  We exhibit a scaling law for the critical SIS stochastic epidemic: If at time
0 the population consists of square root N infected and N - square root N
susceptible individuals, then when time and number currently infected are both
scaled by square root N, the resulting process converges, for large N, to a
diffusion process related to the Feller diffusion by a change of drift. As a
consequence, the rescaled size of the epidemic has a limit law that coincides
with that of a first-passage time for the standard Ornstein- Uhlenbeck process.
These results are the analogues for the SIS epidemic of results of Martin-Lof
for the simple SIR epidemic.
