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Z. Naturforsch. 69a, 81 – 89
(2014)
doi:10.5560/ZNA.2013-0073
Comparison of Numerical Methods of the SEIR Epidemic Model of Fractional Order
1 Department of Mathematics, COMSATS Institute of Information Technology Abbottabad Campus, Pakistan
2 Department of Mathematics, University of Malakand, Chakdara Dir (Lower) Khyber Pakhtunkhawa, Pakistan
3 The University of Jordan, Faculty of Science, Department of Mathermatics, Amman 1194, Jordan
4 Department of Mathematics, Faculty of Arts and Sciences, Ondokuz May?s University, 55139, Samsun, Turkey
Received January 4, 2013 / revised September 26, 2013 / published online December 18, 2013
Reprint requests to: M. K.; E-mail:
madadmath@yahoo.com
In this paper, we consider the SEIR (Susceptible-Exposed-Infected-Recovered) epidemic model by taking into account both standard and bilinear incidence rates of fractional order. First, the non-negative solution of the SEIR model of fractional order is presented. Then, the multi-step generalized differential transform method (MSGDTM) is employed to compute an approximation to the solution of the model of fractional order. Finally, the obtained results are compared with those obtained by the fourth-order Runge-Kutta method and non-standard finite difference (NSFD) method in the integer case.
Key words: Fractional Differential Equations; Epidemic Model; Iterative Method; Non-Standard Scheme; Differential Transform Method.