Arizona State University

It is known from simulations that stochastic epidemic models such as SIR, SIRS produce sustained oscillations, whereas the corresponding deterministic models produce damped oscillations. We use multiscale analysis to identify a parameter range in which stochastic SIR is approximated by a stochastic combination of sinusoids, where the coefficient processes run on a slow time scale. Ornstein-Uhlenbeck excursions form an envelope of the epidemic oscillations.