Conlan, Andrew J. K., Rohani, Pejman, Lloyd, Alun L., Keeling, Matthew James and Grenfell, Bryan T.. (2010) Resolving the impact of waiting time distributions on the persistence of measles. Journal of The Royal Society Interface, Vol.7 (No.45). pp. 623-640. ISSN 1742-5689

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Abstract

Measles epidemics in human populations exhibit what is perhaps the best empirically characterized, and certainly the most studied, stochastic persistence threshold in population biology. A critical community size (CCS) of around 250 000-500 000 separates populations where measles is predominantly persistent from smaller communities where there are frequent extinctions of measles between major epidemics. The fundamental mechanisms contributing to this pattern of persistence, which are long-lasting immunity to re-infection, recruitment of susceptibles, seasonality in transmission, age dependence of transmission and the spatial coupling between communities, have all been quantified and, to a greater or lesser level of success, captured by theoretical models. Despite these successes there has not been a consensus over whether simple models can successfully predict the value of the CCS, or indeed which mechanisms determine the persistence of measles over a broader range of population sizes. Specifically, the level of the CCS has been thought to be particularly sensitive to the detailed stochastic dynamics generated by the waiting time distribution (WTD) in the infectious and latent periods. We show that the relative patterns of persistence between models with different WTDs are highly sensitive to the criterion of comparison-in particular, the statistical measure of persistence that is employed. To this end, we introduce two new statistical measures of persitence-fade-outs post epidemic and fade-outs post invasion. Contrary to previous reports, we demonstrate that, no matter the choice of persistence measure, appropriately parametrized models of measles demonstrate similar predictions for the level of the CCS.

Item Type:	Journal Article
Subjects:	Q Science
Divisions:	Faculty of Science > Life Sciences (2010- ) > Biological Sciences ( -2010) Faculty of Science > Mathematics
Journal or Publication Title:	Journal of The Royal Society Interface
Publisher:	The Royal Society Publishing
ISSN:	1742-5689
Date:	6 April 2010
Volume:	Vol.7
Number:	No.45
Number of Pages:	18
Page Range:	pp. 623-640
Identification Number:	10.1098/rsif.2009.0284
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	DEFRA, Science & Technology Directorate, Department of Homeland Security, Fogarty International Center, National Institutes of Health
Grant number:	PU/T/WL/07/46 SE3230, R01GM83983
URI:	http://wrap.warwick.ac.uk/id/eprint/6375

Data sourced from Thomson Reuters' Web of Knowledge

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