Open AccessStability of HTLV/HIV dual infection model with mitosis and latency
Author(s) -
A. M. Ełaiw,
N. H. AlShamrani
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021059
Subject(s) - cytotoxic t cell , mitosis , exponential stability , human immunodeficiency virus (hiv) , latency (audio) , virology , stability (learning theory) , cell , cell division , immunology , biology , mathematics , microbiology and biotechnology , physics , computer science , genetics , telecommunications , nonlinear system , quantum mechanics , machine learning , in vitro
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.