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

Generation intervals and serial intervals are critical quantities for characterizing outbreak dynamics. Generation intervals characterize the time between infection and transmission, while serial intervals characterize the time between the onset of symptoms in a chain of transmission. They are often used interchangeably, leading to misunderstanding of how these intervals link the epidemic growth rate r and the reproduction number[R] . Generation intervals provide a mechanistic link between r and[R] but are harder to measure via contact tracing. While serial intervals are easier to measure from contact tracing, recent studies suggest that the two intervals give different estimates of[R] from r. We present a general framework for characterizing epidemiological delays based on cohorts (i.e., a group of individuals that share the same event time, such as symptom onset) and show that forward-looking serial intervals, which correctly link[R] with r, are not the same as "intrinsic" serial intervals, but instead change with r. We provide a heuristic method for addressing potential biases that can arise from not accounting for changes in serial intervals across cohorts and apply the method to estimating[R] for the COVID-19 outbreak in China using serial-interval data -- our analysis shows that using incorrectly defined serial intervals can severely bias estimates. This study demonstrates the importance of early epidemiological investigation through contact tracing and provides a rationale for reassessing generation intervals, serial intervals, and[R] estimates, for COVID-19. Significance StatementThe generation- and serial-interval distributions are key, but different, quantities in outbreak analyses. Recent theoretical studies suggest that two distributions give different estimates of the reproduction number[R] from the exponential growth rate r; however, both intervals, by definition, describe disease transmission at the individual level. Here, we show that the serial-interval distribution, defined from the correct reference time and cohort, gives the same estimate of[R] as the generation-interval distribution. We then apply our framework to serial-interval data from the COVID-19 outbreak in China. While our study supports the use of serial-interval distributions in estimating[R] , it also reveals necessary changes to the current understanding and applications of serial-interval distribution.