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Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate

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  • Qiuhua Zhang
  • Kai Zhou

Abstract

In this paper, we consider a stochastic SIQR epidemic model with saturated incidence rate. By constructing a proper Lyapunov function, we obtain the existence and uniqueness of positive solution for this SIQR model. Furthermore, we study the dynamical properties of this stochastic SIQR model; that is, (i) we establish the sufficient condition for the existence of ergodic stationary distribution of the model; (ii) we obtain the extinction of the disease under some conditions. At last, numerical simulations are introduced to illustrate our theoretical results.

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  • Qiuhua Zhang & Kai Zhou, 2019. "Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-12, June.
    • Handle: RePEc:hin:jnlmpe:3575410
    DOI: 10.1155/2019/3575410
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    Cited by:

    1. Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Zhang, Ge & Li, Zhiming & Din, Anwarud, 2022. "A stochastic SIQR epidemic model with Lévy jumps and three-time delays," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    3. M, Pitchaimani & M, Brasanna Devi, 2021. "Stochastic dynamical probes in a triple delayed SICR model with general incidence rate and immunization strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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