An Optimal Control Strategy for HIV Treatment

Abstract

Considering a simple model that describes the spread of HIV in the human body, this work proposes a strategy to minimize the side effects of medication by introducing control variables that represent the evolution of the medication levels with time. The strategy corresponds to an optimization problem with respect to a prescribed performance
function. For a given performance function, an optimal medication strategy is obtained by means of Pontryagin’s maximum principle. To solve the set of nonlinear ordinary differential equations that describe the dynamics of susceptible, infected, active cells and HIV, we make
use of finite difference method.