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Mathematical Problems in Engineering
Volume 2009, Article ID 378614, 12 pages
Research Article

Nonlinear Dynamics and Chaos in a Fractional-Order HIV Model

1Department of Applied Mathematics, Donghua University, Shanghai 201620, China
2College of Information Sciences and Technology, Donghua University, Shanghai 201620, China
3Engineering Research Center of Digitized Textile and Fashion Technology, Ministry of Education, Donghua University, Shanghai 201620, China

Received 18 January 2009; Revised 26 February 2009; Accepted 8 April 2009

Academic Editor: José Roberto Castilho Piqueira

Copyright © 2009 Haiping Ye and Yongsheng Ding. 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 introduce fractional order into an HIV model. We consider the effect of viral diversity on the human immune system with frequency dependent rate of proliferation of cytotoxic T-lymphocytes (CTLs) and rate of elimination of infected cells by CTLs, based on a fractional-order differential equation model. For the one-virus model, our analysis shows that the interior equilibrium which is unstable in the classical integer-order model can become asymptotically stable in our fractional-order model and numerical simulations confirm this. We also present simulation results of the chaotic behaviors produced from the fractional-order HIV model with viral diversity by using an Adams-type predictor-corrector method.