Discrete fractional order SIR epidemic model and it’s stability

Abstract

This paper deals with the fractional order SIR epidemic model in discrete form describing the dynamics of disease propagation in a population. The Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE) points are computed and the stability nature at these points are discussed. Applying next generation matrix method to calculated the basic reproduction number R0. The time plots, phase portraits and bifurcation are presented for different sets of parameter values. The numerical simulations of the discrete fractional-order SIR epidemic model are performed to illustrate the stability of the epidemic model.