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

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.

SARS-CoV-2 Serial Interval Variation, Montana, USA, March 1–July 31, 2020

“…This difference may occur because Ali did not assess additional epidemic waves, which complicates direct NPI comparisons (1). Park agreed with Ali, while also offering a mathematical proof for the relationship between epidemic growth rates, calculated from incidence data, and forward-looking SIs (2,9). Park showed that as growth rates increase, forward SIs lengthen, and that when incidence decreases (either over time or because of external factors) forward SIs shorten (2).…”

“…during March 1-July 31, 2020, identified a mean SI of 5.68 (95% CI 5.27-6.08) days, falling within the bounds of 16 of 24 published estimates from more urbanized settings across the globe (Table 1; Figure 1). However, an aggregate estimate derived from data spanning multiple outbreak stages may not accurately describe Montana-based transmission because changing contact patterns and environmental influences may cause variation (1,2). Temporal analyses suggest that NPIs influenced transmission patterns, as demonstrated by Montana's epidemic curve and fluctuating SI values (Figure 2).…”

Transmission dynamics and epidemiological characteristics of Delta variant infections in China

“…The time-varying forward serial intervals (13,14) and daily numbers of cases were used to estimate the daily R t by applying the statistical methods developed by Cori et al (15). The serial interval distribution and R 0 were obtained by using mean estimates of the serial interval and R t during the exponential growth phase of the Delta outbreak (14).…”

On realized serial and generation intervals given control measures: The COVID-19 pandemic case

“…In addition, we here argue that also the mean values are likely to be different, potentially increasing the estimation bias when using such an approximation. Recently, Park et al developed a theoretical framework that links the serial interval to the reproduction number [19]. Their approach considers various sampling schemes, in particular forward and backward measurements and cohort based sampling, both for individual and pair-based durations, showing that the renewal process between symptomatic cases can be used to estimate R 0 .…”

“…Non-pharmaceutical interventions such as isolation, which decrease the social interactions of diagnosed individuals, affect the realized generation time distribution of only diagnosed individuals, likely causing the aforementioned bias. Moreover, Park et al showed how the serial interval can be used to estimate the basic reproduction number [19]. However, in their analysis, they did not consider the effect of control measures on the realized serial and generation intervals.…”