Using epidemic prevalence data to jointly estimate reproduction and removal

TL;DR

This paper introduces a nonhomogeneous birth-death model for infectious disease dynamics that estimates the effective reproduction number over time using observed symptomatic case data, demonstrated on avian influenza.

Contribution

The study develops a novel nonhomogeneous birth-death model incorporating survival distributions to jointly estimate reproduction and removal rates from epidemic data.

Findings

Estimated R(t) declined below 1 on day 23 in the avian influenza outbreak.

Model effectively captures epidemic dynamics using only symptomatic case data.

Flexible survival distributions improve parameter estimation accuracy.

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.