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Non-Markovian Stochastic Epidemics in Extremely HeterogeneousPopulations

Published online by Cambridge University Press:  24 April 2014

T. House
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Abstract

A feature often observed in epidemiological networks is significant heterogeneity indegree. A popular modelling approach to this has been to consider large populations withhighly heterogeneous discrete contact rates. This paper defines an individual-levelnon-Markovian stochastic process that converges on standard ODE models of such populationsin the appropriate asymptotic limit. A generalised Sellke construction is derived for thismodel, and this is then used to consider final outcomes in the case where heterogeneityfollows a truncated Zipf distribution.

Keywords

ZipfSellkeSIR
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 2: Epidemics models on networks , 2014 , pp. 153 - 160
Copyright
© EDP Sciences, 2014

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