Limit theorems for the spread of epidemics and forest fires
type: Item
instance of: scholarly article
title: Limit theorems for the spread of epidemics and forest fires
zbMATH Open document ID: 0667.92016
DOI: 10.1016/0304-4149(88)90083-X
published in: Stochastic Processes and their Applications
publication date: 1988-01-01T00:00:00Z
review text: In a certain two-dimensional epidemic model, each site of the square lattice may be in any of three states, 1 (healthy), i (infected), or 0 (immune). A healthy site may be infected by an infected neighbour at a certain rate, and an infected site remains infected for a random time before becoming immune. There is a critical value \(\alpha_ c\) of the infection rate \(\alpha\) which marks the onset of the regime in which an epidemic may take place from a single initial infective. This model is related to a certain dependent percolation process. A shape theorem is proved for the epidemic process: if \(\alpha >\alpha_ c\), then the set of sites infected at time t from a single initial infective is approximately tC for some convex set C. Related results are discussed for two-dimensional percolation.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4093236
zbMATH Keywords: forest fires
zbMATH Keywords: two-dimensional epidemic model
zbMATH Keywords: dependent percolation process
zbMATH Keywords: shape theorem
zbMATH Keywords: two-dimensional percolation
author: J. Theodore Cox
author: Rick Durrett
reviewed by: G. R. Grimmett
MaRDI profile type: Publication
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full work available at URL: 0304-4149(88)90083-x
OpenAlex ID: W1976683712
description: scientific article; zbMATH DE number 4093236