Local stability of a fractional order sis epidemic model with specific nonlinear incidence rate and time delay

In this paper, we study the stability of a fractional order SIS epidemic model with specific functional response and time delay, where the fractional derivative is defined in the Caputo sense. Using the theory of stability of differential equations of delayed fractional order systems, we prove that the disease-free equilibrium is locally asymptotically stable when the basic reproduction number R0 < 1. Also, we show that if R0 > 1, the endemic equilibrium is locally asymptotically stable. Numerical simulations are presented to illustrate the theoretical results of this work.