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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 816803, 11 pages
http://dx.doi.org/10.1155/2013/816803
Research Article

Numerical Modeling of Fractional-Order Biological Systems

1Department of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, UAE
2Department of Mathematics, Faculty of Science, Helwan University, Cairo 11795, Egypt

Received 17 May 2013; Accepted 23 June 2013

Academic Editor: Ali H. Bhrawy

Copyright © 2013 Fathalla A. Rihan. 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 provide a class of fractional-order differential models of biological systems with memory, such as dynamics of tumor-immune system and dynamics of HIV infection of CD4+ T cells. Stability and nonstability conditions for disease-free equilibrium and positive equilibria are obtained in terms of a threshold parameter (minimum infection parameter) for each model. We provide unconditionally stable method, using the Caputo fractional derivative of order and implicit Euler’s approximation, to find a numerical solution of the resulting systems. The numerical simulations confirm the advantages of the numerical technique and using fractional-order differential models in biological systems over the differential equations with integer order. The results may give insight to infectious disease specialists.