The outbreak threshold in homogeneous and heterogeneous populations.

<p>(<b>A</b>) A schematic of pathogen emergence. This graph shows the early stages of several strains of an epidemic, where <i>R₀</i> = 1.25. The black line denotes the outbreak threshold (<i>T</i>₀ = 1/Log(<i>R₀</i>) = 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 <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003277#ppat.1003277-Gillespie1" target="_blank">[22]</a>. (<b>B</b>) Outbreak threshold in a homogeneous (black thick line) or in a heterogeneous population, for increasing <i>R₀</i>. The threshold was calculated following the method described by Lloyd-Smith et al. <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003277#ppat.1003277-LloydSmith1" target="_blank">[11]</a> and is shown for different values of <i>k</i>, the dispersion parameter of the offspring distribution, as obtained from data on previous epidemics <a href="http://www.plospathogens.org/article/info:doi/10.1371/journal.ppat.1003277#ppat.1003277-LloydSmith1" target="_blank">[11]</a>. If the threshold lies below one, this means that around only one infected individual is needed to give a high outbreak probability.