  We investigate the global dynamics of a renewal-type epidemic model with
variable susceptibility. We show that in this extended model there exists a
unique endemic equilibrium and prove that it is globally asymptotically stable
when $R_0 > 1$, i.e. when it exists. We also show that the infection-free
equilibrium, which exists always, is globally asymptotically stable for $R_0
\leq 1$.
