Optimal treatment strategies to control acute HIV infection

Various antiretroviral therapies (ART) are administered to symptomatic human immunodeficiency virus (HIV) infected individuals to improve their health. The treatment effectiveness may depend on suppressing development of drug resistance, reduce evolution of new viral strains, minimize serious side effects and the costs of drugs. This paper deals with some results concerning optimal drug administration scheme successful in improving patients' health especially in poorly resourced settings. The model under consideration describes the interaction between the uninfected cells, the latently infected cells, the productively infected cells, and the free viruses. Generally, in viral infection, the drug strategy aspects either the virus infectivity or reduce the virion production. The mathematical model proposed here, deals with both situations with the objective function based on a combination of maximizing benefit relied on T cells count (the white cells that coordinate activities of the immune system) and minimizing the systemic cost. The existence of the optimal control pair is established and the Pontryagin's minimum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward sweep method (FBSM). Our results indicate that early initiation of treatment makes a profound impact in both improving the quality of life and reducing the economic costs of therapy.