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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 136263, 9 pages
Research Article

On Fractional SIRC Model with Salmonella Bacterial Infection

1Department of Mathematical Sciences, College of Science, UAE University, P.O. Box 15551, Al Ain, UAE
2Faculty of Science, Helwan University, Cairo, Egypt
3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 80204, Saudi Arabia
4Department of Mathematics and Computer Sciences, Cankaya University, 06530 Ankara, Turkey
5Institute of Space Sciences, P.O. Box MG-23, 76900 Magurele-Bucharest, Romania
6Department of Mathematics, Bharathiar University, Coimbatore, Tamil Nadu 641046, India

Received 3 March 2014; Accepted 25 March 2014; Published 22 April 2014

Academic Editor: Ali H. Bhrawy

Copyright © 2014 Fathalla A. Rihan 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.


We propose a fractional order SIRC epidemic model to describe the dynamics of Salmonella bacterial infection in animal herds. The infection-free and endemic steady sates, of such model, are asymptotically stable under some conditions. The basic reproduction number is calculated, using next-generation matrix method, in terms of contact rate, recovery rate, and other parameters in the model. The numerical simulations of the fractional order SIRC model are performed by Caputo’s derivative and using unconditionally stable implicit scheme. The obtained results give insight to the modelers and infectious disease specialists.