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Square-Root Dynamics of a SIR-Model in Fractional Order
National Fisheries Research and Development Institute, Busan, South Korea
Department of Mathematics, University of Malakand, Chakdara, Pakistan
Department of Mathematics, University of Malakand, Chakdara, Pakistan
Department of Mathematics, Pusan National University, Busan, South Korea
- 1 National Fisheries Research and Development Institute, Busan, South Korea
- 2 Department of Mathematics, University of Malakand, Chakdara, Pakistan
- 3 Department of Mathematics, University of Malakand, Chakdara, Pakistan
- 4 Department of Mathematics, Pusan National University, Busan, South Korea
Applied Mathematics·Volume 03 (2012)·Pages 1882–1887·Published 12 December 2012·DOI10.4236/am.2012.312257
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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.
KeywordsMathematical ModelSquare Root DynamicsFractional DerivativeNon-Standard Finite Difference SchemeNumerical Analysis
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