Table of Contents
ISRN Biomathematics
Volume 2012, Article ID 215124, 7 pages
Research Article

Optimal Control of a Delayed HIV Infection Model with Immune Response Using an Efficient Numerical Method

Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, P.O. Box 7955, Sidi Othman, Casablanca, Morocco

Received 26 August 2012; Accepted 30 October 2012

Academic Editors: R. P. Bahadur and M. A. Panteleev

Copyright © 2012 Khalid Hattaf and Noura Yousfi. 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 delay-differential equation model with optimal control that describes the interactions between human immunodeficiency virus (HIV), CD4+ T cells, and cell-mediated immune response. Both the treatment and the intracellular delay are incorporated into the model in order to improve therapies to cure HIV infection. The optimal controls represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence for the optimal control pair is established, Pontryagin’s maximum principle is used to characterize these optimal controls, and the optimality system is derived. For the numerical simulation, we propose a new algorithm based on the forward and backward difference approximation.