DYNAMICS OF FRACTIONAL-ORDER EPIDEMIC MODELS WITH GENERAL NONLINEAR INCIDENCE RATE AND TIME-DELAY

Abstract

Abstract: 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. Keywords: epidemic model; fractional calculus; global stability; lyapunov functionals; time-delay