Critical Scaling for the Simple SIS Stochastic Epidemic

Details Critical Scaling for the Simple SIS Stochastic Epidemic Critical Scaling for the Simple SIS Stochastic Epidemic

2005-12-12

arxiv.org/abs/math/0512252v1

Mathematics

Probability

Scientific paper

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.

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