Generation Time Of The Alpha And Delta SARS-CoV-2 Variants: An Epidemiological Analysis

For more information:ali.ma@wecistanche.com

Summary

Background

In May 2021, the delta (B.1.617.2) SARS-CoV-2 variant became dominant in the UK, superseded by the omicron (B.1.1.529) variant in December 2021. The delta variant is associated with increased transmissibility compared with the alpha variant, which was the dominant variant in the UK between December 2020, and May 2021. To understand transmission and the effectiveness of interventions, we aimed to investigate whether the delta variant generation time (the interval between infections in infector–infectee pairs) is shorter—ie, transmissions are happening more quickly—than that of the alpha variant.

Methods

In this epidemiological analysis, we analyzed transmission data from an ongoing UK Health Security Agency (UKHSA) prospective household study. Households were recruited to the study after an index case had a positive PCR test and genomic sequencing was used to determine the variant responsible. By fitting a mathematical transmission model to the data, we estimated the intrinsic generation time (which assumes a constant supply of susceptible individuals throughout infection) and the household generation time (which reflects realized transmission in the study households, accounting for susceptible depletion) for the alpha and delta variants.

Findings

Between February and August 2021, 227 households consisting of 559 participants were recruited to the UKHSA study. The alpha variant was detected or assumed to be responsible for infections in 131 households (243 infections in 334 participants) recruited in February–May, and the delta variant in 96 households (174 infections in 225 participants) in May-August. The mean intrinsic generation time was shorter for the delta variant (4·7 days, 95% credible interval [CI] 4·1–5·6) than the alpha variant (5·5 days, 4·7–6·5), with 92% posterior probability. The mean household generation time was 28% (95% CI 0–48%) shorter for the delta variant (3·2 days, 95% CI 2·5–4·2) than the alpha variant (4·5 days, 3·7–5·4), with 97·5% posterior probability.

Interpretation

The delta variant transmits more quickly in households than the alpha variant, which can be attributed to the faster depletion of susceptible individuals in households and a possible decrease in the intrinsic generation time. Interventions such as contact tracing, testing, and isolation might be less effective if transmission of the virus occurs quickly.

Funding

National Institute for Health Research, UK Health Security Agency, Engineering, and Physical Sciences Research Council, and UK Research and Innovation

William S Hart, Elizabeth Miller, Nick J Andrews, Pauline Waight, Philip K Maini, Sebastian Funk, Robin N Thompson

Mathematical Institute, University of Oxford, Oxford, UK (W S Hart MMath, Prof PK Maini DPhil); Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK (Prof E Miller FRCPath, Prof S Funk Ph.D.); Immunisation and Countermeasures Division (Prof E Miller, P Waight BSc) and Data and Analytical Sciences (Prof N J Andrews Ph.D.), UK Health Security Agency, London, UK; Mathematics Institute (R N Thompson Ph.D.) and Zeeman Institute for Systems Biology and Infectious Disease Epidemiology Research (R N Thompson), University of Warwick, Coventry, UK

Introduction

In May 2021, the delta (B.1.617.2) SARS-CoV-2 variant became dominant in the UK1 and globally.2 This variant presents a higher risk of severe disease compared with previous variants,2,3 although vaccination is still protective.4 The delta variant led to an increase in the growth rate of COVID-19 cases in the UK, outcompeting other variants.1,5 This growth was attributed to increased transmissibility, with a study5 suggesting that the delta variant was 43–68% more transmissible5 than the alpha (B.1.1.7) variant, which was first identified in a sample from September, 2020.6

One way to characterize transmission of a SARS-CoV-2 variant is to measure its speed and strength.7,8 Speed refers to how quickly the variant grows at the population level, which is measured by the exponential growth rate and is inferable from disease incidence data.8 Strength reflects the variant’s transmissibility8 and is typically measured by the time-dependent reproduction number (ie, the number of people that each infected person is expected to infect). The generation time (ie, the time between infection events in infector–infectee pairs) determines the relationship between a variant’s speed and its strength8–11 and is an input used in models to estimate the reproduction number from case notification data.12,13 In principle, an increased growth rate of COVID-19 cases, as observed for the delta variant, is attributable to increased transmissibility, a shorter generation time, or both of these factors.8,14

Previous studies have estimated the SARS-CoV-2 generation time,15–20 with most estimates using data collected early in the COVID-19 pandemic. A household study18 from the UK Health Security Agency (UKHSA) indicated that the generation time of SARS-CoV-2 became shorter between September and November 2020, compared with the earlier months. However, although this period coincided with the emergence of the alpha variant, that variant was responsible for infections in only two households in the UKHSA study, and the delta variant had not yet emerged.18 Therefore, in this epidemiological analysis we compared the effect of these variants on the SARS-CoV-2 generation time using data from an ongoing household study in the UK.

Methods

Study design and data

In this epidemiological analysis, we analyzed transmission data from an ongoing prospective household study conducted by the UKHSA (appendix 1). Because the study began in January 2021, and data were available from February to September 2021, we could analyze the transition from alpha to delta becoming the dominant variant. Households were recruited to the study after an index case had a positive PCR test. The data contain PCR test results (including three tests taken as part of the study), symptom onset dates, ages, and vaccination statuses of participating household members (appendix 1). Genomic sequencing was used to determine the variant responsible for PCR-confirmed infections. Where sequencing data were unavailable, we assumed that the alpha variant was responsible for infections in households in which the index case first tested positive before May 2021, and the delta variant was responsible for infections in households in which the index case first tested positive after May 2021 (data from three unsequenced households recruited during May 2021, were excluded from our analysis).1 A sensitivity analysis was done involving only households in which sequencing was performed.

A full description of the household study protocol is provided in appendix 2 (p 2). The household surveillance protocol was approved by the UKHSA Research Ethics and Governance Group as part of the portfolio of the UKHSA enhanced surveillance activities in response to the COVID-19 pandemic. Verbal informed consent for participation in the study (including data analyses to understand characteristics of household transmission) was obtained by the nurses from household members, who could decline participation in the household study at any time. Consent for children was obtained from a parent or legal guardian. Only anonymized data were provided to non-UKHSA authors.

Mathematical modeling and statistical analysis

We estimated the generation time by fitting a mechanistic model, motivated by compartmental modeling (appendix 2 pp 2–9), to the household transmission data. In this model, each infection is divided into three successive stages (the duration of time in each stage followed independent distributions): latent, presymptomatic, infectious, and symptomatic and infectious.17,18 Unlike standard methods for estimating the generation time,15,16 this approach links an infected host’s infectivity profile to the time at which they develop symptoms.

Data augmentation Markov chain Monte Carlo (MCMC) was used to fit the transmission model to the data18,21 with the following assumptions: (1) an incubation period distribution with a mean of 5·8 days (SD 3·1; obtained from a meta-analysis carried out before the alpha and delta variants emerged);22 (2) entirely asymptomatic, infected hosts being 35% as infectious as those who develop symptoms;23 (3) reduced susceptibility of vaccinated individuals compared with unvaccinated individuals (ie, the probability of transmission between an infectious individual and a susceptible individual is lower if the susceptible individual is vaccinated), using previous estimates;24 (4) no difference in infectiousness between infected individuals with different vaccination statuses; and (5) each household transmission cluster originating from a single primary case, with no further infections introduced into the household from the outside.

We did sensitivity analyses to investigate the robustness of our results to these assumptions. The following four model parameters were estimated for each variant in the parameter fitting procedure: the mean latent period (ie, the time from being infected to becoming infectious), as a proportion of the mean incubation period; the mean symptomatic infectious period; the relative infectiousness of presymptomatic compared with symptomatic infectious hosts; and the overall transmissibility parameter β0, which represents the expected number of household transmissions generated by a single, non-asymptomatic infector in an unvaccinated and otherwise entirely susceptible household, assuming that following each transmission, the infectee is removed and replaced by another susceptible individual. Trace plots and comparisons between prior and posterior distributions of fitted model parameter values are shown in appendix 2 (p 10).

The prior distributions used and central estimates of posterior distributions with 95% credible intervals (CIs) are given in appendix 2 (p 24) for each variant. To test the fitting procedure, we also conducted a simulation study, in which we used the central parameter estimates for each variant to generate synthetic data and refitted our household transmission model to those data (appendix 2 p 11). The intrinsic generation time distribution (the distribution assuming the number of susceptible individuals remains constant throughout infection—ie, supposing that whenever a transmission occurs, the infectee is immediately removed from the population and replaced with another susceptible individual), provides a generalized estimate independent of household size, was calculated for each variant from assumed and estimated model parameter values (Appendix 2 pp 4–5). The household generation time distribution (the distribution of realized generation times within households, accounting for the depletion of susceptible individuals)25 was also estimated for each variant (appendix 2 p 8).

The household generation time is shorter on average than the intrinsic generation time because infected individuals might run out of susceptible individuals to infect within households.9,25 This effect is often caused by multiple infected hosts competing to infect the available susceptible individuals (with only the first potential transmission being realized).26,27 Consequently, realized transmissions occur faster within households than the intrinsic generation time distribution suggests. We calculated the posterior distributions of the mean and SD of the intrinsic and household generation time distributions for each variant. We also combined the estimates obtained in each step of the MCMC procedure (after a burn-in period to allow the parameter inference procedure to identify the relevant region of parameter space and thinning to reduce autocorrelation between estimates used from different iterations) to estimate the entire household generation time distribution (appendix 2 p 13).

By comparing estimates of mean intrinsic and household generation times for the alpha and delta variants obtained in each iteration of the MCMC procedure, we calculated posterior estimates of percentage reduction in these quantities due to the delta variant (compared with the alpha variant). We also calculated the posterior probability that each quantity was smaller for the delta variant than the alpha variant (ie, the proportion of MCMC iterations in which the estimated mean intrinsic or household generation time was shorter for the delta variant). Household generation times were also compared on the basis of vaccination status, date, and age. All analyses were performed in MATLAB (version R2021b).

Results

Between February and August 2021, 227 households and 559 participants were recruited to the UKHSA study (table; shown by vaccination status and age in appendix 2 pp 21–22). The alpha variant was detected or assumed to be responsible for infections in 131 households (243 infections in 334 participants) recruited in February–May, and the delta variant in 96 households (174 infections in 225 participants) in May-August. The mean intrinsic generation time was estimated to be 4·7 days (95% CI 4·1–5·6) for the delta variant and 5·5 days (4·7–6·5) for the alpha variant (figure 1A). Comparing the posterior estimates suggests that the mean intrinsic generation time is 15% (95% CI −7% to 31%) shorter for the delta variant than the alpha variant, with a 92% posterior probability that the delta variant has the shorter mean intrinsic generation time of the two variants (figure 1A). Our results also indicate higher transmissibility within households for the delta variant than for the alpha variant (figure 1B). Estimates of the mean household generation time for the two variants (figure 1C) are shorter than the corresponding intrinsic generation time estimates (figure 1A). The mean household generation time was estimated to be 28% (95% CI 0–48%) shorter for the delta variant (3·2 days, 95% CI 2·5–4·2) than the alpha variant (4·5 days, 3·7–5·4), with 97·5% posterior probability that the delta variant has the shorter mean household generation time of the two variants.

We combined the estimates obtained in each step of the MCMC procedure to estimate the entire household generation time distribution for the alpha and delta variants, which showed that household delta variant transmissions typically occur earlier during SARS-CoV-2 infection than transmissions with the alpha variant (appendix 2 p 13). We also show posterior estimates of the mean and SD of the household serial interval distribution (ie, the period between symptom onset times in infector– infectee pairs; appendix 2 p 14). Similarly to the household generation time, we found a shorter mean household serial interval for the delta variant (1·8 days, 95% CI 1·0–2·4) than the alpha variant (3·5 days, 2·7–4·1). For both variants, the mean household serial interval was shorter than the mean household generation time—by 1·0 days (0·2–1·8) for the alpha variant and 1·5 days (0·7–2·4) for the delta variant—but the household serial interval had a higher SD than the household generation time.

We also explored the effects of vaccination (figure 2A–C), age (figure 2D–E), and month in which the index case first tested positive (figure 2F) on household generation times. We estimated the generation times associated with infectors and infectees with different vaccination statuses and considered different combinations of infector– infectee pairs. The effect of variants on the household generation time was larger than that of vaccination status (figure 2A–C). For both variants, there was no clear effect of the infector or infectee age on the generation time (figures 2D–E). A reduction in household generation time occurred during April–June 2021, probably because the delta variant became dominant in the UK during that time period (figure 2F).1

Finally, we conducted sensitivity analyses considering the robustness of our results to the modeling assumptions (appendix 2 pp 15–20). Assuming a shorter incubation period28 than used in our main analysis22 for both variants or only the delta variant (appendix 2 p 15), led to a larger difference in mean intrinsic generation time between variants than shown in figure 1A (eg, in the sensitivity analysis in which both variants had a shorter incubation period, the estimated mean intrinsic generation time was 27% [95% CI 5–44%] shorter for the delta variant than the alpha variant).

Conversely, when we only considered data from households in which genomic sequencing was conducted (appendix 2 p 20), we did not find a difference in the mean intrinsic generation time between variants; however, posterior distributions of estimated quantities for the delta variant in this sensitivity analysis were wide because sequencing data were unavailable from households recruited after June 2021, by which time the delta variant was dominant.1 Nonetheless, in both of these sensitivity analyses, our finding of a shorter household generation time for the delta variant than for the alpha variant remained unchanged. This finding was robust to the different infectiousness levels of asymptomatic, infected hosts (appendix 2 p 16) and vaccinated, infected hosts (appendix 2 p 17) and to multiple virus introductions into households (Appendix 2 pp 18–19).

Discussion

Novel SARS-CoV-2 variants possess different transmission characteristics to the coronavirus that originally emerged in Wuhan, China.5,14 A key characteristic is the generation time, which measures the speed of transmission.17,25,29 To estimate the generation time, analyzing datasets in which infector–infectee pairs can be determined or estimated is necessary.17,25,29 Household studies provide an opportunity to conduct such analyses.18,21 In our analysis of data from a UKHSA household study, we found that the mean intrinsic generation time was slightly shorter for the delta variant than the alpha variant, but with substantial overlap in the CIs between the variants. For each variant, realized household generation times were shorter on average than intrinsic generation times because the household generation time accounts for the depletion of susceptible individuals within households (potential transmissions with longer generation times are then less likely to occur).

We found a larger difference in the mean household generation time between the variants than expected from the estimated difference in intrinsic generation time alone. This finding is attributable to the increased transmissibility of the delta variant in households, leading to susceptible individuals being infected quickly, thereby being unavailable for infection later (thus shortening the average period between realized transmissions). The effect of the variant on the household generation time was greater than the effects of other factors, including age and vaccination status.

To our knowledge, this is the first study to compare the generation time for different SARS-CoV-2 variants directly, and we are not aware of other generation time estimates for the alpha variant. An estimate for the delta variant based on 55 transmission pairs was stated in China CDC Weekly in 2021,28 although the methods underlying the estimate were not presented. Nonetheless, their mean generation time estimate of 2·9 days28 lies within the CI of our estimate of the mean household generation time for the delta variant (3·2 days, 95% CI 2·5–4·2) and is shorter than the lower limit of the 95% CI of our estimate for the alpha variant (4·5 days, 3·7–5·4).

This observation supports our finding that the delta variant is transmitted more quickly than the alpha variant in households. Because we conducted our analysis before November 2021, we did not analyze the generation time for the newly emerged omicron (B.1.1.529) variant. However, our finding of a different mean household generation time for the alpha versus the delta variant highlights the need for generation time estimates to be updated for the omicron variant when suitable data become available. Other studies have estimated the serial interval (the period between symptom onset times in infector– infectee pairs) for the delta variant.30–32 Recently, preliminary studies have also estimated the serial interval33 and related test-to-test interval34 for the omicron variant.

Although the serial interval is sometimes used as a proxy for the generation time, these two quantities might not follow the same distribution29—eg, the generation time always has positive values, whereas the serial interval can be negative if the presymptomatic transmission is possible. The serial interval distribution often has a higher SD than the generation time distribution,29 and those distributions might not have the same mean value.18 A shorter mean serial interval than generation time (as we found for household transmission in our analysis) can be attributed to presymptomatic transmission because individuals with longer incubation periods might generate more transmissions on average.

This effect, which is captured in our mathematical modeling approach, leads to an expected incubation period that is longer for infectors than infectees in transmission pairs, and therefore, a shorter mean serial interval than generation time18 (since the difference between the generation time and the serial interval is equal to the difference between the incubation periods of the infector and the infectee29). The viral load trajectories of individuals with infections due to the alpha and delta variants have also previously been estimated.35–37 Although estimating how infectiousness varies during infection using viral load data might be possible,38 the timing of realized transmissions depends on factors additional to inherent infectiousness, such as behavior (eg, individuals might be less likely to transmit after developing symptoms and self-isolating) and the availability of susceptible individuals.

Our approach explicitly accounts for changes in transmission risk following symptom onset, and the household generation time accounts for depletion of susceptible individuals within households. Generation time estimates underlie a range of epidemiological analyses, including inference of the time-varying reproduction number12,13 in different regions or countries and the relative transmissibility of different variants.5,14 Such analyses often neglect temporal changes in the generation time. Furthermore, our results highlight that the reproduction number can affect the realized generation time (specifically, higher transmissibility of the delta variant leads to faster transmission within households). This finding underlines the importance of using up-to-date generation time estimates when estimating reproduction numbers.

Overestimation of the mean generation time generally leads to reproduction number estimates that are too high in a growing epidemic, and too low in a declining epidemic.10 When analyzing the transmissibility advantage of the delta variant over the alpha variant, neglecting a potentially shorter generation time for the delta variant would lead to its transmissibility advantage being overestimated.8 Because depletion of susceptible contacts might be less important in determining the timing of transmissions occurring outside households than within households, we expect the overall generation time distribution (accounting for transmissions across all settings) to lie between our household and intrinsic estimates.

Therefore, we expect that inferring the delta variant transmissibility advantage over the alpha variant from incidence data using our household generation time estimates would give a lower bound for the transmissibility advantage (because the observed increased growth rate of the delta variant is explained partly by a substantial generation time reduction). By contrast, inferring the transmissibility advantage of the delta variant using intrinsic generation time estimates would give an upper bound. We note that our estimates of overall transmissibility (β0) of the alpha and delta variants cannot be directly compared with previous estimates of the delta variant’s transmission advantage (eg, an estimate of 43–68% inferred from incidence data5 ).

The value of β0 represents the expected number of household transmissions generated by a single, non-asymptomatic infector in an unvaccinated and entirely susceptible household, assuming that following each transmission, the infectee is removed and replaced by another susceptible individual. As a result, β0 reflects intrinsic transmissibility rather than realized transmission. The intrinsic transmission advantage of the delta variant will only be realized if a sufficient number of susceptible individuals is available for each infector. Limitations of this epidemiological modeling study include the model assumptions and the extent to which data are representative of the wider population. Although we analyzed household data, transmission characteristics might differ between settings, which motivated us to estimate both the household and intrinsic generation times. The intrinsic generation time estimate, which does not account for the depletion of susceptible individuals in households, can be conditioned to specific contact networks and transmission settings (eg, households, schools, workplaces, and social contact networks).

We also conducted sensitivity analyses, confirming that our finding of a shorter household generation time for the delta variant than for the alpha variant was robust to important modeling assumptions. In summary, our analysis indicates that the delta variant is transmitted more quickly than the alpha variant in households. This finding has implications for interventions because measures such as contact tracing are less effective if transmission of the virus occurs quickly. Epidemiological models need to be updated to reflect the generation time of variants driving transmission and assessed further as the characteristics of SARS-CoV-2 transmission continue to change.

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