  We study the classic Susceptible-Infected-Recovered (SIR) model for the
spread of an infectious disease. In this stochastic process, there are two
competing mechanism: infection and recovery. Susceptible individuals may
contract the disease from infected individuals, while infected ones recover
from the disease at a constant rate and are never infected again. Our focus is
the behavior at the epidemic threshold where the rates of the infection and
recovery processes balance. In the infinite population limit, we establish
analytically scaling rules for the time-dependent distribution functions that
characterize the sizes of the infected and the recovered sub-populations. Using
heuristic arguments, we also obtain scaling laws for the size and duration of
the epidemic outbreaks as a function of the total population. We perform
numerical simulations to verify the scaling predictions and discuss the
consequences of these scaling laws for near-threshold epidemic outbreaks.
