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A network epidemic model with preventive rewiring: comparative analysis of the initial phase

This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate ωω (and reconnect to non-infectious individuals with probability αα or else simply drop the edge if α=0α=0 ), so-called preventive rewiring. The models are denoted SIR- ωω and SEIR- ωω , and we focus attention on the early stages of an outbreak, where we derive the expressions for the basic reproduction number R0R0 and the expected degree of the infectious nodes E(DI)E(DI) using two different approximation approaches. The first approach approximates the early spread of an epidemic by a branching process, whereas the second one uses pair approximation. The expressions are compared with the corresponding empirical means obtained from stochastic simulations of SIR- ωω and SEIR- ωω epidemics on Poisson and scale-free networks. Without rewiring of exposed nodes, the two approaches predict the same epidemic threshold and the same E(DI)E(DI) for both types of epidemics, the latter being very close to the mean degree obtained from simulated epidemics over Poisson networks. Above the epidemic threshold, pairwise models overestimate the value of R0R0 computed from simulations, which turns out to be very close to the one predicted by the branching process approximation. When exposed individuals also rewire with α>0α>0 (perhaps unaware of being infected), the two approaches give different epidemic thresholds, with the branching process approximation being more in agreement with simulations.

Un erratum d’aquest article s’ha publicat a ’Bulletin of Mathematical Biology’, 2017, vol. 79, núm. 7, p. 1687-1689. DOI https://doi.org/10.1007/s11538-017-0295-0 o també està disponible al DUGiDocs a http://hdl.handle.net/10256/14329

© Bulletin of Mathematical Biology, 2016, vol. 78, núm. 12, p. 2427-2454

http://hdl.handle.net/10256/14329

Society for Mathematical Biology

Author: Britton, Tom
Juher, David
Saldaña Meca, Joan
Date: 2016 December 1
Abstract: This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate ωω (and reconnect to non-infectious individuals with probability αα or else simply drop the edge if α=0α=0 ), so-called preventive rewiring. The models are denoted SIR- ωω and SEIR- ωω , and we focus attention on the early stages of an outbreak, where we derive the expressions for the basic reproduction number R0R0 and the expected degree of the infectious nodes E(DI)E(DI) using two different approximation approaches. The first approach approximates the early spread of an epidemic by a branching process, whereas the second one uses pair approximation. The expressions are compared with the corresponding empirical means obtained from stochastic simulations of SIR- ωω and SEIR- ωω epidemics on Poisson and scale-free networks. Without rewiring of exposed nodes, the two approaches predict the same epidemic threshold and the same E(DI)E(DI) for both types of epidemics, the latter being very close to the mean degree obtained from simulated epidemics over Poisson networks. Above the epidemic threshold, pairwise models overestimate the value of R0R0 computed from simulations, which turns out to be very close to the one predicted by the branching process approximation. When exposed individuals also rewire with α>0α>0 (perhaps unaware of being infected), the two approaches give different epidemic thresholds, with the branching process approximation being more in agreement with simulations.
Un erratum d’aquest article s’ha publicat a ’Bulletin of Mathematical Biology’, 2017, vol. 79, núm. 7, p. 1687-1689. DOI https://doi.org/10.1007/s11538-017-0295-0 o també està disponible al DUGiDocs a http://hdl.handle.net/10256/14329
Format: application/pdf
Citation: https://doi.org/10.1007/s11538-016-0227-4
ISSN: 0092-8240 (versió paper)
1522-9602 (versió electrònica)
Document access: http://hdl.handle.net/10256/13174
Language: eng
Publisher: Society for Mathematical Biology
Collection: MINECO/PN 2015-2017/MTM2014-52402-C3-3-P
Versió postprint del document publicat a: https://doi.org/10.1007/s11538-016-0227-4
Articles publicats (D-IMAE)
Is part of: © Bulletin of Mathematical Biology, 2016, vol. 78, núm. 12, p. 2427-2454
See also: http://hdl.handle.net/10256/14329
Rights: Tots els drets reservats
Subject: Epidèmies -- Models matemàtics
Epidemics -- Mathematical models
Processos de ramificació
Branching processes
Processos estocàstics
Stochastic processes
Title: A network epidemic model with preventive rewiring: comparative analysis of the initial phase
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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