Estimating effective reproduction number using generation time versus serial interval, with application to covid-19 in the Greater Toronto Area, Canada

BACKGROUND. The effective reproductive number Re(t) is a critical measure of epidemic potential. Re(t) can be calculated in near real time using an incidence time series and the generation time distribution---the time between infection events in an infector-infectee pair. In calculating Re(t), the generation time distribution is often approximated by the serial interval distribution---the time between symptom onset in an infector-infectee pair. However, while generation time must be positive by definition, serial interval can be negative if transmission can occur before symptoms, such as in COVID-19, rendering such an approximation improper in some contexts. METHODS. We developed a method to infer the generation time distribution from parametric definitions of the serial interval and incubation period distributions. We then compared estimates of Re(t) for COVID-19 in the Greater Toronto Area of Canada using: negative-permitting versus non-negative serial interval distributions, versus the inferred generation time distribution. RESULTS. We estimated the generation time of COVID-19 to be Gamma-distributed with mean 3.99 and standard deviation 2.96 days. Relative to the generation time distribution, non-negative serial interval distribution caused overestimation of Re(t) due to larger mean, while negative-permitting serial interval distribution caused underestimation of Re(t) due to larger variance. IMPLICATIONS. Approximation of the generation time distribution of COVID-19 with non-negative or negative-permitting serial interval distributions when calculating Re(t) may result in over or underestimation of transmission potential, respectively.