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Epidemics on networks with preventive rewiring
Author(s) -
Ball Frank,
Britton Tom
Publication year - 2022
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.21066
Subject(s) - epidemic model , fraction (chemistry) , random graph , population , limit (mathematics) , mathematics , graph , parameter space , convergence (economics) , discontinuity (linguistics) , preferential attachment , computer science , statistical physics , combinatorics , complex network , statistics , physics , demography , mathematical analysis , chemistry , organic chemistry , sociology , economics , economic growth
A stochastic SIR (susceptible → infective → recovered) model is considered for the spread of an epidemic on a network, described initially by an Erdős–Rényi random graph, in which susceptible individuals connected to infectious neighbors 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 thresholdλ c, thus not converging to 0 as λ ↓ λ c. The discontinuity is particularly striking when rewiring is necessarily to susceptible individuals in that τ ( λ ) jumps from 0 to 1 as λ passes throughλ c.