Since the discovery of a power-law scaling between the mean and variance
of natural populations, this phenomenon has been observed for a variety
of species. Here, we show that the same form of power-law scaling also
occurs in measles case reports in England and Wales. Remarkably this power
law holds over four orders of magnitude. We consider how the natural experiment
of vaccination affects the slope of the power law. By examining simple
generic models, we are able to predict the effects of stochasticity and
coupling, and we propose a new phenomenon associated with the critical
community size.