Optimal control of a delayed HIV infection model with immune response using an efficient numerical method (Q355900)

Summary: We present a delay-differential equation model with optimal control that describes the interactions between human immunodeficiency virus (HIV), CD4\(^{+}\) T cells, and cell-mediated immune response. Both the treatment and intracellular delays are incorporated into the model in order to improve therapies to cure HIV infection. The optimal controls represent the efficiency of drug treatments in inhibiting viral production and preventing new infections. Existence for the optimal control pair is established, Pontryagin's maximum principle is used to characterize these optimal controls, and the optimality system is derived. For numerical simulations, we propose a new algorithm based on the forward and backward difference approximation.