Predator–prey dynamics in the interaction of HIV with CD4+ T cells, incorporating cytotoxic immune response

Abstract

This study presents a mathematical model describing the interaction between human immunodeficiency virus (HIV) and CD4+ T cells within a predator–prey framework, where HIV acts as the predator and CD4+ T cells serve as the prey. Unlike previous simplified models that treat infected cell death as a constant process, this work introduces an explicit density-dependent cytotoxic immune response mechanism that eliminates infected CD4+ T cells in proportion to both the infected cell and viral populations. The model comprises three ordinary differential equations representing uninfected CD4+ T cells, infected CD4+ T cells, and free virus particles. Mathematical analysis reveals two equilibrium points: a virus-free equilibrium and an endemic equilibrium where all three populations coexist. Stability analysis using linearization and Routh-Hurwitz criteria demonstrates that the virus-free equilibrium is locally asymptotically stable when the basic reproduction number, R 0 falls below unity, while the endemic equilibrium achieves stability under sufficient conditions involving the immune response strength. Numerical simulations employing parameter values informed by recent immunological studies confirm that robust cytotoxic immune responses promote stable chronic infection with reduced viral burden. Global stability analysis via Lyapunov functions and bifurcation analysis further validate these findings. The results highlight the critical role of adaptive immunity in determining HIV persistence and provide a theoretical foundation for understanding immune control mechanisms in untreated HIV infection.