Adaptive immune response in HIV dynamics: an optimal control study

Abstract

This research aims to optimize the control of an HIV infection model. The focus of this paper is on optimizing the control of an HIV infection model. Our mathematical model consists of six non-linear differential equations that illustrate what happens when uninfected cells, exposed cells, actively infected cells, free viruses, and the adaptive immune response interact. Furthermore, adaptive immunity will be characterized by cytotoxic T-lymphocytes (CTLs) and antibodies. The two treatments illustrate how drug therapy can stop the replication of viruses and reduce the risk of new infections. We demonstrate the existence of an optimal control pair and we apply Pontryagin’s minimal approach to delineate these two optimum controls. In the end, numerical simulations are used to show how important effective treatment is for keeping the infection under control.