Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 480378, 9 pages
http://dx.doi.org/10.1155/2011/480378
Research Article

The Fractional SIRC Model and Influenza A

Moustafa El-Shahed1,2 and Ahmed Alsaedi2

1Department of Mathematics, Faculty of Art and Sciences, Qassim University, P.O. Box 3771, Qassim, Unizah 51911, Saudi Arabia
2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 30 July 2011; Accepted 29 August 2011

Academic Editor: Hamdy Nabih Agiza

Copyright © 2011 Moustafa El-Shahed and Ahmed Alsaedi. 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

This paper deals with the fractional-order SIRC model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, 𝑅 0 . We give a detailed analysis for the asymptotic stability of disease-free and positive fixed points. Nonstandard finite difference methods have been used to solve and simulate the system of differential equations.