  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_* ~ N^{1/3} and <t> ~ ln N, respectively.
