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Qualitative study of a stochastic SIS epidemic model with vertical transmission

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  • Zhang, Xiao-Bing
  • Chang, Suqin
  • Shi, Qihong
  • Huo, Hai-Feng

Abstract

In this paper, we study a stochastic SIS epidemic model with vertical infection. By constructing suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of a stationary probability measure of the model. In addition, we also establish sufficient conditions for extinction and persistence of the disease.

Suggested Citation

  • Zhang, Xiao-Bing & Chang, Suqin & Shi, Qihong & Huo, Hai-Feng, 2018. "Qualitative study of a stochastic SIS epidemic model with vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 805-817.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:805-817
    DOI: 10.1016/j.physa.2018.04.022
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    References listed on IDEAS

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    1. Liu, Qun & Jiang, Daqing & Shi, Ningzhong, 2018. "Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 310-325.
    2. Lin, Yuguo & Jiang, Daqing & Wang, Shuai, 2014. "Stationary distribution of a stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 187-197.
    3. Zhao, Yu & Yuan, Sanling, 2017. "Optimal harvesting policy of a stochastic two-species competitive model with Lévy noise in a polluted environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 20-33.
    4. Huo, Hai-Feng & Cui, Fang-Fang & Xiang, Hong, 2018. "Dynamics of an SAITS alcoholism model on unweighted and weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 249-262.
    5. Zhao, Yanan & Jiang, Daqing & O’Regan, Donal, 2013. "The extinction and persistence of the stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4916-4927.
    6. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamical behavior of a stochastic SVIR epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 94-108.
    7. Zhang, Xiao-Bing & Huo, Hai-Feng & Xiang, Hong & Shi, Qihong & Li, Dungang, 2017. "The threshold of a stochastic SIQS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 362-374.
    8. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    9. 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.
    10. 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.
    11. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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    Cited by:

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    2. 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).

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