Wren, L. and Best, A. (2021) How local interactions impact the dynamics of an epidemic. Bulletin of Mathematical Biology, 83 (12). 124. ISSN 0092-8240
Abstract
Susceptible–Infected–Recovered (SIR) models have long formed the basis for exploring epidemiological dynamics in a range of contexts, including infectious disease spread in human populations. Classic SIR models take a mean-field assumption, such that a susceptible individual has an equal chance of catching the disease from any infected individual in the population. In reality, spatial and social structure will drive most instances of disease transmission. Here we explore the impacts of including spatial structure in a simple SIR model. We combine an approximate mathematical model (using a pair approximation) and stochastic simulations to consider the impact of increasingly local interactions on the epidemic. Our key development is to allow not just extremes of ‘local’ (neighbour-to-neighbour) or ‘global’ (random) transmission, but all points in between. We find that even medium degrees of local interactions produce epidemics highly similar to those with entirely global interactions, and only once interactions are predominantly local do epidemics become substantially lower and later. We also show how intervention strategies to impose local interactions on a population must be introduced early if significant impacts are to be seen.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2021. Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Epidemic; SIR; Spatial structure; Pair approximation |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Nov 2021 12:59 |
Last Modified: | 15 Nov 2021 12:59 |
Status: | Published |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s11538-021-00961-w |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:180431 |
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