Annals of Applied Probability

Critical behaviour of the partner model

Eric Foxall

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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.

Article information

Ann. Appl. Probab., Volume 26, Number 5 (2016), 2824-2859.

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

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Zentralblatt MATH identifier

Primary: 60J25: Continuous-time Markov processes on general state spaces 92B99: None of the above, but in this section

SIS model contact process interacting particle systems


Foxall, Eric. Critical behaviour of the partner model. Ann. Appl. Probab. 26 (2016), no. 5, 2824--2859. doi:10.1214/15-AAP1163.

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