A GROWTH-FRAGMENTATION-ISOLATION PROCESS ON RANDOM RECURSIVE TREES AND CONTACT TRACING

Bansaye, Vincent, Gu, Chenlin and Yuan, Linglong ORCID: 0000-0002-7851-1631 (2023) A GROWTH-FRAGMENTATION-ISOLATION PROCESS ON RANDOM RECURSIVE TREES AND CONTACT TRACING ANNALS OF APPLIED PROBABILITY, 33 (6B). pp. 5233-5278. ISSN 1050-5164

PDF gfi.pdf - Author Accepted Manuscript Download (1MB) | Preview

Abstract

We consider a random process on recursive trees, with three types of events. Vertices give birth at a constant rate (growth), each edge may be removed independently (fragmentation of the tree) and clusters (or trees) are frozen with a rate proportional to their sizes (isolation of connected component). A phase transition occurs when the isolation is able to stop the growth-fragmentation process and cause extinction. When the process survives, the number of clusters increases exponentially and we prove that the normalised empirical measure of clusters a.s. converges to a limit law on recursive trees. We exploit the branching structure associated to the size of clusters, which is inherited from the splitting property of random recursive trees. This work is motivated by the control of epidemics and contact tracing where clusters correspond to trees of infected individuals that can be identified and isolated. We complement this work by providing results on the Malthusian exponent to describe the effect of control policies on epidemics.

Item Type:	Article
Uncontrolled Keywords:	Branching process, many-to-two formula, Kesten-Stigum theorem, nonconservative semigroup, random recursive tree, strong law of large numbers, epidemic, contact tracing
Divisions:	Faculty of Science & Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	10 Jan 2024 11:08
Last Modified:	16 Jun 2026 20:03
DOI:	10.1214/23-AAP1947
Related Websites:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3177791
Disclaimer:	The University of Liverpool is not responsible for content contained on other websites from links within repository metadata. Please contact us if you notice anything that appears incorrect or inappropriate.