The outbreak threshold in homogeneous and heterogeneous populations.
(A) A schematic of pathogen emergence. This graph shows the early stages of several strains of an epidemic, where R0 = 1.25. The black line denotes the outbreak threshold (T0 = 1/Log(R0) = 4.48). Blue thin lines show cases in which the pathogen goes extinct and does not exceed the threshold; the red thick line shows an epidemic that exceeds the threshold and persists for a long period of time. Simulations were based on the Gillespie algorithm . (B) Outbreak threshold in a homogeneous (black thick line) or in a heterogeneous population, for increasing R0. The threshold was calculated following the method described by Lloyd-Smith et al.  and is shown for different values of k, the dispersion parameter of the offspring distribution, as obtained from data on previous epidemics . If the threshold lies below one, this means that around only one infected individual is needed to give a high outbreak probability.