Optimal control and infectiology: Application to an HIV/AIDS model

An existing infectious model describing the interaction of HIV virus and the immune system of the human body is utilized to determine the optimal methodology for administering anti-viral medication therapies to fight HIV infection. This work investigates the fundamental role of chemotherapy treatment in controlling the virus reproduction. We work in the nonlinear optimal control framework. The existence and the uniqueness results of the solution are discussed. A characterization of the optimal control via adjoint variables is established. We obtain an optimality system that we seek to solve numerically by a competitive Gauss–Seidel like implicit difference method.