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Delayed hepatitis B epidemic model with stochastic analysis

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  • Din, Anwarud
  • Li, Yongjin
  • Yusuf, Abdullahi

Abstract

Environmental factors such as, humidity and temperature pose significant impacts on the dynamics of hepatitis B virus (HBV). The stochastic modeling has been proved to be a powerful tool for revealing such impacts. With this motive, the present study enacts the formulation and analysis of a stochastic hepatitis B model considering a time-delay in the transmission coefficient, and CTL immune response class. Initially, the model is investigated for the existence of a unique global solution. By using the stochastic Lyapunov functional theory, the model was further analyzed for extinction and persistence of the disease. It is evident that the ergodic stationary distribution exists under certain condition. We infer that the white noise plays a significant role in controlling the infection. Relatively large noise guarantees the extinction of HBV. Similarly, it is inferred that the delay factor is responsible for the periodic occurrence and re-infection of the disease. Additionally, for providing a strong support to the theoretical results, sample trajectories were displayed at the end of the study.

Suggested Citation

  • Din, Anwarud & Li, Yongjin & Yusuf, Abdullahi, 2021. "Delayed hepatitis B epidemic model with stochastic analysis," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921001922
    DOI: 10.1016/j.chaos.2021.110839
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    References listed on IDEAS

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    6. Yusuf, Abdullahi & Acay, Bahar & Mustapha, Umar Tasiu & Inc, Mustafa & Baleanu, Dumitru, 2021. "Mathematical modeling of pine wilt disease with Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    Cited by:

    1. Sayed Murad Ali Shah & Yufeng Nie & Anwarud Din & Abdulwasea Alkhazzan, 2024. "Dynamics of Hepatitis B Virus Transmission with a Lévy Process and Vaccination Effects," Mathematics, MDPI, vol. 12(11), pages 1-24, May.
    2. Zhang, Ge & Li, Zhiming & Din, Anwarud & Chen, Tao, 2024. "Dynamic analysis and optimal control of a stochastic COVID-19 model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 498-517.
    3. 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.
    4. Majeed A. Yousif & Faraidun K. Hamasalh, 2023. "A Hybrid Non-Polynomial Spline Method and Conformable Fractional Continuity Equation," Mathematics, MDPI, vol. 11(17), pages 1-18, September.
    5. Zhang, Ge & Li, Zhiming & Din, Anwarud, 2022. "A stochastic SIQR epidemic model with Lévy jumps and three-time delays," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    6. 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).
    7. Yousef Alnafisah & Moustafa El-Shahed, 2022. "Stochastic Analysis of a Hantavirus Infection Model," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    8. 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.
    9. 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).
    10. Din, Anwarud, 2024. "Bifurcation analysis of a delayed stochastic HBV epidemic model: Cell-to-cell transmission," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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