  This paper is a survey paper on stochastic epidemic models. A simple
stochastic epidemic model is defined and exact and asymptotic model properties
(relying on a large community) are presented. The purpose of modelling is
illustrated by studying effects of vaccination and also in terms of inference
procedures for important parameters, such as the basic reproduction number and
the critical vaccination coverage. Several generalizations towards realism,
e.g. multitype and household epidemic models, are also presented, as is a model
for endemic diseases.
