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R. E. Mickens, R. Buckmire and K. McMurtry, “Numerical Studies of a Nonlinear Heat Equation with Square Root Reaction Term,” Numerical Methods for Partial Differential Equations, Vol. 25, No. 3, 2009, pp. 598-609. doi:10.1002/num.20361

has been cited by the following article:

• 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.