An optimal strategy for HIV multitherapy

The purpose of the paper is to use numerical analysis and optimization tools to suggest improved therapies to try and cure HIV infection. A HIV model of an ordinary differential equation, which includes immune response, neutralizing antibodies and multi-drug effects, is improved. For a fixed time, two drugs treatment strategies are explored based on Pontryagin's Maximum Principle. Four types of treatments are used, and existence and uniqueness results for the optimal control fair are established. The optimality system is derived and then solved numerically using Gradient Projection Method. On the basis of weight factors for controls, we find a well treatment strategy with steady lower dosage of RTIs and PIs during the main part of treatment, almost unchanged higher population of uninfected CD4+T cells and few increase of active virus throughout the duration.