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Dynamical analysis of a stochastic epidemic HBV model with log-normal Ornstein–Uhlenbeck process and vertical transmission term

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  • Wang, Haile
  • Zuo, Wenjie
  • Jiang, Daqing

Abstract

Considering the transmission rate perturbed by log-normal Ornstein–Uhlenbeck process, we develop a stochastic HBV model with vertical transmission term. For higher-dimensional deterministic system, the local asymptotic stability of the endemic equilibrium is given by proving the global stability of the corresponding linearized system. For stochastic system, the existence of stationary distribution is obtained by constructing several suitable Lyapunov functions and using the ergodicity of the Ornstein–Uhlenbeck process and the critical value corresponding to the basic reproduction number for determined system is derived, which means the persistence of the disease. And sufficient conditions for disease extinction are given. Furthermore, by solving five-dimensional Fokker–Planck equation, the exact expression of the probability density function near the quasi-equilibrium is provided to reveal the statistical properties. In the end, numerical simulations illustrate our theoretical results and exhibit the trends of the critical values for persistence and extinction of diseases along with the change of noise intensity and reversion speed.

Suggested Citation

  • Wang, Haile & Zuo, Wenjie & Jiang, Daqing, 2023. "Dynamical analysis of a stochastic epidemic HBV model with log-normal Ornstein–Uhlenbeck process and vertical transmission term," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011372
    DOI: 10.1016/j.chaos.2023.114235
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    References listed on IDEAS

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    1. Zhang, Xiaofeng & Yuan, Rong, 2021. "A stochastic chemostat model with mean-reverting Ornstein-Uhlenbeck process and Monod-Haldane response function," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    2. Zhou, Baoquan & Jiang, Daqing & Han, Bingtao & Hayat, Tasawar, 2022. "Threshold dynamics and density function of a stochastic epidemic model with media coverage and mean-reverting Ornstein–Uhlenbeck process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 15-44.
    3. Shi, Zhenfeng & Zhang, Xinhong & Jiang, Daqing, 2019. "Dynamics of an avian influenza model with half-saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 399-416.
    4. Han, Bingtao & Jiang, Daqing, 2023. "Coexistence and extinction for a stochastic vegetation-water model motivated by Black–Karasinski process," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    5. Ayoubi, Tawfiqullah & Bao, Haibo, 2020. "Persistence and extinction in stochastic delay Logistic equation by incorporating Ornstein-Uhlenbeck process," Applied Mathematics and Computation, Elsevier, vol. 386(C).
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