AM  Vol.3 No.12 , December 2012
Square-Root Dynamics of a SIR-Model in Fractional Order
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.
Cite this paper: Y. Seo, A. Zeb, G. Zaman and I. Jung, "Square-Root Dynamics of a SIR-Model in Fractional Order," Applied Mathematics, Vol. 3 No. 12, 2012, pp. 1882-1887. doi: 10.4236/am.2012.312257.

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