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

Abstract

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.

High infectiousness immediately before COVID-19 symptom onset highlights the importance of continued contact tracing

“…Some previous studies in which the generation time ( Ferretti et al, 2020b ; Davis et al, 2020 ) and/or TOST distributions ( Ferretti et al, 2020b ; He et al, 2020 ; Ashcroft et al, 2020 ) were estimated have considered an alternative assumption that infectiousness depends only on the time since symptom onset, independent of the time of infection. If the serial interval is always positive, which is not the case for COVID-19 ( Du et al, 2020 ), this is equivalent to assuming that the serial interval and generation time distributions are identical ( Lehtinen et al, 2021 ; Cori et al, 2013 ; Britton and Scalia Tomba, 2019 ). In one article ( Ferretti et al, 2020b ), a non-mechanistic model (the Ferretti model) was developed in which a host’s infectiousness could depend on both the time since infection and the time since symptom onset.…”

“…These distributions are important for assessing the effectiveness of public health measures such as isolation ( Ashcroft et al, 2021 ; Wells et al, 2021 ) and contact tracing ( Ferretti et al, 2020a ; Fraser et al, 2004 ; Davis et al, 2020 ). Estimates of the SARS-CoV-2 generation time have typically involved an assumption that a host’s infectiousness is independent of their symptom status ( Ferretti et al, 2020a ; Deng et al, 2020 ; Ganyani et al, 2020 ; Knight and Mishra, 2020 ; Lehtinen et al, 2021 ; Figure 1B , left). However, such an assumption is unjustified ( Lehtinen et al, 2021 ; Bacallado et al, 2020 ) and can lead to a poor fit to data ( Ferretti et al, 2020b ).…”

“…Estimates of the SARS-CoV-2 generation time have typically involved an assumption that a host’s infectiousness is independent of their symptom status ( Ferretti et al, 2020a ; Deng et al, 2020 ; Ganyani et al, 2020 ; Knight and Mishra, 2020 ; Lehtinen et al, 2021 ; Figure 1B , left). However, such an assumption is unjustified ( Lehtinen et al, 2021 ; Bacallado et al, 2020 ) and can lead to a poor fit to data ( Ferretti et al, 2020b ).…”

Caveats on COVID-19 Herd Immunity Threshold: the Spain case

“…[26,28]). However, though GT and serial interval have the same mean, serial interval presents a larger variance [17], which will underestimate R0 when using Eq. 6 [16].…”

Evolution of resistance to COVID-19 vaccination with dynamic lockdown

“…SARS-COV-2 research has drawn on a very long history of epidemiological research 26,27,[36][37][38][28][29][30][31][32][33][34][35] . Due to the global and urgent nature of the pandemic, many studies that could inform policymaking have been conducted 5,39,48,[40][41][42][43][44][45][46][47] .…”