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Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity

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  • Wang, Tianlei
  • Hu, Zhixing
  • Liao, Fucheng
  • Ma, Wanbiao

Abstract

In this paper, we investigate the dynamical behavior of a virus infection model with general incidence rate and humoral immunity. By using suitable Lyapunov functional and the LaSalle's invariance principle, we establish the global stability of the three equilibria. The uninfected equilibrium E0 is globally asymptotically stable if R0≤1, the infected equilibrium without immunity E1 is globally asymptotically stable if R1≤1 and R0>1, the infected equilibrium with humoral immunity E2 is globally asymptotically stable if R1>1. We check our theorems with numerical simulation in the end.

Suggested Citation

  • Wang, Tianlei & Hu, Zhixing & Liao, Fucheng & Ma, Wanbiao, 2013. "Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 13-22.
    • Handle: RePEc:eee:matcom:v:89:y:2013:i:c:p:13-22
    DOI: 10.1016/j.matcom.2013.03.004
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    References listed on IDEAS

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    1. Ji, Yu & Min, Lequan & Zheng, Yu & Su, Yongmei, 2010. "A viral infection model with periodic immune response and nonlinear CTL response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2309-2316.
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    Cited by:

    1. Ahmed M. Elaiw & Safiya F. Alshehaiween & Aatef D. Hobiny, 2019. "Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions," Mathematics, MDPI, vol. 7(9), pages 1-27, September.
    2. Elaiw, Ahmed M. & Alshehaiween, Safiya F. & Hobiny, Aatef D., 2020. "Impact of B-cell impairment on virus dynamics with time delay and two modes of transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Elaiw, Ahmed M. & Alshaikh, Matuka A., 2020. "Global stability of discrete pathogen infection model with humoral immunity and cell-to-cell transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Geng, Yan & Xu, Jinhu & Hou, Jiangyong, 2018. "Discretization and dynamic consistency of a delayed and diffusive viral infection model," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 282-295.
    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. Lin, Jiazhe & Xu, Rui & Tian, Xiaohong, 2017. "Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 516-530.
    7. Wang, Yan & Liu, Xianning, 2017. "Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 138(C), pages 31-48.
    8. Hattaf, Khalid, 2020. "Global stability and Hopf bifurcation of a generalized viral infection model with multi-delays and humoral immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    9. Wang, Xia & Song, Xinyu & Tang, Sanyi & Rong, Libin, 2016. "Analysis of HIV models with multiple target cell populations and general nonlinear rates of viral infection and cell death," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 87-103.
    10. Sun, Hongquan & Li, Jin, 2020. "A numerical method for a diffusive virus model with general incidence function, cell-to-cell transmission and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    11. Wang, Jinliang & Guo, Min & Liu, Xianning & Zhao, Zhitao, 2016. "Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 149-161.

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