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The threshold of a stochastic SIS epidemic model with imperfect vaccination

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  • Liu, Qun
  • Jiang, Daqing
  • Shi, Ningzhong
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

In this paper, we analyze the threshold RvS of a stochastic SIS epidemic model with partially protective vaccination of efficacy e∈[0,1]. Firstly, we show that there exists a unique global positive solution of the stochastic system. Then RvS>1 is verified to be sufficient for persistence in the mean of the system. Furthermore, three conditions for the disease to die out are given, which improve the previously-known results on extinction of the disease. We also obtain that large noise will exponentially suppress the disease from persisting regardless of the value of the basic reproduction number RvS.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "The threshold of a stochastic SIS epidemic model with imperfect vaccination," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 78-90.
    • Handle: RePEc:eee:matcom:v:144:y:2018:i:c:p:78-90
    DOI: 10.1016/j.matcom.2017.06.004
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Liu, Qun & Chen, Qingmei, 2015. "Analysis of the deterministic and stochastic SIRS epidemic models with nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 140-153.
    4. 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:

    1. Maria Gamboa & Maria Jesus Lopez-Herrero, 2020. "The Effect of Setting a Warning Vaccination Level on a Stochastic SIVS Model with Imperfect Vaccine," Mathematics, MDPI, vol. 8(7), pages 1-23, July.
    2. Zhou, Xueyong & Shi, Xiangyun & Wei, Ming, 2022. "Dynamical behavior and optimal control of a stochastic mathematical model for cholera," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Salah Abuasad & Ahmet Yildirim & Ishak Hashim & Samsul Ariffin Abdul Karim & J.F. Gómez-Aguilar, 2019. "Fractional Multi-Step Differential Transformed Method for Approximating a Fractional Stochastic SIS Epidemic Model with Imperfect Vaccination," IJERPH, MDPI, vol. 16(6), pages 1-15, March.
    4. Meng, Lan & Zhu, Wei, 2022. "Analysis of SEIR epidemic patch model with nonlinear incidence rate, vaccination and quarantine strategies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 489-503.
    5. Rathinasamy, A. & Chinnadurai, M. & Athithan, S., 2021. "Analysis of exact solution of stochastic sex-structured HIV/AIDS epidemic model with effect of screening of infectives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 213-237.

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