Analysis of a Discrete-Time Fractional Order SIR Epidemic Model for Childhood Diseases

Abstract

In this paper, a discrete-time fractional order SIR epidemic model for a childhood disease with constant vaccination program is investigated. The local asymptotic stability and bifurcation of the equilibrium points are analyzed using basic reproduction number. Flip and Neimark-Sacker (N-S) bifurcations are investigated for endemic equilibrium point and numerical simulations are carried out to illustrate the dynamical behaviors of the model. Chaos phenomenon is observed through numerical simulation inside the flip and N-S bifurcation regions. Results of the numerical simulations support the theoretical analysis.