Global stability of infection-free state and endemic infection state of a modified human immunodeficiency virus infection model

This study proposes a modified human immunodeficiency virus (HIV) infection differential equation model with a saturated infection rate. This model has an infection-free equilibrium point and an endemic infection equilibrium point. Using Lyapunov functions and LaSalle's invariance principle shows that if the model's basic reproductive number R₀ < 1, the infection-free equilibrium point is globally asymptotically stable, otherwise the endemic infection equilibrium point is globally asymptotically stable. It is shown that a forward bifurcation will occur when R₀ = 1. The basic reproductive number R₀ of the modified model is independent of plasma total CD4⁺ T cell counts and thus the modified model is more reasonable than the original model proposed by Buonomo and Vargas-De-León. Based on the clinical data from HIV drug resistance database of Stanford University, using the proposed model simulates the dynamics of two group patients' anti-HIV infection treatments. The simulation results have shown that the first 4 weeks' treatments made the two group patients' R'₀ < 1, respectively. After the period, drug resistance made the two group patients' R'₀ > 1. The results explain why the two group patients' mean CD4⁺ T cell counts raised and mean HIV RNA levels declined in the first period, but contrary in the following weeks.