Current HIV/AIDS treatments effectively reduce viral loads to undetectable levels as measured by conventional clinical assays, but immune recovery remains highly variable among patients. To assess the long-term treatment efficacy, we propose a mathematical model that incorporates latently infected CD4 \(^+\) T cells and the homeostatic proliferation of CD4 \(^+\) T cells. We investigate the dynamics of this model both theoretically and numerically, demonstrating that homeostatic proliferation can induce bistability, which implies that steady-state CD4 \(^+\) T cell count is sensitively affected by initial conditions. The model exhibits rich dynamics, including saddle node bifurcations, Hopf bifurcations, and saddle node bifurcations related to periodic orbits. The interplay between homeostatic proliferation and latent HIV infection significantly influences the model’s dynamic behavior. Additionally, we integrate combination antiretroviral therapy (cART) into the model and fit the revised model to clinical data on long-term CD4 \(^+\) T cell counts before and after treatment. Quantitative analysis estimates the effects of long-term cART, revealing an increasing sensitivity of steady-state CD4 \(^+\) T cell count to drug efficacy. Correlation analysis indicates that the heightened activation of latently infected cells helps enhance treatment efficacy. These findings underscore the critical roles of CD4 \(^+\) T cell homeostatic proliferation and latently infected cell production in HIV persistence despite treatment, providing valuable insights for understanding disease progression and developing more effective therapies, potentially towards eradication.
