model Incorporating Media Coverage," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, December.
    11. Ming Liu & Yihong Xiao, 2012. "Modeling and Analysis of Epidemic Diffusion within Small‐World Network," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    12. Feng Rao, 2013. "Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
    13. Feng Rao, 2013. "Dynamical Analysis of a Stochastic Predator‐Prey Model with an Allee Effect," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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    Cited by:

    1. Bo Wang & Jianhua Zhang & Haifeng Guo & Yuwang Zhang & Xiaotuo Qiao, 2016. "Model Study of Information Dissemination in Microblog Community Networks," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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