Epidemic threshold in pairwise models for clustered networks: closures and fast correlations

Barnard, Rosanna C, Berthouze, Luc, Simon, Péter and Kiss, István (2019) Epidemic threshold in pairwise models for clustered networks: closures and fast correlations. Journal of Mathematical Biology. ISSN 0303-6812 (Accepted)

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Abstract

The 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.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Informatics
School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Mathematics Applied to Biology Research Group
Subjects: Q Science
Q Science > QA Mathematics
Depositing User: Alice Jackson
Date Deposited: 03 May 2019 11:44
Last Modified: 06 Jun 2019 13:37
URI: http://sro.sussex.ac.uk/id/eprint/83502

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