Comparison of Numerical Methods of the SEIR Epidemic Model of Fractional Order

Zeb A., Khan M., Zaman G., Momani S., Ertürk V. S.

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, vol.69, no.1-2, pp.81-89, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 1-2
  • Publication Date: 2014
  • Doi Number: 10.5560/zna.2013-0073
  • Journal Name: ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.81-89
  • Keywords: Fractional Differential Equations, Epidemic Model, Iterative Method, Non-Standard Scheme, Differential Transform Method, PARTIAL-DIFFERENTIAL-EQUATIONS, TRANSFORM METHOD
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, we consider the SEW (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.