This book uses rigorous analytic methods to determine the behaviour of spatial, deterministic models of certain multi-type epidemic processes where infection is spread by means of contact distributions. Results obtained include the existence of travelling wave solutions, the asymptotic speed of propagation and the spatial final size. The relationship with contact branching processes is also explored.

A model has been formulated in to describe the spatial spread of an epidemic involving n types of individuals, when triggered by the introduction of infectives from outside. Wave solutions for such a model have been investigated in and have been shown only to exist at certain speeds. This paper establishes that the asymptotic speed of propagation, as defined in Aronson and Weinberger, of such an epidemic is in fact c0, the minimum speed at which wave solutions exist. This extends the known result for the one-type and host-vector epidemics.

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