AUTHOR=AlShamrani Noura H. , Halawani Reham H. , Elaiw Ahmed M. 

TITLE=Stability of generalized models for HIV-1 dynamics with impaired CTL immunity and three pathways of infection

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=10

YEAR=2024

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2024.1412357

DOI=10.3389/fams.2024.1412357

ISSN=2297-4687

ABSTRACT=<p>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<sup>+</sup>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 (ℜ<sub>0</sub>) 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 (<italic>O</italic><sub>0</sub>) and the virus-persistence steady state (<italic>O</italic><sub>1</sub>). More precisely, <italic>O</italic><sub>0</sub> achieves global asymptotic stability when ℜ<sub>0</sub> ≤ 1, whereas <italic>O</italic><sub>1</sub> attains global asymptotic stability when ℜ<sub>0</sub> &gt; 1. To demonstrate the impact of the parameter values on ℜ<sub>0</sub>, we examine the sensitivity analysis. It is illustrated that ℜ<sub>0</sub> comprises three components, namely <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>ℜ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mrow><mml:mstyle mathvariant="script"><mml:mi>E</mml:mi></mml:mstyle></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, <inline-formula><mml:math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>ℜ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mrow><mml:mstyle mathvariant="script"><mml:mi>P</mml:mi></mml:mstyle></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, and <inline-formula><mml:math id="M3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>ℜ</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mrow><mml:mstyle mathvariant="script"><mml:mi>K</mml:mi></mml:mstyle></mml:mrow></mml:mrow></mml:msub></mml:math></inline-formula>, 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, ℜ<sub>0</sub> 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 ℜ<sub>0</sub>, thereby impeding the replication of HIV-1.</p>