Optimizing Chemotherapy in an HIV Model by a Pair of Optimal Control

We introduce a medical control model, in the sense of an optimal control problem, which simulates the interaction of immune system with Human Immunodeficiency Virus (HIV) . This model shows the strategy of chemotherapy treatment. In fact, the simulated optimal control pair, (u1,u2) control the percentage effect of the chemotherapy on the CD4 + T cells and the virus production . An objective function is characterized based on maximizing T cells and minimizing the cost of chemotherapy treatment. In this article, a new approach is introduced to find an optimal pair control for obtaining an optimal HIV treatment. By using an embedding method, optimal control problem transfers into a modified problem in an appropriate measure space, in which the existence of optimal pair is guaranteed by compactness of the space, and the metamorphosed problem in measure space is a type of an infinite dimensional linear programming problem, whose solution can be approximated by that of a finite-dimensional one.