A basic issue in ecology is the relation between extinction and population size. One of the clearest manifestations of a population threshold for extinction is the critical community size below which infections like measles do not persist. The current generation of stochastic models overestimates the observed critical community size for measles, generating much less persistence of infection than is observed. The inclusion of a more biologically realistic model for the duration of infection produced a much closer fit to the actual critical community size and explains previously undescribed high-frequency oscillations in measles incidence.