Statistical Estimation of the Reproductive Number From Case Notification Data

Abstract

The reproductive number, or reproduction number, is a valuable metric in understanding infectious disease dynamics. There is a large body of literature related to its use and estimation. In the last 15 years, there has been tremendous progress in statistically estimating this number using case notification data. These approaches are appealing because they are relevant in an ongoing outbreak (e.g., for assessing the effectiveness of interventions) and do not require substantial modeling expertise to be implemented. In this article, we describe these methods and the extensions that have been developed. We provide insight into the distinct interpretations of the estimators proposed and provide real data examples to illustrate how they are implemented. Finally, we conclude with a discussion of available software and opportunities for future development.

Keywords: infectious disease outbreaks; reproduction number; reproductive number; serial interval.

Figure 1

Estimates of the basic reproductive number derived using data cumulatively collected during the exponential growth phase of the outbreaks for the 2009 H1N1 influenza pandemic (A) and the 2003 severe acute respiratory syndrome outbreak (B). The sequential Bayes (SB) and White and Pagano maximum likelihood (ML) estimators are shown. Estimates for each day depict the estimate of obtained using data available at that point. The horizontal dotted line is positioned at the critical value of 1 for .

Figure 2

Epidemic curve data and time-varying estimated reproductive numbers () derived using an instantaneous estimator, a smoothed instantaneous estimator, and the Wallinga and Teunis (WT) estimator for the 2009 H1N1 influenza pandemic (A) and the 2003 severe acute respiratory syndrome outbreak (B). The horizontal dotted line is positioned at the critical value of 1 for . Inst, instantaneous.