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

  • Knight, Jesse1, 2
  • Mishra, Sharmistha1, 2, 3, 4
  • 1 Institute of Medical Science, University of Toronto, Canada
  • 2 MAP Centre for Urban Health Solutions, Unity Health Toronto, Canada
  • 3 Division of Infectious Disease, Department of Medicine, University of Toronto, Canada
  • 4 Institute of Health Policy, Management and Evaluation, Dalla Lana School of Public Health, University of Toronto, Canada
Published Article
Infectious Disease Modelling
KeAi Publishing
Publication Date
Nov 01, 2020
DOI: 10.1016/j.idm.2020.10.009
PMID: 33163739
PMCID: PMC7604055
PubMed Central


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.

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