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Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence

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  • Rajasekar, S.P.
  • Pitchaimani, M.

Abstract

A stochastic SIRS model with logistic growth and nonlinear incidence rate is probed in this paper. We exemplify that the proposed stochastic SIRS model reveals a global and positive solution. By applying suitable Lyapunov functions, the sufficient conditions for the existence of ergodic stationary distribution of the solution to the stochastic SIRS model are derived. Furthermore, we acquire the sufficient conditions for extinction of the infectious disease.

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  • Rajasekar, S.P. & Pitchaimani, M., 2020. "Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    • Handle: RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320301120
    DOI: 10.1016/j.amc.2020.125143
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    References listed on IDEAS

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    1. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2019. "Dynamic threshold probe of stochastic SIR model with saturated incidence rate and saturated treatment function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    2. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
    3. Rajasekar, S.P. & Pitchaimani, M., 2019. "Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 207-221.
    4. 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.
    5. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
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    5. Han, Bingtao & Zhou, Baoquan & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary solution, extinction and density function for a high-dimensional stochastic SEI epidemic model with general distributed delay," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    6. Sabbar, Yassine & Kiouach, Driss & Rajasekar, S.P. & El-idrissi, Salim El Azami, 2022. "The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
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    13. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    14. 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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