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Type: Journal article
Title: Integrating stochasticity and network structure into an epidemic model
Author: Dangerfield, C.
Ross, J.
Citation: Journal of the Royal Society Interface, 2009; 6(38):761-774
Publisher: The Royal Society Publishing
Issue Date: 2009
ISSN: 1742-5689
Statement of
C.E Dangerfield, J.V Ross and M.J Keeling
Abstract: While the foundations of modern epidemiology are based upon deterministic models with homogeneous mixing, it is being increasingly realized that both spatial structure and stochasticity play major roles in shaping epidemic dynamics. The integration of these two confounding elements is generally ascertained through numerical simulation. Here, for the first time, we develop a more rigorous analytical understanding based on pairwise approximations to incorporate localized spatial structure and diffusion approximations to capture the impact of stochasticity. Our results allow us to quantify, analytically, the impact of network structure on the variability of an epidemic. Using the susceptible–infectious–susceptible framework for the infection dynamics, the pairwise stochastic model is compared with the stochastic homogeneous-mixing (mean-field) model—although to enable a fair comparison the homogeneous-mixing parameters are scaled to give agreement with the pairwise dynamics. At equilibrium, we show that the pairwise model always displays greater variation about the mean, although the differences are generally small unless the prevalence of infection is low. By contrast, during the early epidemic growth phase when the level of infection is increasing exponentially, the pairwise model generally shows less variation.
Keywords: noise
pair wise moment closure diffusion approximation
Rights: Copyright © The Royal Society 2011
DOI: 10.1098/rsif.2008.0410
Appears in Collections:Aurora harvest 2
Mathematical Sciences publications

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