Dynamics of fractional-order epidemic models with general nonlinear incidence rate and time-delay

In this paper, we study the dynamics of a fractional-order epidemic model with general nonlinear incidence rate functionals and time-delay. We investigate the local and global stability of the steady-states. We deduce the basic reproductive threshold parameter, so that if R₀ < 1, the disease-free steady-state is locally and globally asymptotically stable. However, for R₀ > 1, there exists a positive (endemic) steady-state which is locally and globally asymptotically stable. A Holling type III response function is considered in the numerical simulations to illustrate the effectiveness of the theoretical results.