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Spatial epidemics with large finite range

Part of: Special processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Mathew D. Penrose
Mathew D. Penrose*
Affiliation:
University of Durham
*
∗ Postal address: Department of Mathematical Sciences, University of Durham, South Road, Durham, DH1 3LE, UK.
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Abstract

In the epidemic with removal with range r, each site z, once infected, remains so for a period of time Tz , the variables Tz being i.i.d. with mean μ. While infected, a site infects its healthy r-neighbours independently at total rate α. After infection, sites become immune. We show that the critical rate of infection αc (r), above which an epidemic starting from a single site may continue forever, converges to μ–1 as r →∞.

Keywords

EPIDEMICSFOREST FIRESPERCOLATIONMEAN-FIELD LIMIT

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K40: Other physical applications of random processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 933 - 939
Copyright
Copyright © Applied Probability Trust 1996 

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