Behavior of a Discrete Fractional Order SIR Epidemic Model
About this article
DOI:
https://doi.org/10.14419/ijet.v7i4.10.21310Keywords:
Epidemic Model, Fractional Order, Stability, Bifurcation, Discretization Process.Abstract
In this paper we investigate the dynamical behavior of a SIR epidemic model of fractional order. Disease Free Equilibrium point, Endemic Equilibrium point and basic reproductive number are obtained. Time series plots, phase portraits and bifurcation diagrams are presented for suitable parameter values. Also some numerical examples are provided to illustrate the dynamics of the system.
References
Fred Brauer (2008), Mathematical Epidemiology, Springer.
Leah Edelstein-Keshet (2005), Mathematical Model in Biology, SI-AM, Random House, New York.
K.S.Miller and B.Ross (1993), An Introduction to The Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, INC
Keith B. Oldham and Jerome Spanier (1974), The Fractional Calcu-lus Theory and Applications of Differentiation and Integration to Arbitrary Order, Dover Publications, INC, pp.1-234.
Saber Elaydi (2008), An Introduction to Difference Equations, Third Edition, Springer International Edition, First Indian Reprint, pp.1-539.
View more references (2)
Ivo Petras (2010), Fractional order Nonlinear Systems-Modeling, Analysis and Simulation, Higher Education Press, Springer Interna-tional Edition, pp. 1-218.
Sanaaa Moussa Salman (2017), On a Discretized Fractional-Order SIR Model for Influenza, Progress in Fractional Differentiation and Application, Vol.3 , No.2, 163-173.