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Rigorous lower bounds for the critical infection rate in the diffusive contact process

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Aidan Sudbury
Aidan Sudbury*
Affiliation:
Monash University
*
∗ Postal address: School of Mathematical Sciences, Monash University, PO Box 28M, VIC 3800, Australia. Email address: [email protected]
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Abstract

The contact process is an interacting particle system which models a spatially restricted infection. In the basic contact process the infection can only spread to an uninfected neighbour, but the diffusive contact process allows an infected individual to move to an uninfected site. If the infection rate is too low, the process will die out. If the individual can move (or diffuse), the disease can spread with a lower infection rate. An idea of the relationship between these rates is obtained by obtaining rigorous lower bounds for the critical infection rate for various values of the diffusion rate. In this paper we also improve the lower bound for the critical infection rate for the basic contact process from 1.539 to 1.5517.

Keywords

Infinite particle systemcontact processdiffusive contact process

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 1074 - 1078
Copyright
Copyright © by the Applied Probability Trust 2001 

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