A diusion-based HIV model with inammatory cytokines and adaptive immune impairment

N. H. AlShamrani^*

• University of Jeddah, Jeddah, Saudi Arabia

HIV continues to pose a critical threat to global public health, contributing to a high number of deaths worldwide. The virus predominantly attacks CD4 + T lymphocytes, which are essential for coordinating immune responses. A progressive decline in these cells is a hallmark of HIV pathogenesis. Recent research has underscored the role of inammatory cytokines in promoting viral spread and exacerbating immune dysfunction. This study presents a spatially structured model of HIV infection incorporating the role of inammatory cytokines. The model consists of six interacting components: healthy CD4 + T cells, HIV-infected cells, inammatory cytokines, free viral particles, cytotoxic T lymphocytes (CTLs), and antibodies. It accounts for both cellfree (virus-to-cell) and direct (cell-to-cell) modes of transmission. The model also captures the suppression of adaptive immune responses involving CTLs and B cells. Motivated by recent ndings that immune and infected cells, as well as viruses, may migrate from high to low concentration areas, we introduce diusion terms to represent spatial movement, resulting in a system of nonlinear partial dierential equations. We rst establish the model's mathematical well-posedness by proving the existence and boundedness of global solutions. A basic reproduction number R 0 is derived, serving as a threshold parameter that governs the stability of two equilibria: the HIV-free equilibrium (FE) and the HIV-persistent equilibrium (PE). By constructing suitable Lyapunov functions and applying LaSalle's invariance principle, we demonstrate that FE is globally asymptotically stable when R 0 ≤ 1, while PE becomes globally stable if R 0 > 1. Numerical simulations are performed to validate the analytical results, and a sensitivity analysis of R 0 is carried out to evaluate the impact of critical model parameters.