This paper is devoted to the study of
travelling wave solutions for a simple epidemic model. This model
consists in a single scalar equation with age-dependence and
spatial structure. We prove the existence of travelling waves for
a continuum of admissible wave speeds as well as some qualitative
properties, like exponential decay and monotonicity with respect
to the direction of front's propagation.
Our proofs extensively use the comparison principle that allows us
to construct suitable sub and super-solutions or to use the classical
sliding method to obtain qualitative properties of the wave front.