Math. Model. Nat. Phenom.
Volume 9, Number 2, 2014Epidemics models on networks
|Page(s)||153 - 160|
|Published online||24 April 2014|
Non-Markovian Stochastic Epidemics in Extremely Heterogeneous Populations
Warwick Mathematics Institute, University of Warwick, Coventry, CV4 7AL,
Corresponding author. E-mail: T.A.House@warwick.ac.uk
A feature often observed in epidemiological networks is significant heterogeneity in degree. A popular modelling approach to this has been to consider large populations with highly heterogeneous discrete contact rates. This paper defines an individual-level non-Markovian stochastic process that converges on standard ODE models of such populations in the appropriate asymptotic limit. A generalised Sellke construction is derived for this model, and this is then used to consider final outcomes in the case where heterogeneity follows a truncated Zipf distribution.
Mathematics Subject Classification: 92B05 / 05C82
Key words: Zipf / Sellke / SIR
© EDP Sciences, 2014
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