FRANK BALL frank.ball@nottingham.ac.uk
Professor of Applied Probability
Epidemics on networks with preventive rewiring
Ball, Frank; Britton, Tom
Authors
Tom Britton
Abstract
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.
Citation
Ball, F., & Britton, T. (2022). Epidemics on networks with preventive rewiring. Random Structures and Algorithms, 61(2), 250-297. https://doi.org/10.1002/rsa.21066
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 |
DOI | https://doi.org/10.1002/rsa.21066 |
Keywords | Applied Mathematics; Computer Graphics and Computer-Aided Design; General Mathematics; Software |
Public URL | https://nottingham-repository.worktribe.com/output/6396623 |
Publisher URL | https://onlinelibrary.wiley.com/doi/full/10.1002/rsa.21066 |
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Epidemics on networks
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Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
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