The requirements for the eradication of HIV in infected individuals are unknown. Intermittent administration of the immune activator interleukin-2 (IL-2) in combination with highly-active antiretroviral therapy (HAART) has been suggested as an effective strategy to realize long-term control of HIV replication in vivo. However, potential latent virus reservoirs are considered to be a major impediment in achieving this goal. In this paper, a new mathematical model is designed and used to monitor the interactions between HIV, CD4+ T-cells, CD8+ T-cells, productively infected and latently infected CD4+ T-cells, and to evaluate therapeutic strategies during the first 3 years of HIV infection. The model shows that current anti-HIV therapies, including intermittent IL-2 and HAART, are insufficient in achieving eradication of HIV. However, it suggests that the HIV eradication may indeed be theoretically feasible if such therapy is administered continuously (without interruption) under some specified conditions. These conditions may realistically be achieved using an agent (such as a putative anti-HIV vaccine) that brings about a concomitant increase in the proliferation of HIVspecific CD4+ T- and CD8+ T-cells and the differentiation of CD8+ T-cells into anti-HIV cytotoxic T lymphocytes (CTLs).