Stability Analysis and Bifurcation Control For a Fractional Order SIR Epidemic Model with Delay

In this paper, a delayed fractional SIR epidemic model with incommensurate orders is considered. Firstly, the stability is investigated and the conditions of the existence for Hopf bifurcation are attained by analyzing its characteristic equation. When the delay exceeds the critical value, a Hopf bifurcation occurs, the system loses its stability. An fractional PD control method is proposed to control the bifurcation behaviors of the delayed fractional SIR epidemic model. Finally, some numerical simulations are given to illustrate the validity of theoretical analysis.