Optimal control of HIV stochastic model through genetic algorithm

Abstract

This paper presents an optimal control of a HIV stochastic model through drug therapy. The model shows the effect of anti-retrovirus drugs in different stages of infection. The optimal controller is achieved by Genetic Algorithm (GA). In this paper we find appropriate efficacies of a drug that minimize the virus particles for a deterministic model and stochastic model. To design the optimal stochastic controller, the stochastic model is converted to a deterministic model. Genetic Algorithm provides discrete constraints. A nonlinear constraint changed into two linear constraints by discretization. In the first part of simulation, the behavior of the system with constant value of efficacy is shown. Finally, for the objective of this problem different values of efficacy are found, which leads to the best drug dosage. The results demonstrate that optimal control by ignoring statistical properties, will not be efficient.