Spatial Epidemics: Critical Behavior in One Dimension
| dc.creator | Lalley, Steven P. | |
| dc.date | 2007-01-24 | |
| dc.date | 2007-07-25 | |
| dc.date.accessioned | 2026-07-07T08:20:02Z | |
| dc.date.available | 2026-07-07T08:20:02Z | |
| dc.description | In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent p-coin tosses. Spatial variants of these models are proposed, in which finite populations of size N are situated at the sites of a lattice and infectious contacts are limited to individuals at neighboring sites. Scaling laws for these models are given when the infection parameter p is such that the epidemics are critical. It is shown that in all cases there is a critical threshold for the numbers initially infected: below the threshold, the epidemic evolves in essentially the same manner as its branching envelope, but at the threshold evolves like a branching process with a size-dependent drift. The corresponding scaling limits are super-Brownian motions and Dawson-Watanabe processes with killing, respectively. | |
| dc.identifier | https://arxiv.org/abs/math/0701698 | |
| dc.identifier | http://arxiv.org/abs/math/0701698 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134967 | |
| dc.subject | Probability | |
| dc.subject | 60H30; 60K35 | |
| dc.title | Spatial Epidemics: Critical Behavior in One Dimension | |
| dc.type | text |