Free terminal time optimal control problem for the treatment of HIV infection

Abstract

In this work, an optimal control approach is presented in order to propose an optimal therapy for the treatment HIV infection using a combination of two appropriate treatment strategies. Theoptimal treatment duration and the optimal medications amount are considered. The main objectiveof this study is to be able to maximize the benefit based on number of healthy CD4+T-cells and CTLimmune cells and to minimize the infection level and the overall treatment cost while optimizing theduration of therapy. The free terminal time optimal control problem is formulated and the Pontryagin's maximum principle is employed to provide the explicit formulations of the optimal controls. Thecorresponding optimality system with the additional transversality condition for the terminal time isderived and solved numerically using an adapted iterative method with a Runge-Kutta fourth orderscheme and a gradient method routine.