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

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

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


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.

Original languageEnglish (US)
Article numbere2011548118
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number2
StatePublished - Jan 12 2020

All Science Journal Classification (ASJC) codes

  • General


  • Generation interval
  • Infectious disease modeling
  • Reproduction number
  • Serial interval


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