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