A practical generation interval-based approach to inferring the strength of epidemics from their speed

Sang Woo Park; David Champredon; Joshua S. Weitz; Jonathan Dushoff

We do not expect to know the full distribution g(Ï„ ) -particularly while an epidemic is ongoing -so we are interested in approximations to R based on limited information. We follow the approach of [29] and approximate the generation interval with a gamma distribution. We prefer the gamma distribution to the standard normal approximation used in many applications for a number of reasons. First, it is more biologically realistic, since it is confined to non-negative values. Second, it has a convenient momentgenerating function, and provides a corresponding simple form for the r-R relationship that can be parameterized with only two parameters that have biologically relevant meanings that can assist in explaining intuition behind the r-R relationship. Third, it generalizes the result obtained from simple Susceptible-Infectious-Recovered (SIR) models, and approximately matches Susceptible-Exposed-Infectious-Recovered (SEIR), in the case where the latent period and infectious period are similar (see Appendix). While the gamma approximation has been applied to infer R in previous outbreaks (Table 1) , its theoretical properties and practical importance has not yet been explored in depth.