## The Annals of Applied Probability

### Critical behaviour of the partner model

Eric Foxall

#### 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 $R_{0}$ 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

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

Dates
Revised: October 2015
First available in Project Euclid: 19 October 2016

https://projecteuclid.org/euclid.aoap/1476884305

Digital Object Identifier
doi:10.1214/15-AAP1163

Mathematical Reviews number (MathSciNet)
MR3563195

Zentralblatt MATH identifier
1353.60086

#### Citation

Foxall, Eric. Critical behaviour of the partner model. Ann. Appl. Probab. 26 (2016), no. 5, 2824--2859. doi:10.1214/15-AAP1163. https://projecteuclid.org/euclid.aoap/1476884305

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