Abstract
This study proposes a mathematical model for HIV-1 infection and investigates their qualitative dynamics such as stability, bistability, and bifurcation properties. The model builds on existing HIV-1 models by incorporating the effects of antiretroviral therapy (ART) and modeling immune-cell dynamics through non-monotone functional responses, capturing may help to gain insights into immune activation behaviors. Further, this study discusses the presence of bistability and bifurcation phenomena, indicating that HIV-1 infection dynamics can switch between multiple equilibriums depending on model parameters and initial conditions. To ensure the disease spread in the community, this study determines the formula to calculate the basic reproduction number for the model. Theoretically, this study performs the disease-free, immune-free, and infection steady-state analysis to determine the threshold conditions focusing on saddle-node, trans-critical and Hopf-type bifurcation relies on significant parameters. The study also works on a data-driven modeling approach to determine the appropriate population parameters of the model with the help of clinical trials performed on human patients for 15 weeks.