The analysis of the GC growth and component distribution was performed on networks generated using gZ2.5 and kR1. For KZ100, the average number of connections per node is hkiz1.7. For random networks, the percolation transition occurs at hkiZ1, above which the network will support large epidemics, i.e. epidemics that scale with total population size (e.g. Moore & Newman 2000; Kao et al. 2006) . Thus, hkiz1.7 supports only a narrow range of epidemiological parameters over which large epidemics can occur. To circumvent this problem, the networks used below were generated using the same parameter values, but only nodes with kR3 were accepted during the network generation process , resulting in networks with hkiz6.