The paper presents a mathematical model of 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 shows that the uninfected state is stable when the number of infectious virions produced per infected T cell, N, is below a critical value, Ncrit. When N exceeds Ncrit, the uninfected state becomes unstable, and the endemically infected state can be stable or unstable, surrounded by a stable limit cycle. The model predicts that HIV infection leads to T-cell depletion through the establishment of a new steady state. The dynamics of this process are analyzed numerically and via the quasi-steady-state approximation. The model also considers the effects of AZT on viral growth and T-cell population dynamics. Two versions of the model are studied: one with a constant source of T cells and another where the source decreases with viral load. The latter provides more realistic predictions. The model explains the long latency between HIV infection and the onset of clinical AIDS, as well as the low concentration of free virus observed in the blood. It also shows that different viral strains, characterized by varying numbers of infectious virions, can cause different amounts of T-cell depletion and generate depletion at different rates. The model is not meant to be a comprehensive model of HIV's interaction with the immune system but focuses on the kinetics and degree of T-cell depletion caused by viral cytopathicity. The model is used to show that slow/low strains can be relevant to the population dynamics of slow/low escape mutants, and that replacing slow/low strains with rapid/high strains in end-stage disease can lead to significant T-cell depletion. The model's parameters are estimated based on in vivo conditions, and the results are used to understand the dynamics of HIV infection and the immune response.The paper presents a mathematical model of 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 shows that the uninfected state is stable when the number of infectious virions produced per infected T cell, N, is below a critical value, Ncrit. When N exceeds Ncrit, the uninfected state becomes unstable, and the endemically infected state can be stable or unstable, surrounded by a stable limit cycle. The model predicts that HIV infection leads to T-cell depletion through the establishment of a new steady state. The dynamics of this process are analyzed numerically and via the quasi-steady-state approximation. The model also considers the effects of AZT on viral growth and T-cell population dynamics. Two versions of the model are studied: one with a constant source of T cells and another where the source decreases with viral load. The latter provides more realistic predictions. The model explains the long latency between HIV infection and the onset of clinical AIDS, as well as the low concentration of free virus observed in the blood. It also shows that different viral strains, characterized by varying numbers of infectious virions, can cause different amounts of T-cell depletion and generate depletion at different rates. The model is not meant to be a comprehensive model of HIV's interaction with the immune system but focuses on the kinetics and degree of T-cell depletion caused by viral cytopathicity. The model is used to show that slow/low strains can be relevant to the population dynamics of slow/low escape mutants, and that replacing slow/low strains with rapid/high strains in end-stage disease can lead to significant T-cell depletion. The model's parameters are estimated based on in vivo conditions, and the results are used to understand the dynamics of HIV infection and the immune response.