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Dynamical behaviors of a stochastic HTLV-I infection model with general infection form and Ornstein–Uhlenbeck process

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  • Shi, Zhenfeng
  • Jiang, Daqing

Abstract

In this study, considering the Ornstein–Uhlenbeck process to perturb the infection rate, we develop a HTLV-I infection model with general infection form. By constructing several suitable Lyapunov functions and a compact set, and then using the strong law of numbers and Fatou’s lemma, we obtain sufficient conditions for the existence and uniqueness of the ergodic stationary distribution η(⋅) for the stochastic model. This implies long-term persistence of HTLV-I infection in a biological sense. Moreover, by using Itô’s integral stochastic model is transformed into the corresponding linearized system. Then solving the Fokker–Planck equation, we obtain the exact expression of probability density function around the quasi-equilibrium of the stochastic model. In addition, sufficient conditions for the extinction of HTLV-I infection are established. Finally, considering different incidence rate functions, we employ numerical simulations to support our results.

Suggested Citation

  • Shi, Zhenfeng & Jiang, Daqing, 2022. "Dynamical behaviors of a stochastic HTLV-I infection model with general infection form and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922009687
    DOI: 10.1016/j.chaos.2022.112789
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    References listed on IDEAS

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    1. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    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. Qi, Kai & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Virus dynamic behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 548-570.
    4. Wang, Yan & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "A stochastic HIV infection model with T-cell proliferation and CTL immune response," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 477-493.
    5. Mandal, Partha Sarathi & Banerjee, Malay, 2012. "Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1216-1233.
    6. 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. Han, Cheng & Wang, Yan & Jiang, Daqing, 2023. "Dynamics analysis of a stochastic HIV model with non-cytolytic cure and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
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    4. 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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