Abstract
In the literature, several mathematical models have been formulated and developed to describe the within-host dynamics of either human immunodeficiency virus (HIV) or human T-lymphotropic virus type I (HTLV-I) monoinfections. In this paper, we formulate and analyze a novel within-host dynamics model of HTLV-HIV coinfection taking into consideration the response of cytotoxic T lymphocytes (CTLs). The uninfected mathrm{CD} 4^{+}mathrm{T} cells can be infected via HIV by two mechanisms, free-to-cell and infected-to-cell. On the other hand, the HTLV-I has two modes for transmission, (i) horizontal, via direct infected-to-cell touch, and (ii) vertical, by mitotic division of active HTLV-infected cells. It is well known that the intracellular time delays play an important role in within-host virus dynamics. In this work, we consider six types of distributed-time delays. We investigate the fundamental properties of solutions. Then, we calculate the steady states of the model in terms of threshold parameters. Moreover, we study the global stability of the steady states by using the Lyapunov method. We conduct numerical simulations to illustrate and support our theoretical results. In addition, we discuss the effect of multiple time delays on stability of the steady states of the system.
Highlights
During the past several decades many human viruses and their associated diseases, such as human immunodeficiency virus (HIV), hepatitis C virus (HCV), hepatitis B virus (HBV), dengue virus, human T-lymphotropic virus type I (HTLV-I), and recently coronavirus, have been recognized
2 The multiple delays model we extend system (3) by taking under consideration multiple types of distributed-time delays and mitosis of active HTLV-infected cells
We find that system (5) has eight possible steady states. (i) Infection-free steady state, Ð0 = (S0, 0, 0, 0, 0, 0, 0, 0), where S0 = η/
Summary
During the past several decades many human viruses and their associated diseases, such as human immunodeficiency virus (HIV), hepatitis C virus (HCV), hepatitis B virus (HBV), dengue virus, human T-lymphotropic virus type I (HTLV-I), and recently coronavirus, have been recognized. 4 – 1), and 4 is the HTLV-specific CTL immunity reproduction number in case of HTLV monoinfection and is stated as follows:. (vi) Persistent HTLV-HIV coinfection steady state with only effective HIV-specific CTL, Ð5 = (S5, L5, I5, E5, Y5, V5, C5I , 0), where. (vii) Persistent HTLV-HIV coinfection steady state with only effective HTLV-specific CTL, Ð6 = (S6, L6, I6, E6, Y6, V6, 0, C6Y ), where aε(γ + λ) S6 = P(bθ1H6 + εθ2) = S1, Y6. The parameter 7 is the competed HIV-specific CTL immunity reproduction number in case of HTLV-HIV coinfection. The parameter 8 is the competed HTLV-specific CTL immunity reproduction number in case of HTLV-HIV coinfection.
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