Predicting the likely success of invasions is vitally important in ecology
and especially epidemiology. Whether an organism can successfully invade
and persist in the short term is highly dependent upon the spatial correlations
that develop in the early stages of invasion. By modelling the correlations
between individuals we are to understand the role of spatial heterogeneity
in invasion dynamics without the need for large-scale computer simulations.
Here, a natural methodology is developed for modelling the behaviour of
individuals in a fixed network. This formulation is applied to the spread
of a disease through a structured network to determine invasion thresholds
and some statistical properties of a single epidemic.