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

Abstract

We consider a stochastic model of infection spread incorporating monogamous partnership dynamics. In [Ann. Appl. Probab. 26 (2016) 1297–1328], a basic reproduction number R0 is defined with the property that if R0<1 the infection dies out within O(logN) units of time, while if R0>1 the infection survives for at least eγN units of time, for some γ>0. Here, we consider the critical case R0=1 and show that the infection dies out within O(N) units of time, and moreover that this estimate is sharp.

Citation

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Eric Foxall. "Critical behaviour of the partner model." Ann. Appl. Probab. 26 (5) 2824 - 2859, October 2016. https://doi.org/10.1214/15-AAP1163

Information

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

Subjects:
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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