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

The limit as κ → 0 is reasonably easy to interpret. The incidence is increasing by a factor of exp(ρ) in the time it takes for an average disease generation. If κ = 0, the generation interval is fixed, so the average case must cause exactly R = exp(ρ) new cases. If variation in the generation time (i.e., κ) increases, then some new cases will be produced before, and some after, the mean generation time. Since we assume the disease is increasing exponentially, infections that occur early on represent a larger proportion of the population, and thus will have a disproportionate effect: individuals don't have to produce as many lifetime infections to sustain the growth rate, and thus we expect R < exp(ρ) (as shown by [44] ).