The Annals of Applied Statistics

Using epidemic prevalence data to jointly estimate reproduction and removal

Jan van den Broek and Hiroshi Nishiura

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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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Ann. Appl. Stat., Volume 3, Number 4 (2009), 1505-1520.

First available in Project Euclid: 1 March 2010

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Nonhomogeneous birth–death process epidemic double-binomial Burr distribution proportional rate model accelerated event-time model avian influenza


van den Broek, Jan; Nishiura, Hiroshi. Using epidemic prevalence data to jointly estimate reproduction and removal. Ann. Appl. Stat. 3 (2009), no. 4, 1505--1520. doi:10.1214/09-AOAS270.

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