Short- and Long-Term Optimal Control of a Mathematical Model for HIV Infection of CD4+T Cells

The main goal of this study was to develop a theoretical short- and long-term optimal control treatment of HIV infection of CD4+T cells. The aim of the mathematical model used herein is to make the free HIV virus particles in the blood decrease, while administering a treatment that is less toxic to patients. Pontryagin’s classical control theory is applied to a mathematical model of HIV infection of CD4+T cells characterized by a system of nonlinear differential equations with the following unknown functions: the concentration of susceptible CD4+T cells, CD4+T cells infected by the HIV viruses and free HIV virus particles in the blood