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Global stability and Hopf bifurcation of a generalized viral infection model with multi-delays and humoral immunity

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  • Hattaf, Khalid

Abstract

The aim of this paper is to develop a mathematical model for viral infection with humoral immunity and two modes of transmission that are the classical virus-to-cell infection and the direct cell-to-cell transmission. These both modes are modeled by two general incidence functions. Also, the model incorporates three delays including two distributed delays in cell infection and virus production, and one discrete delay that models the time needed to activate the immune response. We first prove the well-posedness of the developed model and the biological existence of equilibria. Further, the global stability of equilibria and the existence of Hopf bifurcation are investigated by using the direct and indirect Lyapunov methods. An important number of viral infection models and the corresponding results presented in recent studies are improved and extended.

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  • 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).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320564
    DOI: 10.1016/j.physa.2019.123689
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    References listed on IDEAS

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    1. Khalid Hattaf & Noura Yousfi, 2018. "Qualitative Analysis of a Generalized Virus Dynamics Model with Both Modes of Transmission and Distributed Delays," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-7, February.
    2. 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.
    3. 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.
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