Estimating effective reproduction number using generation time versus serial interval, with application to COVID-19 in the Greater Toronto Area, Canada
Abstract
B <sc>ackground</sc>
The effective reproductive 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 <sc>covid</sc> -19, rendering such an approximation improper in some contexts.
M <sc>ethods</sc>
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 <sc>covid</sc> -19 in the Greater Toronto Area of Canada using: negative-permitting versus non-negative serial interval distributions, versus the inferred generation time distribution.
R <sc>esults</sc>
We estimated the generation time of <sc>covid</sc> -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.
I <sc>mplications</sc>
Approximation of the generation time distribution of <sc>covid</sc> -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.
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