In this talk, we will describe a mechanism that generates oscillations
in simple stochastic models of epidemic dynamics. We will show that,
first, intrinsic (demographic) stochasticity can generate large
coherent fluctuations which behave as sustained oscillations and that,
second, the power spectrum of these fluctuations can be calculated
analytically using the system size expansion. The application of this
analysis to the problem of the modeling of recurrent epidemics shows
that, in systems whose sizes represent real populations, the role of
stochastic effects becomes fundamental for the interpretation of
historical data.