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Dynamics of two time delays differential equation model to HIV latent infection

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  • Liu, Huijuan
  • Zhang, Jia-Fang

Abstract

In this paper, we studied a HIV latent infection model with two time delays, where one delay is the time between viral entry into a cell and establishment of HIV latency and the other delay is the time between cell infection and viral production. The infection usually considered is linear, but in this article we consider that the infection rate of modeling HIV infection is nonlinear, where the rate of infection is βTV1+bV, and logistic growth of the uninfected target cells T. We defined the basic reproductive number and showed the local and global stability of the disease-free equilibrium and the permanence of the infected equilibrium. Furthermore, we discussed the dynamics of system under the three conditions: (1) τ1=τ2=0, (2) τ1=0,τ2>0, (3) τ1>0,τ2∈[0,τ2∗).

Suggested Citation

  • Liu, Huijuan & Zhang, Jia-Fang, 2019. "Dynamics of two time delays differential equation model to HIV latent infection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 384-395.
    • Handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:384-395
    DOI: 10.1016/j.physa.2018.09.087
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    References listed on IDEAS

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    1. Huo, Hai-Feng & Yang, Peng & Xiang, Hong, 2018. "Stability and bifurcation for an SEIS epidemic model with the impact of media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 702-720.
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    Cited by:

    1. Ahmed M. Elaiw & Noura H. AlShamrani, 2020. "HTLV/HIV Dual Infection: Modeling and Analysis," Mathematics, MDPI, vol. 9(1), pages 1-32, December.
    2. 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.
    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. Noura H. AlShamrani & Reham H. Halawani & Wafa Shammakh & Ahmed M. Elaiw, 2023. "Global Properties of HIV-1 Dynamics Models with CTL Immune Impairment and Latent Cell-to-Cell Spread," Mathematics, MDPI, vol. 11(17), pages 1-29, August.
    5. Noura H. AlShamrani & Ahmed Elaiw & Aeshah A. Raezah & Khalid Hattaf, 2023. "Global Dynamics of a Diffusive Within-Host HTLV/HIV Co-Infection Model with Latency," Mathematics, MDPI, vol. 11(6), pages 1-47, March.
    6. Haokun Sui & Leilei Han & Yuting Ding, 2022. "Dynamic Analysis of a Delayed Carbon Emission-Absorption Model for China’s Urbanization and Population Growth," Mathematics, MDPI, vol. 10(17), pages 1-13, August.
    7. Prakash, M. & Rakkiyappan, R. & Manivannan, A. & Cao, Jinde, 2019. "Dynamical analysis of antigen-driven T-cell infection model with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 266-281.

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