Table of Contents
Journal of Nonlinear Dynamics
Volume 2014, Article ID 945158, 8 pages
Research Article

Optimal Control of a Delayed HIV Infection Model via Fourier Series

1Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad 9177948953, Iran
2The Center of Excellence on Modelling and Control Systems (CEMCS), Mashhad 9177948953, Iran

Received 27 May 2014; Revised 13 August 2014; Accepted 14 August 2014; Published 26 August 2014

Academic Editor: Giovanni P. Galdi

Copyright © 2014 Gh. Ghanbari and M. H. Farahi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a delayed optimal control which describes the interaction of the immune system with the human immunodeficiency virus (HIV) and CD4+ T-cells. In order to improve the therapies, treatment and the intracellular delays are incorporated into the model. The optimal control in this model represents the efficiency of drug treatment in preventing viral production and new infections. The optimal pair of control and trajectories of this nonlinear delay system with quadratic cost functional is obtained by Fourier series approximation. The method is based on expanding time varying functions in the nonlinear delay system into their Fourier series with unknown coefficients. Using operational matrices for integration, product, and delay, the problem is reduced to a set of nonlinear algebraic equations.