Exact and approximate formulas for contact tracing on random trees.
Branching process
Contact tracing
Message passing model
Network
Stochastic SIR model
Tree
Journal
Mathematical biosciences
ISSN: 1879-3134
Titre abrégé: Math Biosci
Pays: United States
ID NLM: 0103146
Informations de publication
Date de publication:
03 2020
03 2020
Historique:
received:
16
10
2019
revised:
23
01
2020
accepted:
23
01
2020
pubmed:
6
2
2020
medline:
3
11
2020
entrez:
5
2
2020
Statut:
ppublish
Résumé
We consider a stochastic susceptible-infected-recovered (SIR) model with contact tracing on random trees and on the configuration model. On a rooted tree, where initially all individuals are susceptible apart from the root which is infected, we are able to find exact formulas for the distribution of the infectious period. Thereto, we show how to extend the existing theory for contact tracing in homogeneously mixing populations to trees. Based on these formulas, we discuss the influence of randomness in the tree and the basic reproduction number. We find the well known results for the homogeneously mixing case as a limit of the present model (tree-shaped contact graph). Furthermore, we develop approximate mean field equations for the dynamics on trees, and - using the message passing method - also for the configuration model. The interpretation and implications of the results are discussed.
Identifiants
pubmed: 32014418
pii: S0025-5564(20)30015-8
doi: 10.1016/j.mbs.2020.108320
pii:
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Review
Langues
eng
Sous-ensembles de citation
IM
Pagination
108320Commentaires et corrections
Type : ErratumIn
Informations de copyright
Copyright © 2020 Elsevier Inc. All rights reserved.
Déclaration de conflit d'intérêts
Declaration of Competing Interest None.