title: Travelling waves and spatial hierarchies in measles epidemics.
abstract: Spatio-temporal travelling waves are striking manifestations of predator-prey and host-parasite dynamics. However, few systems are well enough documented both to detect repeated waves and to explain their interaction with spatio-temporal variations in population structure and demography. Here, we demonstrate recurrent epidemic travelling waves in an exhaustive spatio-temporal data set for measles in England and Wales. We use wavelet phase analysis, which allows for dynamical non-stationarity--a complication in interpreting spatio-temporal patterns in these and many other ecological time series. In the pre-vaccination era, conspicuous hierarchical waves of infection moved 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 waves-spread via infective 'sparks' from large 'core' cities to smaller 'satellite' towns. Thus, the spatial hierarchy of host population structure is a prerequisite for these infection waves.
authors.affiliation: Zoology Department, University of Cambridge, Downing Street, Cambridge CB2 3EJ, UK. b.t.grenfell@zoo.cam.ac.uk
authors.forename: B T
authors.initials: BT
authors.lastname: Grenfell
authors.forename: O N
authors.initials: ON
authors.lastname: Bjørnstad
authors.forename: J
authors.initials: J
authors.lastname: Kappey
mesh_terms: D000465:Algorithms; D002947:Cities; D004196:Disease Outbreaks; D004739:England / Q000453:epidemiology; D004812:Epidemiologic Methods; D006801:Humans; D008457:Measles / Q000453:epidemiology*; D008954:Models, Biological; D012621:Seasons; D014505:Urban Population; D014852:Wales / Q000453:epidemiology