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Estimating the within-household infection rate in emerging SIR epidemics among a community of households

Ball, Frank; Shaw, Laurence


Professor of Applied Probability

Laurence Shaw


This paper is concerned with estimation of the within household infection rate λL for a susceptible → infective → recovered epidemic among a population of households, from observation of the early, exponentially growing phase of an epidemic. Specifically, it is assumed that an estimate of the exponential growth rate is available from general data on an emerging epidemic and more-detailed, household-level data are available in a sample of households. Estimates of λL obtained using the final size distribution of single-household epidemics are usually biased owing to the emerging nature of the epidemic. A new method, which accounts correctly for the emerging nature of the epidemic, is developed by exploiting the asymptotic theory of supercritical branching processes and proved to yield a strongly consistent estimator of λL as the population and sampled households both tend to infinity in an appropriate fashion. The theory is illustrated by simulations which demonstrate that the new method is feasible for finite populations and numerical studies are used to explore how changes to the parameters governing the spread of an epidemic affect the bias of estimates based on single-household final size distributions.


Ball, F., & Shaw, L. (in press). Estimating the within-household infection rate in emerging SIR epidemics among a community of households. Journal of Mathematical Biology, 71(6), doi:10.1007/s00285-015-0872-5

Journal Article Type Article
Acceptance Date Mar 9, 2015
Online Publication Date Mar 28, 2015
Deposit Date Jun 22, 2016
Journal Journal of Mathematical Biology
Print ISSN 0303-6812
Electronic ISSN 1432-1416
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 71
Issue 6
Keywords Household epidemic model, SIR epidemic, Emerging epidemic,
Parameter estimation, Branching process
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Copyright Statement Copyright information regarding this work can be found at the following address:
Additional Information The final publication is available at Springer via