Abstract: Considering Logistic growth and saturated infection rate, we established a class of fractional-order time delay epidemic models with different orders. Firstly, by using Jacobi matrix and eigenvalue trajectory method, we analyzed the local stability of the model and gave the basic reproduction number. Secondly, we selected the bifurcation parameter as the time delay, and gave the sufficient condition for the occurrence of Hopf bifurcation at the endemic equilibrium point. Finally, the correctness of theoretical analysis was verified by numerical simulations. The research results show that the change of fractional-order may affect the stability of the system.

Key words: different orders, fractional-order, time delay, SIR model, Hopf bifurcation, equilibrium point, stability