Exact and approximate formulas for contact tracing on random trees

Abstract

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. 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.

24 pages, 9 figures

References in corpus (9)

• Random graphs with arbitrary degree distributions and their applications
• A message passing approach for general epidemic models
• Edge-Based Compartmental Modeling for Infectious Disease Spread Part I: An Overview
• Random graphs as models of networks
• Pairwise-like models for non-Markovian epidemics on networks
• Exact equations for SIR epidemics on tree graphs
• Message passing and moment closure for susceptible-infected-recovered epidemics on finite networks
• Stochastic epidemic models featuring contact tracing with delays
• The effect of delay on contact tracing

Cited by in corpus (4)

• Automated Contact Tracing: a game of big numbers in the time of COVID-19
• Digital Herd Immunity and COVID-19
• Parameter estimation for contact tracing in graph-based models
• Epidemics with asymptomatic transmission: Sub-critical phase from recursive contact tracing