Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 568315, 29 pages
Research Article

Multiobjective Optimal Control of HIV Dynamics

Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 91775-1159, Iran

Received 31 August 2010; Revised 30 November 2010; Accepted 22 December 2010

Academic Editor: Wei-Chiang Hong

Copyright © 2010 Hassan 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.


Various aspects of the interaction of HIV with the human immune system can be modeled by a system of ordinary differential equations. This model is utilized, and a multiobjective optimal control problem (MOOCP) is proposed to maximize the CD4+ T cells population and minimize both the viral load and drug costs. The weighted sum method is used, and continuous Pareto optimal solutions are derived by solving the corresponding optimality system. Moreover, a model predictive control (MPC) strategy is applied, with the final goal of implementing Pareto optimal structured treatment interruptions (STI) protocol. In particular, by using a fuzzy approach, the MOOCP is converted to a single-objective optimization problem to derive a Pareto optimal solution which among other Pareto optimal solutions has the best satisfaction performance. Then, by using an embedding method, the problem is transferred into a modified problem in an appropriate space in which the existence of solution is guaranteed by compactness of the space. The metamorphosed problem is approximated by a linear programming (LP) model, and a piecewise constant solution which shows the desired combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies is achieved.