Optimal control in chemotherapy of a viral infection

Abstract

In this study we develop some results concerning the optimal chemotherapy in case of HIV (human immunodeficiency virus). Generally, in viral infection, the drug strategy affects either the virus infectivity or reduce the virion production. The mathematical model proposed here, deals with the first situation, and represents an optimal control problem, with the state equation given by an ODE and 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 of chemotherapy. We demonstrate the existence of an optimal control and introduce the first order necessary optimality conditions in order to derive an algorithm to approximate the optimal chemotherapy strategy. Conclusive numerical simulations are presented.