Forward-looking serial intervals correctly link epidemic growth to reproduction numbers

David J. D. Earn,Benjamin M. Bolker,Michael Li,Bryan T. Grenfell,Kaiyuan Sun,Jonathan Dushoff,Sang Woo Park,Joshua S. Weitz,David Champredon

doi:10.1073/pnas.2011548118

Abstract

The reproduction number R and the growth rate r are critical epidemiological quantities. They are linked by generation intervals, the time between infection and onward transmission. Because generation intervals are difficult to observe, epidemiologists often substitute serial intervals, the time between symptom onset in successive links in a transmission chain. Recent studies suggest that such substitution biases estimates of R based on r. Here we explore how these intervals vary over the course of an epidemic, and the implications for R estimation. Forward-looking serial intervals, measuring time forward from symptom onset of an infector, correctly describe the renewal process of symptomatic cases and therefore reliably link R with r. In contrast, backward-looking intervals, which measure time backward, and intrinsic intervals, which neglect population-level dynamics, give incorrect R estimates. Forward-looking intervals are affected both by epidemic dynamics and by censoring, changing in complex ways over the course of an epidemic. We present a heuristic method for addressing biases that arise from neglecting changes in serial intervals. We apply the method to early (21 January to February 8, 2020) serial interval-based estimates of R for the COVID-19 outbreak in China outside Hubei province; using improperly defined serial intervals in this context biases estimates of initial R by up to a factor of 2.6. This study demonstrates the importance of early contact tracing efforts and provides a framework for reassessing generation intervals, serial intervals, and R estimates for COVID-19.

Highlights

The reproduction number R and the growth rate r are critical epidemiological quantities
We describe the forward incubation periods and the forward generation intervals using a joint probability distribution because onset of symptoms and transmission potential jointly depend on the life history of a disease; for example, if an infected individual can only transmit the disease after symptom onset, the forward generation interval will necessarily be longer than the forward incubation period
We have shown that the initial forward serial interval distribution—measured from the cohort of infectors who developed symptoms during the exponential growth phase of an epidemic—provides the correct link between the exponential growth rate r and the initial reproduction number R

Summary

Introduction

The reproduction number R and the growth rate r are critical epidemiological quantities They are linked by generation intervals, the time between infection and onward transmission. In some cases, even take negative values in the presence of presymptomatic transmission [11], whereas generation intervals must be positive These distributions were clearly and distinctly defined over a decade ago [7], the need for a better conceptual and theoretical framework for understanding their differences is becoming clearer as the COVID-19 pandemic unfolds. The growth rate r and the reproduction number R are linked by the generation interval distribution [6], where the generation interval is defined as the time between when an individual (infector) is infected and when that individual infects another person (infectee) [7]

Methods

Results

Conclusion