This study investigates a mathematical modeling approach to the formulation of treatment strategies for rapid-progressors to AIDS (RPs), who experience a considerably faster progression than other patients and constitute approximately 10% of the infected population. This presents a first attempt to produce optimal schedules for rapid-progressors, as this has not been considered in the literature to-date. A previously formulated model for typical-progressors was modified to predict the entire trajectory of the disease in RPs by estimation of immune system parameters only. The latter have been suggested to be key in determining the degree of progression and the ability of the model to reproduce this phenomenon via replication of clinical data from this class of patients validates the formulation. Moreover, the model also replicates clinical data from long-term non-progressors (LTNPs) and this further validates this work. Our optimal control results have shown that, unlike continuous therapy, which is not effective in controlling disease progression in RPs, structured treatment interruptions (STIs) prove to be very effective. This work reinforces their promising potential and should encourage further experimental and clinical work to examine their inclusion in HIV treatment guidelines.