Deterministic SIR (Susceptible-Infected-Recovered) epidemic models with host demography are a textbook example of a dynamical system exhibiting damped oscillations to a stable focus. Real epidemics, however, often end in *fade-out* of the pathogen: after a major epidemic, when relatively few susceptible individuals remain, stochasticity in individual transmission and recovery results in the extinction of the pathogen.

Since foundational work of M. S. Bartlett in 1960, there has been sustained interest in predicting the probability of — and time to — fade-out as a function of the transmissibility of the pathogen and the size of the host population. I will present recent work on the problem, which uses coupled deterministic and branching process approximations to obtain rigorous estimates on the fade-out probability.

This is joint work with David Earn, Jonathan Dushoff and Ben Bolker