TITLE:
Square-Root Dynamics of a SIR-Model in Fractional Order
AUTHORS:
Young Il Seo, Anwar Zeb, Gul Zaman, Il Hyo Jung
KEYWORDS:
Mathematical Model; Square Root Dynamics; Fractional Derivative; Non-Standard Finite Difference Scheme; Numerical Analysis
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.12,
December
14,
2012
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.