Optimal control theory applied to the anti-viral treatment of AIDS

Abstract

This work concerns a particular application of the Optimal Control Theory to a model related to HIV infection dynamics. The mathematical model adopted in this work was proposed by Nowak et al., 1996 and describes the dynamics of viral concentration in terms of interaction with CD4 cells and the cytotoxic T lymphocytes, which are responsible for the immune defense of the organism. The control variable is the drug dose, which, in turn, affects the rate of infection of CD4 cells by HIV virus. The cost function to be minimized is a weighted sum of the final viral load and the accumulated side effects. Simulation results show that the optimal control scheme can achieve improved quality of the treatment in terms of reduction in the viral load and quantity of administered drugs, but has the inconvenience related to the necessity of frequent and periodic laboratory analysis to provide feedback information to adjust the doses.