A different approach of optimal control on an HIV immunology model

Abstract

A system of ordinary differential equation, which describes the interaction of HIV and T cells in the immune system, is utilized, and optimal representing drug treatment strategies of this model are explored. Control model, in the sense of an optimal control problem shows the strategy of chemotherapy treatment setting through a dynamic treatment. In this model, the optimal control pair represents the percentage effect the chemotherapy on the CD4+T cells and virus production. An objective function characterized based on maximizing T cells and minimizing the systemic cost of the chemotherapy. The optimal control could characterize by using Pontryagin’s Maximum Principle. Then by using an embedding method, we transfer the problem in to a modified problem in measure space. This transformation is an injection; one-one mapping, so the optimal pair and its image under the transformation could be identified. New problem could be solved by a linear programming problem.

Keywords

• Chemotherapy
• HIV
• Linear programming
• Measure theory
• Optimal control pair
• System of ordinary differential equation