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

Knight, Jesse; Mishra, Sharmistha

Background. The effective reproduction number R(e)(t) is a critical measure of epidemic potential. R(e)(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 R(e)(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 R(e)(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 R(e)(t) due to larger mean, while negative-permitting serial interval distribution caused underestimation of R(e)(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 R(e)(t) may result in over or underestimation of transmission potential, respectively.