Critical scaling for the SIS stochastic epidemic
- 1 September 2006
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 43 (3) , 892-898
- https://doi.org/10.1239/jap/1158784956
Abstract
We exhibit a scaling law for the criticalSISstochastic epidemic. If at time 0 the population consists ofinfected andsusceptible individuals, then when the time and the number currently infected are both scaled by, the resulting process converges, asN→ ∞, 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 analogs for the SIS epidemic of results of Martin-Löf (1998) and Aldous (1997) for the simple SIR epidemic.Keywords
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