| Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 2, 2014
Epidemics models on networks
|
|
|---|---|---|
| Page(s) | 153 - 160 | |
| DOI | https://doi.org/10.1051/mmnp/20149210 | |
| Published online | 24 April 2014 | |
Non-Markovian Stochastic Epidemics in Extremely Heterogeneous Populations
Warwick Mathematics Institute, University of Warwick, Coventry, CV4 7AL,
UK.
⋆
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.