Skip to main content

Research Repository

Advanced Search

Epidemics on networks with preventive rewiring

Ball, Frank; Britton, Tom

Epidemics on networks with preventive rewiring Thumbnail


Professor of Applied Probability

Tom Britton


A stochastic SIR (susceptible → infective → recovered) model is considered for the spread of an epidemic on a network, described initially by an Erd˝os-R´enyi random graph, in which susceptible individuals connected to infectious neighbours may drop or rewire such connections. A novel construction of the model is used to derive a deterministic model for epidemics started with a positive fraction initially infected and prove convergence of the scaled stochastic model to that deterministic model as the population size n → ∞. For epidemics initiated by a single infective that take off, we prove that for part of the parameter space, in the limit as n → ∞, the final fraction infected τ (λ) is discontinuous in the infection rate λ at its threshold λc, thus not converging to 0 as λ ↓ λc. The discontinuity is particularly striking when rewiring is necessarily to susceptible individuals in that τ (λ) jumps from 0 to 1 as λ passes through λc.


Ball, F., & Britton, T. (2022). Epidemics on networks with preventive rewiring. Random Structures and Algorithms, 61(2), 250-297.

Journal Article Type Article
Acceptance Date Aug 23, 2021
Online Publication Date Dec 7, 2021
Publication Date 2022-09
Deposit Date Oct 8, 2021
Publicly Available Date Dec 8, 2022
Journal Random Structures and Algorithms
Print ISSN 1042-9832
Electronic ISSN 1098-2418
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 61
Issue 2
Pages 250-297
Keywords Applied Mathematics; Computer Graphics and Computer-Aided Design; General Mathematics; Software
Public URL
Publisher URL


You might also like

Downloadable Citations