Typical SIR epidemics on the five network types shown in . These are from left to right: random, lattice, small world (top row), spatial and scale-free (bottom row). Each graph shows 100 epidemic curves (grey) together with the average for all major epidemics (black) for a single example of each network type; therefore, all variability within each graph is a result of the stochastic nature of transmission and not variation in the network. All five networks contain 10000 individuals, although all individuals are not necessarily interconnected as part of a giant component. For the spatial and scale-free networks, approximately 88 and 74% are part of the giant component and can therefore potentially become infected. For these networks, the proportion of infectious individuals has been rescaled as a fraction of the giant component. In all networks, the average number of contacts per individual is approximately 4, although for the scale-free network, there is considerable heterogeneity with one individual having 85 contacts. For consistency, the small-world network is formed from a two-dimensional lattice (not a one-dimensional circle as shown in ) with 10 additional random ‘long-range’ contacts. The dashed lines show the effect on the mean epidemic of increasing the number of long-range contacts to 20 and 100. (*τ*=1, *g*=0.5, *b*=*d*=0).

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