Size of Outbreaks Near the Epidemic Threshold
Abstract
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 N2/3 with N the population size. This scaling law implies that the average outbreak size <n> scales as N1/3. Moreover, the maximal and the average duration of an outbreak grow as t* ~ N1/3 and <t> ~ ln N, respectively.
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