Critical Scaling for the Simple SIS Stochastic Epidemic
Probability
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0512252,
title = {Critical Scaling for the Simple SIS Stochastic Epidemic},
author = {R. G. Dolgoarshinnykh Steven P. Lalley},
journal= {arXiv preprint arXiv:math/0512252},
year = {2007}
}