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

where G i , E i and I i are the sampled intrinsic generation interval, latent period, and infectious period, respectively, and U represents a uniform random deviate. This implicitly assumes that infectiousness is constant across the infectious period [13] . We sample from latent and infectious periods obtained from observations (for empirical distributions), or by using a uniform set of quantiles (for parametric distributions). For the purpose of constructing pseudo-realistic distributions, we do not attempt to correct for the fact that observed intervals may be sampled in a context more relevant to backward than to intrinsic generation intervals (see [8] ). We sample latent periods at random, and infectious periods by length-weighted resampling (since longer infectious period implies more opportunities to infect). For our examples, we used 10,000 quantiles for each parametric distribution and 10,000 sampled generation intervals for each disease (see Appendix). We then calculate "exact" relationships (for our pseudo-realistic distributions) by substituting sampled generation intervals into the exact speedstrength relationship (5) . This relationship is then compared to the corresponding gamma-approximated relationship (6) .