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

Infectious disease outbreaks are often characterized by the reproduction number R and exponential rate of growth r. R provides information about outbreak control and predicted final size, but estimating R is difficult, while r can often be estimated directly from incidence data. These quantities are linked by the generation interval - the time between when an individual is infected by an infector, and when that infector was infected. It is often infeasible to obtain the exact shape of a generation-interval distribution, and to understand how this shape affects estimates of R. We show that estimating generation interval mean and variance provides insight into the relationship between R and r. We use examples based on Ebola, rabies and measles to explore approximations based on gamma-distributed generation intervals, and find that use of these simple approximations are often sufficient to capture the r-R relationship and provide robust estimates of R.