On the relationship between serial interval, infectiousness profile and generation time

Lehtinen, S.; Ashcroft, P.; Bonhoeffer, S.

The timing of transmission plays a key role in the dynamics and controllability of an epidemic. However, observing the distribution of generation times (time interval between the points of infection of an infector and infectee in a transmission pair) requires data on infection times, which are generally unknown. The timing of symptom onset is more easily observed; the generation time distribution is therefore often estimated based on the serial interval distribution (distribution of time intervals between symptom onset of an infector and an infectee). This estimation follows one of two approaches: i) approximating the generation time distribution by the serial interval distribution; or ii) deriving the generation time distribution from the serial interval and incubation period (time interval between infection and symptom onset in a single individual) distributions. These two approaches make different -- and not always explicitly stated -- assumptions about the relationship between infectiousness and symptoms, resulting in different generation time distributions with the same mean but unequal variances. Here, we clarify the assumptions that each approach makes and show that neither set of assumptions is plausible for most pathogens. However, the variances of the generation time distribution derived under each assumption can reasonably be considered as upper (approximation with serial interval) and lower (derivation from serial interval) bounds. Thus, we suggest a pragmatic solution is to use both approaches and treat these as edge cases in downstream analysis. We discuss the impact of the variance of the generation time distribution on the controllability of an epidemic through strategies based on contact tracing, and we show that underestimating this variance is likely to overestimate controllability.