Numerical Simulation for the Fractional SIRC Model and Influenza A

Authors

M. M. Khader, Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh: 11566, Saudi Arabia\\ Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
N. H. Sweilam
A. M. S. Mahdy
N. K. Abdel Moniem

Author Country (or Countries)

Egypt

Abstract

In this paper, A Chebyshev spectral method is presented to study the deals with the fractional SIRC model associated with the evolution of influenza A disease in human population. The properties of the Chebyshev polynomials are used to derive an approximate formula of the Caputo fractional derivative. This formula reduces the SIRC model to the solution of a system of algebraic equations which is solved using Newton iteration method. The convergence analysis and an upper bound of the error of the derived formula are given. We compared our numerical solutions with those numerical solutions using fourth-order Runge-Kutta method. The obtained results of the SIRC model show the simplicity and the efficiency of the proposed method. Also, illustration for propagation of influenza A virus and the relation between the four cases of it along the time at the fractional derivative are given.

Suggested Reviewers

N/A

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/080311

Recommended Citation

M. Khader, M.; H. Sweilam, N.; M. S. Mahdy, A.; and K. Abdel Moniem, N. (2014) "Numerical Simulation for the Fractional SIRC Model and Influenza A," Applied Mathematics & Information Sciences: Vol. 08: Iss. 3, Article 11.
DOI: http://dx.doi.org/10.12785/amis/080311
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss3/11