EVIDENCE FOR A FRACTAL STOCHASTIC PROCESS UNDERLYING MEASLES EPIDEMICS IN BRITAIN

Abstract

The variability in measles incidence during the pre-vaccination period of 1944 to 1966, as recorded from 366 communities in England and Wales, was examined for properties of fractal stochastic processes. The power spectral density, Fano factor, and Allan factor were computed from the incidence time-series, and all revealed power-law scaling. As well, the distribution histogram for the weekly incidence approximated a geometric distribution. These features constituted evidence for a fractal stochastic process with underlying geometric statistics at play in the development and resolution of measles epidemics.