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Stability of HTLV/HIV dual infection model with mitosis and latency
A M Elaiw1,2, N H AlShamrani1,3
1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
Insights
This study models Human T-lymphotropic virus (HTLV) and Human Immunodeficiency Virus (HIV) dual infections, including Cytotoxic T Lymphocyte (CTL) responses. Mathematical analysis reveals the complex dynamics and stability of these co-infections.
Area of Science:
- Mathematical Biology
- Immunology
- Virology
Background:
- Human T-lymphotropic virus (HTLV) and Human Immunodeficiency Virus (HIV) are significant global health concerns.
- Dual infections with HTLV and HIV can alter disease progression and immune responses.
- Understanding the interplay between these viruses and the host immune system, particularly Cytotoxic T lymphocytes (CTLs), is crucial.
Purpose of the Study:
- To formulate and analyze a mathematical model for HTLV/HIV dual infection.
- To incorporate the role of CTLs in the immune response to both viruses.
- To investigate the transmission dynamics and stability of single and dual infections.
Main Methods:
- Development of an eight-compartment mathematical model.
- Analysis of model solutions for nonnegativity and boundedness.
- Calculation of steady states and threshold parameters.
- Application of the Lyapunov-LaSalle asymptotic stability theorem.
- Numerical simulations to validate theoretical findings.
Main Results:
- The model captures distinct transmission routes for HIV (free-to-cell, infected-to-cell) and HTLV (horizontal, vertical).
- Global stability of all model steady states was proven using the Lyapunov-LaSalle theorem.
- Numerical simulations supported the theoretical analysis and illustrated infection dynamics.
- Comparison between single and dual infection dynamics was performed.
Conclusions:
- The developed mathematical model provides a robust framework for studying HTLV/HIV co-infections.
- The CTL response plays a significant role in controlling viral loads.
- The study offers insights into the complex interactions governing dual viral infections and their impact on immune dynamics.
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 CD4+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 CD4+T cell by two ways, free-to-cell and infected-to-cell. Infected-to-cell spread of HIV occurs when uninfected CD4+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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