Square-Root Dynamics of a SIR-Model in Fractional Order

Young Il Seo, Anwar Zeb, Gul Zaman, Il Hyo Jung

Department of Mathematics, Pusan National University, Busan, South Korea.
Department of Mathematics, University of Malakand, Chakdara, Pakistan.
National Fisheries Research and Development Institute, Busan, South Korea.

DOI: 10.4236/am.2012.312257                

Abstract

In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented and a discrete-time finite difference scheme is constructed using the nonstandard finite difference (NSFD) method. A comparative study of the classical Runge-Kutta method and ODE45 is presented in the case of integer order derivatives. The solutions obtained are presented graphically.

Keywords

Mathematical Model; Square Root Dynamics; Fractional Derivative; Non-Standard Finite Difference Scheme; Numerical Analysis

Conflicts of Interest

The authors declare no conflicts of interest.

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