Global behaviour of an SIR epidemic model with time delay

We study the stability of a delay susceptible-infective-recovered epidemic model with time delay. The model is formulated under the assumption that all individuals are susceptible, and we analyse the global stability via two methods-by Lyapunov functionals, and-in terms of the variance of the variables. The main theorem shows that the endemic equilibrium is stable. If the basic reproduction number R-o is less than unity, by LaSalle invariance principle, the disease-free equilibrium E-s is globally stable and the disease always dies out. By applying the integral averaging theory, we also investigate the stability in variance of the model. Copyright (c) 2006 John Wiley & Sons, Ltd.