The Annals of Applied Probability

Critical behaviour of the partner model

Eric Foxall

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

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1476884305

Digital Object Identifier
doi:10.1214/15-AAP1163

Mathematical Reviews number (MathSciNet)
MR3563195

Zentralblatt MATH identifier
1353.60086

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

Keywords
SIS model contact process interacting particle systems

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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References

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