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Dynamics of a stochastic SIR epidemic model with saturated incidence

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  • Liu, Qun
  • Chen, Qingmei

Abstract

In this paper, the dynamics of a stochastic SIR epidemic model with saturated incidence is investigated. Firstly, we prove that the system has a unique global positive solution with any positive initial value. Then we verify that random effect may lead the disease to extinction under a simple condition. Thirdly, we establish a sufficient condition for persistence in the mean of the disease. Moreover, we show that there is a stationary distribution to the stochastic system under certain parametric restrictions. Finally, some numerical simulations are carried out to confirm the analytical results.

Suggested Citation

  • Liu, Qun & Chen, Qingmei, 2016. "Dynamics of a stochastic SIR epidemic model with saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 155-166.
    • Handle: RePEc:eee:apmaco:v:282:y:2016:i:c:p:155-166
    DOI: 10.1016/j.amc.2016.02.022
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    References listed on IDEAS

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    1. Lu, Qiuying, 2009. "Stability of SIRS system with random perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(18), pages 3677-3686.
    2. Wang, Fengyan & Wang, Xiaoyi & Zhang, Shuwen & Ding, Changming, 2014. "On pulse vaccine strategy in a periodic stochastic SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 127-135.
    3. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
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    Cited by:

    1. Zhang, Yue & Li, Yang & Zhang, Qingling & Li, Aihua, 2018. "Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 178-187.
    2. Sun, Shulin & Zhang, Xiaofeng, 2018. "Asymptotic behavior of a stochastic delayed chemostat model with nonmonotone uptake function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 38-56.
    3. Li, Yan & Ye, Ming & Zhang, Qimin, 2019. "Strong convergence of the partially truncated Euler–Maruyama scheme for a stochastic age-structured SIR epidemic model," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    4. Liu, Jiamin & Wei, Fengying, 2016. "Dynamics of stochastic SEIS epidemic model with varying population size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 241-250.
    5. Acuña-Zegarra, Manuel Adrian & Díaz-Infante, Saúl, 2018. "Stochastic asymptotic analysis of a multi-host model with vector transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 243-260.

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