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 HIV. This model shows the strategy of chemotherapy treatment. In fact, the simulated optimal control pair, (u(1),u(2)), represents the virus production and the percentage effect of the chemotherapy on the CD4(+) T cells. We define an objective function characterized based on maximizing T cells and minimizing the cost of the chemotherapy treatment. In this paper, we introduce a new approach to find the optimal pair control for the simulated optimal control on treatment of HIV. By using an embedding method, optimal control problem transfers into a modified on the measure space, where now the existence of optimal pair is guaranteed by compactness of the space, and the metamorphosed problem in measure space is a kind of an infinite dimensional linear programming problem, whose solution can be approximated by that of a finite- dimensional one.