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The global dynamics for a stochastic SIS epidemic model with isolation

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  • Chen, Yiliang
  • Wen, Buyu
  • Teng, Zhidong

Abstract

In this paper, we investigate the dynamical behavior for a stochastic SIS epidemic model with isolation which is as an important strategy for the elimination of infectious diseases. It is assumed that the stochastic effects manifest themselves mainly as fluctuation in the transmission coefficient, the death rate and the proportional coefficient of the isolation of infective. It is shown that the extinction and persistence in the mean of the model are determined by a threshold value R0S. That is, if R0S<1, then disease dies out with probability one, and if R0S>1, then the disease is stochastic persistent in the means with probability one. Furthermore, the existence of a unique stationary distribution is discussed, and the sufficient conditions are established by using the Lyapunov function method. Finally, some numerical examples are carried out to confirm the analytical results.

Suggested Citation

  • Chen, Yiliang & Wen, Buyu & Teng, Zhidong, 2018. "The global dynamics for a stochastic SIS epidemic model with isolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1604-1624.
  • Handle: RePEc:eee:phsmap:v:492:y:2018:i:c:p:1604-1624
    DOI: 10.1016/j.physa.2017.11.085
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    Citations

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    Cited by:

    1. Amador, J. & Gómez-Corral, A., 2020. "A stochastic epidemic model with two quarantine states and limited carrying capacity for quarantine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    2. Tan, Yiping & Cai, Yongli & Sun, Xiaodan & Wang, Kai & Yao, Ruoxia & Wang, Weiming & Peng, Zhihang, 2022. "A stochastic SICA model for HIV/AIDS transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. Piqueira, José Roberto C. & Cabrera, Manuel A.M. & Batistela, Cristiane M., 2021. "Malware propagation in clustered computer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    4. Gao, Miaomiao & Jiang, Daqing, 2019. "Analysis of stochastic multimolecular biochemical reaction model with lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 601-613.
    5. Lin Hu & Lin-Fei Nie, 2022. "Dynamics of a Stochastic HIV Infection Model with Logistic Growth and CTLs Immune Response under Regime Switching," Mathematics, MDPI, vol. 10(19), pages 1-20, September.
    6. Luo, Yantao & Huang, Jianhua & Teng, Zhidong & Liu, Qun, 2024. "Role of ART and PrEP treatments in a stochastic HIV/AIDS epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 337-357.
    7. Wu, Qingchu & Zhou, Rong & Hadzibeganovic, Tarik, 2019. "Conditional quenched mean-field approach for recurrent-state epidemic dynamics in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 71-79.
    8. Senapati, Abhishek & Panday, Pijush & Samanta, Sudip & Chattopadhyay, Joydev, 2020. "Disease control through removal of population using Z-control approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).

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