We study an S--I type epidemic model in an age-structured population, with mortality due to the disease. A threshold quantity is found that controls the stability of the
disease-free equilibrium and guarantees the existence of an
endemic equilibrium. We obtain conditions on the age-dependence of the susceptibility to infection that imply the uniqueness of the endemic equilibrium. An example with two
endemic equilibria is shown. Finally, we analyse numerically how the stability of the endemic equilibrium is affected by the extra-mortality and by the possible periodicities induced by
the demographic age-structure.
