  This article focuses, in the context of epidemic models, on rare events that
may possibly correspond to crisis situations from the perspective of Public
Health. In general, no close analytic form for their occurrence probabilities
is available and crude Monte-Carlo procedures fail. We show how recent
intensive computer simulation techniques, such as interacting branching
particle methods, can be used for estimation purposes, as well as for
generating model paths that correspond to realizations of such events.
Applications of these simulation-based methods to several epidemic models are
also considered and discussed thoroughly.
