Stability of HTLV/HIV dual infection model with mitosis and latency

A. M. Elaiw; N. H. AlShamrani; A. M. Elaiw; N. H. AlShamrani

doi:10.3934/mbe.2021059

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 2: 1077-1120. doi: 10.3934/mbe.2021059

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Research article

Stability of HTLV/HIV dual infection model with mitosis and latency

A. M. Elaiw ^{1,2
,
,},
N. H. AlShamrani ^1,3

1.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut 71452, Egypt
3.
Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia

Received: 01 December 2020 Accepted: 28 December 2020 Published: 11 January 2021

In this paper, we formulate and analyze an HTLV/HIV dual infection model taking into consideration the response of Cytotoxic T lymphocytes (CTLs). The model includes eight compartments, uninfected CD$ 4^{+} $T cells, latent HIV-infected cells, active HIV-infected cells, free HIV particles, HIV-specific CTLs, latent HTLV-infected cells, active HTLV-infected cells and HTLV-specific CTLs. The HIV can enter and infect an uninfected CD$ 4^{+} $T cell by two ways, free-to-cell and infected-to-cell. Infected-to-cell spread of HIV occurs when uninfected CD$ 4^{+} $T cells are touched with active or latent HIV-infected cells. In contrast, there are two modes for HTLV-I transmission, (ⅰ) horizontal, via direct infected-to-cell touch, and (ⅱ) vertical, by mitotic division of active HTLV-infected cells. We analyze the model by proving the nonnegativity and boundedness of the solutions, calculating all possible steady states, deriving a set of key threshold parameters, and proving the global stability of all steady states. The global asymptotic stability of all steady states is proven by using Lyapunov-LaSalle asymptotic stability theorem. We performed numerical simulations to support and illustrate the theoretical results. In addition, we compared between the dynamics of single and dual infections.
- HTLV/HIV dual infection,
- viral and cellular infections,
- global stability,
- mitotic transmission,
- latency,
- CTL-mediated immune response,
- Lyapunov function
Citation: A. M. Elaiw, N. H. AlShamrani. Stability of HTLV/HIV dual infection model with mitosis and latency[J]. Mathematical Biosciences and Engineering, 2021, 18(2): 1077-1120. doi: 10.3934/mbe.2021059

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Abstract

In this paper, we formulate and analyze an HTLV/HIV dual infection model taking into consideration the response of Cytotoxic T lymphocytes (CTLs). The model includes eight compartments, uninfected CD$ 4^{+} $T cells, latent HIV-infected cells, active HIV-infected cells, free HIV particles, HIV-specific CTLs, latent HTLV-infected cells, active HTLV-infected cells and HTLV-specific CTLs. The HIV can enter and infect an uninfected CD$ 4^{+} $T cell by two ways, free-to-cell and infected-to-cell. Infected-to-cell spread of HIV occurs when uninfected CD$ 4^{+} $T cells are touched with active or latent HIV-infected cells. In contrast, there are two modes for HTLV-I transmission, (ⅰ) horizontal, via direct infected-to-cell touch, and (ⅱ) vertical, by mitotic division of active HTLV-infected cells. We analyze the model by proving the nonnegativity and boundedness of the solutions, calculating all possible steady states, deriving a set of key threshold parameters, and proving the global stability of all steady states. The global asymptotic stability of all steady states is proven by using Lyapunov-LaSalle asymptotic stability theorem. We performed numerical simulations to support and illustrate the theoretical results. In addition, we compared between the dynamics of single and dual infections.

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