  We investigate the global dynamics of a general Kermack-McKendrick-type
epidemic model formulated in terms of a system of renewal equations.
Specifically, we consider a renewal model for which both the force of infection
and the infected removal rates are arbitrary functions of the infection age,
$\tau$, and use the direct Lyapunov method to establish the global asymptotic
stability of the equilibrium solutions. In particular, we show that the basic
reproduction number, $R_0$, represents a sharp threshold parameter such that
for $R_0\leq 1$, the infection-free equilibrium is globally asymptotically
stable; whereas the endemic equilibrium becomes globally asymptotically stable
when $R_0 > 1$, i.e. when it exists.
