OPTIMAL CONTROL OF HIV-1 INFECTION MODEL WITH LOGISTIC GROWTH USING DISCRETE DELAY

Abstract

We investigate an optimal treatment strategies with mathematical population model of HIV-1 infection dynamics. We establish the existence of an optimal control for this model and provide necessary conditions for the optimal treatment. Pontryagin’s maximum principle is used to characterize these optimal controls, and the optimality system is derived. The optimal treatment strategy is obtained by solving the corresponding optimality system numerically. For the numerical simulation, we propose a new algorithm based on the Euler forward and backward difference approximation.