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The extinction and persistence of the stochastic hepatitis B epidemic model

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  • Khan, Tahir
  • Khan, Amir
  • Zaman, Gul

Abstract

We discuss the dynamic of a stochastic hepatitis B epidemic model. A stochastic hepatitis B model is formulated with a varying population environment for a long term behavior. The proposed model consists of three classes, namely the susceptible individuals in which the transmission rate is distributed by white noise, the infected individuals in which the same perturbation occurs and the recovered individuals. We derive sufficient conditions for the extinction and the persistence. Finally, we carry out the numerical simulations to support our analytical results.

Suggested Citation

  • Khan, Tahir & Khan, Amir & Zaman, Gul, 2018. "The extinction and persistence of the stochastic hepatitis B epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 123-128.
    • Handle: RePEc:eee:chsofr:v:108:y:2018:i:c:p:123-128
    DOI: 10.1016/j.chaos.2018.01.036
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    References listed on IDEAS

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    Cited by:

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    2. Tingting Xue & Xiaolin Fan & Yan Xu, 2023. "Kinetic Behavior and Optimal Control of a Fractional-Order Hepatitis B Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
    3. Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2022. "Ergodic stationary distribution of stochastic epidemic model for HBV with double saturated incidence rates and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
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    5. Boukanjime, Brahim & El Fatini, Mohamed, 2019. "A stochastic Hepatitis B epidemic model driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 796-806.
    6. Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution and extinction of a stochastic staged progression AIDS model with staged treatment and second-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Wu, Shuying & Yuan, Sanling & Lan, Guijie & Zhang, Tonghua, 2024. "Understanding the dynamics of hepatitis B transmission: A stochastic model with vaccination and Ornstein-Uhlenbeck process," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    8. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing, 2021. "Ergodic property, extinction and density function of a stochastic SIR epidemic model with nonlinear incidence and general stochastic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    9. Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2020. "Stochastic permanence of an epidemic model with a saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.
    11. Li, Xiao-Ping & Din, Anwarud & Zeb, Anwar & Kumar, Sunil & Saeed, Tareq, 2022. "The impact of Lévy noise on a stochastic and fractal-fractional Atangana–Baleanu order hepatitis B model under real statistical data," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    12. Zhou, Baoquan & Jiang, Daqing & Dai, Yucong & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Stationary distribution and probability density function of a stochastic SVIS epidemic model with standard incidence and vaccination strategies," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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