Epidemics on networks with preventive rewiring

Ball, Frank; Britton, Tom

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