Dynamics of an HIV model with immune response and two types of infected cells

This research investigates a mathematical model for human immunodeficiency virus (HIV) infections that incorporates cytotoxic T lymphocyte (CTL) immune responses and two types of infected cells. Additionally, the model reflects the effect of antiretroviral therapies. By using the next-generation matrix method, the basic reproduction number $R_0$ and the CTL immune reproduction number $R_1$ are calculated. The existence and stability of equilibria are discussed. In particular, if $R_0<1$, then the infection-free equilibrium is globally asymptotically stable. Moreover, through analyzing the transmission dynamics of HIV within the human body under the influence of drug treatment, this study provides a theoretical foundation to optimize antiretroviral therapy strategies.