Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 893474, 17 pages
Research Article

Fuzzy Modeling and Control of HIV Infection

1Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad 91775-1159, Iran
2Department of Infectious Diseases, Imam Reza Hospital, Mashhad University of Medical Sciences, Mashhad 91379-13316, Iran

Received 20 September 2011; Revised 28 December 2011; Accepted 2 January 2012

Academic Editor: Jacek Waniewski

Copyright © 2012 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.


The present study proposes a fuzzy mathematical model of HIV infection consisting of a linear fuzzy differential equations (FDEs) system describing the ambiguous immune cells level and the viral load which are due to the intrinsic fuzziness of the immune system's strength in HIV-infected patients. The immune cells in question are considered CD4+ T-cells and cytotoxic T-lymphocytes (CTLs). The dynamic behavior of the immune cells level and the viral load within the three groups of patients with weak, moderate, and strong immune systems are analyzed and compared. Moreover, the approximate explicit solutions of the proposed model are derived using a fitting-based method. In particular, a fuzzy control function indicating the drug dosage is incorporated into the proposed model and a fuzzy optimal control problem (FOCP) minimizing both the viral load and the drug costs is constructed. An optimality condition is achieved as a fuzzy boundary value problem (FBVP). In addition, the optimal fuzzy control function is completely characterized and a numerical solution for the optimality system is computed.