  We calculate both the exponential and pre-factor contributions in a WKB
approximation of the master equation for a stochastic SIR model with highly
oscillatory dynamics. Fixing the basic parameters of the model we investigate
how the outbreak distribution changes with the population size. We show that
this distribution rapidly becomes highly non-Gaussian, acquiring large tails
indicating the presence of rare, but large outbreaks, as the population is made
smaller. The analytic results are found to be in excellent agreement with
simulations until the systems become so small that the dynamics are dominated
by fade-out of the disease.
