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Global Dynamics of a Diffusive Within-Host HTLV/HIV Co-Infection Model with Latency

Author

Listed:
  • Noura H. AlShamrani

    (Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia)

  • Ahmed Elaiw

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut 71524, Egypt)

  • Aeshah A. Raezah

    (Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia)

  • Khalid Hattaf

    (Equipe de Recherche en Modélisation et Enseignement des Mathématiques (ERMEM), Centre Régional des Métiers de l’Education et de la Formation (CRMEF), Derb Ghalef, Casablanca 20340, Morocco)

Abstract

In several publications, the dynamical system of HIV and HTLV mono-infections taking into account diffusion, as well as latently infected cells in cellular transmission has been mathematically analyzed. However, no work has been conducted on HTLV/HIV co-infection dynamics taking both factors into consideration. In this paper, a partial differential equations (PDEs) model of HTLV/HIV dual infection was developed and analyzed, considering the cells’ and viruses’ spatial mobility. CD 4 + T cells are the primary target of both HTLV and HIV. For HIV, there are three routes of transmission: free-to-cell (FTC), latent infected-to-cell (ITC), and active ITC. In contrast, HTLV transmits horizontally through ITC contact and vertically through the mitosis of active HTLV-infected cells. In the beginning, the well-posedness of the model was investigated by proving the existence of global solutions and the boundedness. Eight threshold parameters that determine the existence and stability of the eight equilibria of the model were obtained. Lyapunov functions together with the Lyapunov–LaSalle asymptotic stability theorem were used to investigate the global stability of all equilibria. Finally, the theoretical results were verified utilizing numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1523-:d:1103224
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    References listed on IDEAS

    as
    1. 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.
    2. Elaiw, Ahmed M. & Al Agha, Afnan D., 2019. "Stability of a general HIV-1 reaction–diffusion model with multiple delays and immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    3. Luo, Yantao & Zhang, Long & Zheng, Tingting & Teng, Zhidong, 2019. "Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Mojaver, Aida & Kheiri, Hossein, 2015. "Mathematical analysis of a class of HIV infection models of CD4+ T-cells with combined antiretroviral therapy," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 258-270.
    5. Alan S. Perelson & Paulina Essunger & Yunzhen Cao & Mika Vesanen & Arlene Hurley & Kalle Saksela & Martin Markowitz & David D. Ho, 1997. "Decay characteristics of HIV-1-infected compartments during combination therapy," Nature, Nature, vol. 387(6629), pages 188-191, May.
    6. Ahmed M. Elaiw & Afnan D. Al Agha, 2022. "Global Stability of a Reaction–Diffusion Malaria/COVID-19 Coinfection Dynamics Model," Mathematics, MDPI, vol. 10(22), pages 1-31, November.
    7. Alex Sigal & Jocelyn T. Kim & Alejandro B. Balazs & Erez Dekel & Avi Mayo & Ron Milo & David Baltimore, 2011. "Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy," Nature, Nature, vol. 477(7362), pages 95-98, September.
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    Cited by:

    1. Chowdhury, Sourav & Ghosh, Jayanta Kumar & Ghosh, Uttam, 2024. "Co-infection dynamics between HIV-HTLV-I disease with the effects of Cytotoxic T-lymphocytes, saturated incidence rate and study of optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 195-218.

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