Frontiers in Applied Mathematics and Statistics (Aug 2024)
Stability of generalized models for HIV-1 dynamics with impaired CTL immunity and three pathways of infection
Abstract
Highly active antiretroviral therapy (HAART) stands out as the most effective treatment for human immunodeficiency virus type-1 (HIV-1). While total eradication is still difficult, HAART can dramatically lower the virus's plasma viral level below the detection threshold. The activation of latently infected cells is considered to be the main obstacle to the total eradication of HIV-1 infection. This study investigates the dynamic characteristics of two generalized HIV-1 infection models taking into account the impairment of cytotoxic T lymphocytes (CTLs). These models include CD4+T cells that are latently infected and equipped with the capability to engage in cell-to-cell infection and elude immune responses. We introduce models featuring three infection pathways: virus-to-cell (VTC), latent cell-to-cell (L-CTC), and active cell-to-cell (A-CTC). The three pathways' infection rates are characterized by general functions, which cover the many types of infection rates documented in the literature. The second model integrates three distinct types of distributed-time delays. We demonstrate the validity of the suggested models, through their well-posedness. We determine the basic reproduction ratio (ℜ0) of the systems. Lyapunov functions and LaSalle's invariance principle are employed to verify that the global stability of both the virus-free steady state (O0) and the virus-persistence steady state (O1). More precisely, O0 achieves global asymptotic stability when ℜ0 ≤ 1, whereas O1 attains global asymptotic stability when ℜ0 > 1. To demonstrate the impact of the parameter values on ℜ0, we examine the sensitivity analysis. It is illustrated that ℜ0 comprises three components, namely ℜ0E, ℜ0P, and ℜ0K, corresponding to the transmissions of VTC, L-CTC, and A-CTC, respectively. Thus, if the L-CTC pathway is disregarded in the HIV-1 infection model, ℜ0 may be underestimated, which could lead to inadequate or erroneous medication therapy focused on eradicating HIV-1 within the body. To demonstrate the associated mathematical outcomes, we conduct numerical simulations through an illustrative example. Specifically, we delve into how the dynamics of HIV-1 are influenced by both immune impairment and time delay. Our findings suggest a significant role of reduced immunity in the progression of the infection. Furthermore, time delays possess the potential to markedly reduce ℜ0, thereby impeding the replication of HIV-1.
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