Modeling HIV Infection With Density‐Dependent Diffusion: The Role of Immune Evasion and CTL‐Mediated Immunity

Immune response plays a crucial role in orchestrating cell migration and signal transduction during early HIV infection, facilitating both viral progression and the establishment of immune evasion mechanisms. However, the influence of density‐dependent diffusion on these processes remains poorly understood. In this paper, we examine the impact of density‐dependent diffusion on HIV infection using a reaction‐diffusion model, in which the movement of cytotoxic T lymphocytes (CTLs) is dependent on the concentration of infected cells. By employing energy estimation techniques, we establish the global existence and stability of the model's solutions and explore its threshold dynamics. We demonstrate the global stability of equilibria and the persistence of HIV infection by using Lyapunov functionals and uniform persistence theory. Numerical simulations not only validate our theoretical results but also reveal that stronger immune responses can lead to higher viral loads of immune‐escape variants, thereby highlighting the selective pressures that shape viral adaptability. Under density‐dependent diffusion, regions with high densities of infected cells tend to correspond to low densities of CTL, and different density‐dependent diffusion functions significantly influence the peak density distributions. Our findings emphasize the importance of studying density‐dependent CTL chemotaxis to better understand immune cell behavior within the host.