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An SIR epidemic on a weighted network

Published online by Cambridge University Press:  26 December 2019

Kristoffer Spricer Open the ORCID record for Kristoffer Spricer [Opens in a new window]  and
Tom Britton
Kristoffer Spricer*
Affiliation:
Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
Tom Britton
Affiliation:
Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden
*
*Corresponding author. Email: kspricer@hotmail.com
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Abstract

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We introduce a weighted configuration model graph, where edge weights correspond to the probability of infection in an epidemic on the graph. On these graphs, we study the development of a Susceptible–Infectious–Recovered epidemic using both Reed–Frost and Markovian settings. For the special case of having two different edge types, we determine the basic reproduction numberR0, the probability of a major outbreak, and the relative final size of a major outbreak. Results are compared with those for a calibrated unweighted graph. The degree distributions are based on both theoretical constructs and empirical network data. In addition, bivariate standard normal copulas are used to model the dependence between the degrees of the two edge types, allowing for modeling the correlation between edge types over a wide range. Among the results are that the weighted graph produces much richer results than the unweighted graph. Also, while R0 always increases with increasing correlation between the two degrees, this is not necessarily true for the probability of a major outbreak nor for the relative final size of a major outbreak. When using copulas we see that these can produce results that are similar to those of the empirical degree distributions, indicating that in some cases a copula is a viable alternative to using the full empirical data.

Keywords

epidemicsbasic reproduction numberweighted graphconfiguration modelfinal sizemajor outbreakcopula
Type
Original Article
Information
Network Science , Volume 7 , Issue 4 , December 2019 , pp. 556 - 580
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Cambridge University Press 2019

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