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Spatial spread for ecological and epidemiological models

A wide variety of phenomena of geographical spread can be described in terms of a mechanism of growth (e.g. birth, infection) and a spatial 'contact distribution' which describes how the locations of the individual(s) involved in a migratory move, or infection at a distance, are spatially related. The basic models for such phenomena are naturally discrete and stochastic. Such models have however only recently begun to be studied; earlier workers believed, perhaps wrongly, that continuous deterministic models would prove much more tractable. Recent work, both on deterministic and on discrete stochastic models, has in part confirmed results based on a deterministic diffusion approximation, but has also exposed their limitations. Research of this sort is not intended to be immediately applicable, but will, it is hoped, offer food for thought to those who have to deal with the spread of species, and of diseases such as rabies, foot-and-mouth and Dutch elm disease.