The paper examines a model for HIV infection of CD4+ T cells, considering four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The model explains several puzzling quantitative features of HIV infection, such as the long latency period and low concentration of free virus in the blood. It exhibits two steady states: an uninfected state and an endemically infected state. The stability of these states depends on the parameter \( N \), the number of infectious virions produced per actively infected T cell. If \( N \) is less than a critical value \( N_{\text{crit}} \), the uninfected state is stable, while if \( N > N_{\text{crit}} \), the uninfected state is unstable, and the endemically infected state can be stable or unstable, with a stable limit cycle. Numerical bifurcation techniques are used to map out the parameter regimes of these behaviors. The model predicts that different viral strains can cause different levels of T-cell depletion, and it considers two versions of the model with different assumptions about the source of T-cell replenishment. The dynamics of the establishment of the new steady state are examined using numerical simulations and the quasi-steady-state approximation. The model also predicts that T-cell depletion occurs through the establishment of a new steady state, and it provides insights into the factors affecting the degree of depletion.The paper examines a model for HIV infection of CD4+ T cells, considering four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The model explains several puzzling quantitative features of HIV infection, such as the long latency period and low concentration of free virus in the blood. It exhibits two steady states: an uninfected state and an endemically infected state. The stability of these states depends on the parameter \( N \), the number of infectious virions produced per actively infected T cell. If \( N \) is less than a critical value \( N_{\text{crit}} \), the uninfected state is stable, while if \( N > N_{\text{crit}} \), the uninfected state is unstable, and the endemically infected state can be stable or unstable, with a stable limit cycle. Numerical bifurcation techniques are used to map out the parameter regimes of these behaviors. The model predicts that different viral strains can cause different levels of T-cell depletion, and it considers two versions of the model with different assumptions about the source of T-cell replenishment. The dynamics of the establishment of the new steady state are examined using numerical simulations and the quasi-steady-state approximation. The model also predicts that T-cell depletion occurs through the establishment of a new steady state, and it provides insights into the factors affecting the degree of depletion.