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Ergodic stationary distribution of a stochastic SIRS epidemic model incorporating media coverage and saturated incidence rate

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  • Zhang, Yan
  • Fan, Kuangang
  • Gao, Shujing
  • Liu, Yingfen
  • Chen, Shihua

Abstract

This study investigates the disease dynamics of a SIRS epidemic model as affected by environment fluctuations and media coverage. A unique global positive solution for the epidemic model is obtained. The stochastic endemic dynamics of the system is discussed by constructing suitable Lyapunov functions, and the ergodic stationary distribution of the stochastic model is established based on the method of Khasminskii. The extinction of the epidemic disease is also analyzed.

Suggested Citation

  • Zhang, Yan & Fan, Kuangang & Gao, Shujing & Liu, Yingfen & Chen, Shihua, 2019. "Ergodic stationary distribution of a stochastic SIRS epidemic model incorporating media coverage and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 671-685.
    • Handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:671-685
    DOI: 10.1016/j.physa.2018.09.124
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    References listed on IDEAS

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    1. Liu, Wenbin & Zheng, Qiben, 2015. "A stochastic SIS epidemic model incorporating media coverage in a two patch setting," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 160-168.
    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. Teng, Zhidong & Wang, Lei, 2016. "Persistence and extinction for a class of stochastic SIS epidemic models with nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 507-518.
    4. Liu, Meng & Bai, Chuanzhi, 2016. "Optimal harvesting of a stochastic mutualism model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 301-309.
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    Cited by:

    1. 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).
    2. Tan, Yiping & Cai, Yongli & Wang, Xiaoqin & Peng, Zhihang & Wang, Kai & Yao, Ruoxia & Wang, Weiming, 2023. "Stochastic dynamics of an SIS epidemiological model with media coverage," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 1-27.
    3. Xuewen Tan & Wenjie Qin & Guangyao Tang & Changcheng Xiang & Xinzhi Liu, 2019. "Models to Assess the Effects of Nonsmooth Control and Stochastic Perturbation on Pest Control: A Pest-Natural-Enemy Ecosystem," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    4. Sk, Tahajuddin & Biswas, Santosh & Sardar, Tridip, 2022. "The impact of a power law-induced memory effect on the SARS-CoV-2 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    5. Jin, Xihua & Jia, Jianwen, 2020. "Qualitative study of a stochastic SIRS epidemic model with information intervention," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    6. 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).

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