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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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    12. Antonio Barrera & Patricia Román-Román & Francisco Torres-Ruiz, 2021. "Hyperbolastic Models from a Stochastic Differential Equation Point of View," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
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