The Epidemic Threshold Concept

<div><p>(A) Expected infection attack rates during measles outbreaks in an idealised homogeneously mixing population.</p> <p>(B) Expected infection attack rates during measles outbreaks in a population protected by solid herd immunity.</p> <p>(C) Expected infection attack rates during measles outbreaks in a heterogeneous population consisting of a small community embedded in a larger population. The expectations are calculated for a stochastic “susceptible–exposed–infectious–recovered” (SEIR) model, with measles basic reproduction number <i>R</i>₀ = 17 [<a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020316#pmed-0020316-b02" target="_blank">2</a>], and ten imported measles cases per year. The population structure is as reported for the Netherlands, where a small community of 300 000 persons with a variable fraction of susceptible individuals exists in a larger population of 15 million persons with a fraction of susceptible individuals of 0.043 [<a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020316#pmed-0020316-b21" target="_blank">21</a>].</p> <p>Dark blue markers correspond to major outbreaks; light blue markers correspond to minor outbreaks. The solid gray line indicates the approximation, near the threshold, of the infection attack rate: two infections occur per susceptible individual in excess of the threshold.</p>