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Analysis of HIV models with multiple target cell populations and general nonlinear rates of viral infection and cell death

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  • Wang, Xia
  • Song, Xinyu
  • Tang, Sanyi
  • Rong, Libin

Abstract

HIV can infect different cell populations such as CD4+ T cells and macrophages. In this paper, we study the global property of the solution of an HIV model with two target cell populations. The model includes general nonlinear rates of viral infection and cell death. For each class of target cells, the time delay between viral entry into cells and viral production is included in the model. We obtain the basic reproductive number of the model, which is shown to provide a threshold condition determining the long-term behavior of the solution of the model. Specifically, we show that the infection-free equilibrium is globally asymptotically stable when the basic reproductive number is less than or equal to 1, and that the infected equilibrium is globally asymptotically stable when the basic reproductive number is greater than 1. We also extend the model with two target cell populations to a general model with n populations. Similar global properties are obtained for the general model. Numerical simulations are performed to illustrate the stability results and to evaluate the relative contribution to viral production from the two cell populations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:124:y:2016:i:c:p:87-103
    DOI: 10.1016/j.matcom.2015.11.011
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Li, Hui-zhong & Liu, Xiang-dong & Yan, Rui & Liu, Cheng, 2020. "Hopf bifurcation analysis of a tumor virotherapy model with two time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    2. Ahmed M. Elaiw & Taofeek O. Alade & Saud M. Alsulami, 2018. "Global Stability of Within-Host Virus Dynamics Models with Multitarget Cells," Mathematics, MDPI, vol. 6(7), pages 1-19, July.

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