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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 963864, 20 pages
http://dx.doi.org/10.1155/2012/963864
Research Article

Stability and Feedback Stabilization of HIV Infection Model with Two Classes of Target Cells

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511, Egypt

Received 3 April 2012; Accepted 24 June 2012

Academic Editor: Mingshu Peng

Copyright © 2012 A. M. Elaiw and A. M. Shehata. 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

We study the stability and feedback stabilization of the uninfected steady state of a human immunodeficiency virus (HIV) infection model. The model is a 6-dimensional nonlinear ODEs that describes the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages, and takes into account the Cytotoxic T Lymphocytes (CTLs) immune response. Lyapunov function is constructed to establish the global asymptotic stability of the uninfected steady state of the model. In a control system framework, the HIV infection model incorporating the effect of Highly Active AntiRetroviral Therapy (HAART) is considered as a nonlinear control system with drug dose as control input. We developed treatment schedules for HIV-infected patients by using Model Predictive Control (MPC-)based method. The MPC is constructed on the basis of an approximate discrete-time model of the HIV infection model. The MPC is applied to the stabilization of the uninfected steady state of the HIV infection model. Besides model inaccuracies that HIV infection model suffers from, some disturbances/uncertainties from different sources may arise in the modelling. In this work the disturbances are modelled in the HIV infection model as additive bounded disturbances. The robustness of the MPC against small model uncertainties or disturbances is also shown.