## The Annals of Applied Statistics

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

### Using epidemic prevalence data to jointly estimate reproduction and removal

Jan van den Broek and Hiroshi Nishiura

#### Abstract

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.

#### Article information

**Source**

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

**Dates**

First available: 1 March 2010

**Permanent link to this document**

http://projecteuclid.org/euclid.aoas/1267453950

**Digital Object Identifier**

doi:10.1214/09-AOAS270

**Zentralblatt MATH identifier**

05696888

**Mathematical Reviews number (MathSciNet)**

MR2752144

#### Citation

van den Broek, Jan; Nishiura, Hiroshi. Using epidemic prevalence data to jointly estimate reproduction and removal. The Annals of Applied Statistics 3 (2009), no. 4, 1505--1520. doi:10.1214/09-AOAS270. http://projecteuclid.org/euclid.aoas/1267453950.