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Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence

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  • Liu, Qun
  • Jiang, Daqing
  • Shi, Ningzhong
  • Hayat, Tasawar
  • Ahmad, Bashir

Abstract

In this paper, we consider a stochastic SEIR epidemic model with standard incidence. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution to the model. Our result does not depend on the positive endemic equilibrium E∗ of the deterministic system, which improves the previous result to a greater extent. Moreover, we also establish sufficient conditions for extinction of the disease.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of a stochastic SEIR epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 58-69.
    • Handle: RePEc:eee:phsmap:v:476:y:2017:i:c:p:58-69
    DOI: 10.1016/j.physa.2017.02.028
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    Cited by:

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    16. Kiouach, Driss & El-idrissi, Salim El Azami & Sabbar, Yassine, 2023. "An improvement of the extinction sufficient conditions for a higher-order stochastically disturbed AIDS/HIV model," Applied Mathematics and Computation, Elsevier, vol. 447(C).
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    24. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Dynamical behavior of a higher order stochastically perturbed SIRI epidemic model with relapse and media coverage," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    25. Lan, Guijie & Chen, Zhewen & Wei, Chunjin & Zhang, Shuwen, 2018. "Stationary distribution of a stochastic SIQR epidemic model with saturated incidence and degenerate diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 61-77.

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