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Integrating stochasticity and network structure into an epidemic model

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Dangerfield, C. E., Ross, Joshua V. and Keeling, Matthew James. (2009) Integrating stochasticity and network structure into an epidemic model. Journal of The Royal Society Interface, Vol.6 (No.38). pp. 761-774. ISSN 1742-5689

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Official URL: http://dx.doi.org/10.1098/rsif.2008.0410

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics R Medicine > RA Public aspects of medicine
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Epidemics -- Mathematical models
Journal or Publication Title:	Journal of The Royal Society Interface
Publisher:	The Royal Society Publishing
ISSN:	1742-5689
Date:	6 September 2009
Volume:	Vol.6
Number:	No.38
Number of Pages:	14
Page Range:	pp. 761-774
Identification Number:	10.1098/rsif.2008.0410
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Leverhulme Trust (LT), Sixth Framework Programme (European Commission) (FP6), Wellcome Trust (London, England)
Grant number:	513715 (FP6)
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URI:	http://wrap.warwick.ac.uk/id/eprint/27558