Y. Xia, O. N.Bjørnstad and B. T. Grenfell: Measles metapopulation dynamics: a gravity model for pre-vaccination epidemiological coupling and dynamics.

American Naturalist (2004) 164: 267-281

Abstract. Infectious diseases provide a particularly clear illustration of the spatio-temporal underpinnings of consumer-resource dynamics. The paradigm is provided by extremely contagious, acute, immunizing childhood infections. Partially synchronized, unstable oscillations are punctuated by local extinctions. This, in turn, can result in spatial differentiation in the timing of epidemics, and -- depending on the nature of spatial contagion -- may result in travelling waves. Measles are one of a few systems documented well enough to reveal all of these properties and how they are affected by spatio-temporal variations in population structure and demography. Based on a gravity coupling model and a time series susceptible-infected-recovered (TSIR) model for local dynamics, we propose a metapopulation model for regional measles dynamics. The model can capture all the major spatio-temporal properties in pre-vaccination epidemics of measles in England and Wales.

Key words: Gravity models, Measles, SIR model, Phase difference, TSIR model, Wavelet.