The effects of local spatial structure on epidemiological invasions

Predicting the likely success of invasions is vitally important in ecology and especially epidemiology. Whether an organism can successfully invade an d persist in the short-term is highly dependent on the spatial correlations that develop in the early stages of invasion. By modelling the correlation s between individuals, we are able to understand the role of spatial hetero geneity in invasion dynamics without the need for large-scale computer simu lations. Here, a natural methodology is developed for modelling the behavio ur of individuals in a fixed network. This formulation is applied to the sp read of a disease through a structured network to determine invasion thresh olds and some statistical properties of a single epidemic.