Numerical treatment for solving fractional SIRC model and influenza A

• DOI: 10.1007/s40314-013-0079-6
• Publication Date: 2013-10-02T09:33:53Z
• Authors: M. M. Khader; Mohammed M. Babatin
• Keywords: Finite difference; Chebyshev iteration

This paper presents an accurate numerical method for solving fractional SIRC model. In this work, we propose a method so called fractional Chebyshev finite difference method. In this technique, we approximate the proposed model with a finite dimensional problem. The method is based on the combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The Caputo fractional derivative is replaced by a difference quotient and the integral by a finite sum. By this method, the given problem is reduced to a problem for solving a system of algebraic equations, and by solving this system, we obtain the solution of SIRC model. Special attention is given to study the convergence analysis and estimate an error upper bound of the obtained approximate formula. We compare our numerical solutions with those numerical solutions using fourth-order Runge–Kutta method. The obtained numerical results show the simplicity and the efficiency of the proposed method.