The timing of transmission plays a key role in the dynamics and controllability of an epidemic. However, observing generation times—the time interval between the infection of an infector and an infectee in a transmission pair—requires data on infection times, which are generally unknown. The timing of symptom onset is more easily observed; generation times are therefore often estimated based on serial intervals—the time interval 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—the 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.

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关于序列间隔、传染性特征和世代时间的关系

传播时机对流行病的动态和可控性起着关键作用。然而，观察世代时间——传播对中感染者和被感染者之间的时间间隔——需要有关感染时间的数据，而这些数据通常是未知的。更容易观察到症状发作的时间；因此，世代时间通常是根据连续间隔（感染者和感染者症状出现之间的时间间隔）来估计的。该估计遵循以下两种方法之一：(i) 通过序列间隔分布近似世代时间分布或 (ii) 从序列间隔和潜伏期（单个个体感染和症状发作之间的时间间隔）推导出世代时间分布——分布。这两种方法对传染性和症状之间的关系做出了不同的假设，但并不总是明确说明，从而导致具有相同平均值但不等方差的不同世代时间分布。在这里，我们澄清了每种方法所做的假设，并表明对于大多数病原体而言，任何一组假设都不合理。然而，在每个假设下导出的生成时间分布的方差可以合理地被视为上限（与序列间隔的近似值）和下限（从序列间隔推导）。因此，我们建议一种务实的解决方案是同时使用这两种方法，并将它们视为下游分析中的边缘情况。我们通过基于接触者追踪的策略讨论了世代时间分布的方差对流行病可控性的影响，