Barnard2019_Article_EpidemicThresholdInPairwiseMod.pdf (919.72 kB)
Epidemic threshold in pairwise models for clustered networks: closures and fast correlations
Version 2 2023-06-12, 09:05
Version 1 2023-06-09, 17:42
journal contribution
posted on 2023-06-12, 09:05 authored by Rosanna Barnard, Luc BerthouzeLuc Berthouze, Péter Simon, Istvan KissThe epidemic threshold is probably the most studied quantity in the modelling of epidemics on networks. For a large class of networks and dynamics, it is well studied and understood. However, it is less so for clustered networks where theoretical results are mostly limited to idealised networks. In this paper we focus on a class of models known as pairwise models where, to our knowledge, no analytical result for the epidemic threshold exists. We show that by exploiting the presence of fast variables and using some standard techniques from perturbation theory we are able to obtain the epidemic threshold analytically. We validate this new threshold by comparing it to the threshold based on the numerical solution of the full system. The agreement is found to be excellent over a wide range of values of the clustering coefficient, transmission rate and average degree of the network. Interestingly, we find that the analytical form of the threshold depends on the choice of closure, highlighting the importance of model selection when dealing with real-world epidemics. Nevertheless, we expect that our method will extend to other systems in which fast variables are present.
Funding
EPSRC; EP/M506667/1
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- Published
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- Published version
Journal
Journal of Mathematical BiologyISSN
0303-6812Publisher
SpringerExternal DOI
Department affiliated with
- Informatics Publications
Research groups affiliated with
- Mathematics Applied to Biology Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2019-05-03First Open Access (FOA) Date
2019-06-06First Compliant Deposit (FCD) Date
2019-05-02Usage metrics
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