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A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate

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  • Liu, Qun
  • Jiang, Daqing
  • Hayat, Tasawar
  • Alsaedi, Ahmed
  • Ahmad, Bashir

Abstract

In this paper, we consider a stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate. We establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the stochastic model by constructing a suitable stochastic Lyapunov function, which provides us a good description of persistence. We find that the hypothetical conditions on the nonlinear function are relative weak and valid for many forms of incidence rate.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    • Handle: RePEc:eee:phsmap:v:551:y:2020:i:c:s037843712030011x
    DOI: 10.1016/j.physa.2020.124152
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    References listed on IDEAS

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    Cited by:

    1. Huyi Wang & Ge Zhang & Tao Chen & Zhiming Li, 2023. "Threshold Analysis of a Stochastic SIRS Epidemic Model with Logistic Birth and Nonlinear Incidence," Mathematics, MDPI, vol. 11(7), pages 1-17, April.
    2. Benazzouz, Meryem & Caraballo, Tomás & El Fatini, Mohamed & Laaribi, Aziz, 2024. "Discontinuous stochastic modeling and discrete numerical approximation for Tuberculosis model with relapse," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Zhang, Yuexia & Pan, Dawei, 2021. "Layered SIRS model of information spread in complex networks," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    4. Yousef Alnafisah & Moustafa El-Shahed, 2022. "Stochastic Analysis of a Hantavirus Infection Model," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    5. Shuang Li, 2024. "SIR Epidemic Model with General Nonlinear Incidence Rate and Lévy Jumps," Mathematics, MDPI, vol. 12(2), pages 1-21, January.
    6. Han, Bingtao & Jiang, Daqing & Zhou, Baoquan & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SIRSI epidemic model with saturation incidence rate and logistic growth," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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