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December 2009 Using epidemic prevalence data to jointly estimate reproduction and removal
Jan van den Broek, Hiroshi Nishiura
Ann. Appl. Stat. 3(4): 1505-1520 (December 2009). DOI: 10.1214/09-AOAS270


This study proposes a nonhomogeneous birth–death model which captures the dynamics of a directly transmitted infectious disease. Our model accounts for an important aspect of observed epidemic data in which only symptomatic infecteds are observed. The nonhomogeneous birth–death process depends on survival distributions of reproduction and removal, which jointly yield an estimate of the effective reproduction number R(t) as a function of epidemic time. We employ the Burr distribution family for the survival functions and, as special cases, proportional rate and accelerated event-time models are also employed for the parameter estimation procedure. As an example, our model is applied to an outbreak of avian influenza (H7N7) in the Netherlands, 2003, confirming that the conditional estimate of R(t) declined below unity for the first time on day 23 since the detection of the index case.


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Jan van den Broek. Hiroshi Nishiura. "Using epidemic prevalence data to jointly estimate reproduction and removal." Ann. Appl. Stat. 3 (4) 1505 - 1520, December 2009.


Published: December 2009
First available in Project Euclid: 1 March 2010

zbMATH: 1185.62192
MathSciNet: MR2752144
Digital Object Identifier: 10.1214/09-AOAS270

Keywords: accelerated event-time model , avian influenza , Burr distribution , double-binomial , Epidemic , Nonhomogeneous birth–death process , proportional rate model

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.3 • No. 4 • December 2009
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