Optimal Control of an HIV Infection Model with Logistic Growth, CTL Immune Response and Infected Cells in Eclipse Phase

Abstract

This paper deals with an optimal control problem for an HIV infection model with logistic growth, cytotoxic T-lymphocytes (CTL) immune response, and infected cells in eclipse phase. The model under consideration describes the interaction between the uninfected cells, the latently infected cells, the productively infected cells, the free viruses, and the CTL cells. The two treatments represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence of the optimal control pair is established and the Pontryagin’s minimum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward difference approximation. Finally, numerical simulations are performed in order to show the role of optimal therapy in controlling the infection severity.