Travelling waves and spatial hierarchies in measles epidemics

Spatio-temporal travelling waves are striking manifestations of predator-pr ey and host-parasite dynamics. However, few systems are well enough documen ted both to detect repeated waves and to explain their interaction with spa tio-temporal variations in population structure and demography. Here, we de monstrate recurrent epidemic travelling waves in an exhaustive spatio-tempo ral data set for measles in England and Wales. We use wavelet phase analysi s, which allows for dynamical nonstationarity-a complication in interpretin g spatio-temporal patterns in these and many other ecological time series. In the prevaccination era, conspicuous hierarchical waves of infection move d regionally from large cities to small towns; the introduction of measles vaccination restricted but did not eliminate this hierarchical contagion. A mechanistic stochastic model suggests a dynamical explanation for the wave s-spread via infective 'sparks' from large 'core' cities to smaller 'satell ite' towns. Thus, the spatial hierarchy of host population structure is a p rerequisite for these infection waves.