Open Access
October 2016 Critical behaviour of the partner model
Eric Foxall
Ann. Appl. Probab. 26(5): 2824-2859 (October 2016). DOI: 10.1214/15-AAP1163


We consider a stochastic model of infection spread incorporating monogamous partnership dynamics. In [Ann. Appl. Probab. 26 (2016) 1297–1328], a basic reproduction number $R_{0}$ is defined with the property that if $R_{0}<1$ the infection dies out within $O(\log N)$ units of time, while if $R_{0}>1$ the infection survives for at least $e^{\gamma N}$ units of time, for some $\gamma>0$. Here, we consider the critical case $R_{0}=1$ and show that the infection dies out within $O(\sqrt{N})$ units of time, and moreover that this estimate is sharp.


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Eric Foxall. "Critical behaviour of the partner model." Ann. Appl. Probab. 26 (5) 2824 - 2859, October 2016.


Received: 1 August 2015; Revised: 1 October 2015; Published: October 2016
First available in Project Euclid: 19 October 2016

zbMATH: 1353.60086
MathSciNet: MR3563195
Digital Object Identifier: 10.1214/15-AAP1163

Primary: 60J25 , 92B99

Keywords: contact process , interacting particle systems , SIS model

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.26 • No. 5 • October 2016
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