This research gives a thorough examination of a human immunodeficiency virus (HIV) infection model that includes quiescent cells and immune response dynamics in the host. The model, represented by a system of ordinary differential equations, captures the complex interaction between the host's immune response and viral infection. The study focuses on the model's fundamental aspects, such as equilibrium analysis, computing the basic reproduction number (Formula presented.), stability analysis, bifurcation phenomena, numerical simulations, and sensitivity analysis. The analysis reveals both an infection equilibrium, which indicates the persistence of the illness, and an infection-free equilibrium, which represents disease control possibilities. Applying matrix-theoretical approaches, stability analysis proved that the infection-free equilibrium is both locally and globally stable for (Formula presented.). For the situation of (Formula presented.), the infection equilibrium is locally asymptotically stable via the Routh-Hurwitz criterion. We also studied the uniform persistence of the infection, demonstrating that the infection remains present above a positive threshold under certain conditions. The study also found a transcritical forward-type bifurcation at (Formula presented.), indicating a critical threshold that affects the system's behavior. The model's temporal dynamics are studied using numerical simulations, and sensitivity analysis identifies the most significant variables by assessing the effects of parameter changes on system behavior. © 2025 The Author(s). Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.