Global stability of an SIS epidemic model with delays

In this paper, we consider the global dynamics of the S(E)IS model with delays denoting an incubation time. By constructing a Lyapunov functional, we prove stability of a disease‐free equilibrium E0 under a condition different from that in the recent paper. Then we claim that R0≤1 is a necessary and sufficient condition under which E0 is globally asymptotically stable. We also propose a discrete model preserving positivity and global stability of the same equilibria as the continuous model with distributed delays, by means of discrete analogs of the Lyapunov functional.