Travelling waves and spatial hierarchies in measles epidemics

B. T. Grenfell (), O. N. Bjørnstad and J. Kappey
Additional contact information
B. T. Grenfell: University of Cambridge
O. N. Bjørnstad: University of Cambridge
J. Kappey: University of Cambridge

Nature, 2001, vol. 414, issue 6865, 716-723

Abstract: 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.

Date: 2001
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DOI: 10.1038/414716a

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