Size of outbreaks near the epidemic threshold.

The spread of infectious diseases near the epidemic threshold is investigated. Scaling laws for the size and the duration of outbreaks originating from a single infected individual in a large susceptible population are obtained. The maximal size of an outbreak n(*) scales as N(2/3) with N the population size. This scaling law implies that the average outbreak size [n]scales as N(1/3). Moreover, the maximal and the average duration of an outbreak grow as t(*) approximately N(1/3) and [t] approximately ln N, respectively.