On the basis of the human immunodeficiency virus (HIV) infection dynamics model proposed by Adams, the authors propose an extended model that aims at incorporating the influence of activation-induced apoptosis of CD4+ and CD8+ T-cells on the immune system response of HIV-infected patients. Through this model, the authors study the influence of this phenomenon on the time evolution of specific cell populations such as plasma concentrations of HIV copies, or blood concentrations of CD4+ and CD8+ T-cells. In particular, this study shows that depending on its intensity, the apoptosis phenomenon can either favour or mitigate the long-term evolution of the HIV infection.