Nugent, Andrew, Southall, Emma and Dyson, Louise (2022) Exploring the role of the potential surface in the behaviour of early warning signals. Journal of Theoretical Biology, 554 . 111269. doi:10.1016/j.jtbi.2022.111269 ISSN 0022-5193.

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Abstract

The theory of critical slowing down states that a system displays increasing relaxation times as it approaches a critical transition. These changes can be seen in statistics generated from timeseries data, which can be used as early warning signals of a transition. Such early warning signals would be of value for emerging infectious diseases or to understand when an endemic disease is close to elimination. However, in applications to a variety of epidemiological models there is frequent disagreement with the general theory of critical slowing down, with some indicators performing well on prevalence data but not when applied to incidence data. Furthermore, the alternative theory of critical speeding up predicts contradictory behaviour of early warning signals prior to some stochastic transitions. To investigate the possibility of observing critical speeding up in epidemiological models we characterise the behaviour of common early warning signals in terms of a system’s potential surface and noise around a quasi-steady state. We then describe a method to obtain these key features from timeseries data, taking as a case study a version of the SIS model, adapted to demonstrate either critical slowing down or critical speeding up. We show this method accurately reproduces the analytic potential surface and diffusion function, and that these results can be used to determine the behaviour of early warning signals and correctly identify signs of both critical slowing down and critical speeding up.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics R Medicine > RA Public aspects of medicine R Medicine > RC Internal medicine
Divisions:	Faculty of Science, Engineering and Medicine > Science > Life Sciences (2010- ) Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Emerging infectious diseases, Epidemiology -- Mathematical models, Stochastic analysis
Journal or Publication Title:	Journal of Theoretical Biology
Publisher:	Elsevier
ISSN:	0022-5193
Official Date:	7 December 2022
Dates:	Date Event 7 December 2022 Published 23 September 2022 Available 29 August 2022 Accepted 17 March 2022 Submitted
Volume:	554
Number of Pages:	8
Article Number:	111269
DOI:	10.1016/j.jtbi.2022.111269
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	27 September 2022
Date of first compliant Open Access:	28 September 2022
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID EP/S022244/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266

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