  We investigate the global behaviour of a SIRI epidemic model with distributed
delay and relapse. From the theory of functional differential equations with
delay, we prove that the solution of the system is unique, bounded, and
positive, for all time. The basic reproduction number $R_{0}$ for the model is
computed. By means of the direct Lyapunov method and LaSalle invariance
principle, we prove that the disease free equilibrium is globally
asymptotically stable when $R_{0} < 1$. Moreover, we show that there is a
unique endemic equilibrium, which is globally asymptotically stable, when
$R_{0} > 1$.
