Computational and Mathematical Methods in Medicine
Volume 2011 (2011), Article ID 674318, 9 pages
doi:10.1155/2011/674318
Research Article

Optimal Control of HIV Dynamic Using Embedding Method

Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad 91775, Iran

Received 30 December 2010; Accepted 22 February 2011

Academic Editor: Haitao Chu

Copyright © 2011 H. Zarei et al. 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.

Abstract

This present study proposes an optimal control problem, with the final goal of implementing an optimal treatment protocol which could maximize the survival time of patients and minimize the cost of drug utilizing a system of ordinary differential equations which describes the interaction of the immune system with the human immunodeficiency virus (HIV). Optimal control problem transfers into a modified problem in measure space using an embedding method in which the existence of optimal solution is guaranteed by compactness of the space. Then the metamorphosed problem is approximated by a linear programming (LP) problem, and by solving this LP problem a suboptimal piecewise constant control function, which is more practical from the clinical viewpoint, is achieved. The comparison between the immune system dynamics in treated and untreated patients is introduced. Finally, the relationships between the healthy cells and virus are shown.