Inferring the differences in incubation-period and generation-interval distributions of the Delta and Omicron variants of SARS-CoV-2.

Estimating the differences in the incubation-period, serial-interval, and generation-interval distributions of SARS-CoV-2 variants is critical to understanding their transmission. However, the impact of epidemic dynamics is often neglected in estimating the timing of infection-for example, when an epidemic is growing exponentially, a cohort of infected individuals who developed symptoms at the same time are more likely to have been infected recently. Here, we reanalyze incubation-period and serial-interval data describing transmissions of the Delta and Omicron variants from the Netherlands at the end of December 2021. Previous analysis of the same dataset reported shorter mean observed incubation period (3.2 d vs. 4.4 d) and serial interval (3.5 d vs. 4.1 d) for the Omicron variant, but the number of infections caused by the Delta variant decreased during this period as the number of Omicron infections increased. When we account for growth-rate differences of two variants during the study period, we estimate similar mean incubation periods (3.8 to 4.5 d) for both variants but a shorter mean generation interval for the Omicron variant (3.0 d; 95% CI: 2.7 to 3.2 d) than for the Delta variant (3.8 d; 95% CI: 3.7 to 4.0 d). The differences in estimated generation intervals may be driven by the "network effect"-higher effective transmissibility of the Omicron variant can cause faster susceptible depletion among contact networks, which in turn prevents late transmission (therefore shortening realized generation intervals). Using up-to-date generation-interval distributions is critical to accurately estimating the reproduction advantage of the Omicron variant.

Spatially explicit effective reproduction numbers from incidence and mobility data.

Current methods for near real-time estimation of effective reproduction numbers from surveillance data overlook mobility fluxes of infectors and susceptible individuals within a spatially connected network (the metapopulation). Exchanges of infections among different communities may thus be misrepresented unless explicitly measured and accounted for in the renewal equations. Here, we first derive the equations that include spatially explicit effective reproduction numbers, ℛk(t), in an arbitrary community k. These equations embed a suitable connection matrix blending mobility among connected communities and mobility-related containment measures. Then, we propose a tool to estimate, in a Bayesian framework involving particle filtering, the values of ℛk(t) maximizing a suitable likelihood function reproducing observed patterns of infections in space and time. We validate our tools against synthetic data and apply them to real COVID-19 epidemiological records in a severely affected and carefully monitored Italian region. Differences arising between connected and disconnected reproduction numbers (the latter being calculated with existing methods, to which our formulation reduces by setting mobility to zero) suggest that current standards may be improved in their estimation of disease transmission over time.

Correlation between times to SARS-CoV-2 symptom onset and secondary transmission undermines epidemic control efforts.

Severe acute respiratory coronavirus 2 (SARS-CoV-2) infections have been associated with substantial presymptomatic transmission, which occurs when the generation interval-the time between infection of an individual with a pathogen and transmission of the pathogen to another individual-is shorter than the incubation period-the time between infection and symptom onset. We collected a dataset of 257 SARS-CoV-2 transmission pairs in Japan during 2020 and jointly estimated the mean incubation period of infectors (4.8 days, 95 % CrI: 4.4-5.1 days), mean generation interval to when they infect others (4.3 days, 95 % credible interval [CrI]: 4.0-4.7 days), and the correlation (Kendall's tau: 0.5, 95 % CrI: 0.4-0.6) between these two epidemiological parameters. Our finding of a positive correlation and mean generation interval shorter than the mean infector incubation period indicates ample infectiousness before symptom onset and suggests that reliance on isolation of symptomatic COVID-19 cases as a focal point of control efforts is insufficient to address the challenges posed by SARS-CoV-2 transmission dynamics.

The unmitigated profile of COVID-19 infectiousness.

Quantifying the temporal dynamics of infectiousness of individuals infected with SARS-CoV-2 is crucial for understanding the spread of COVID-19 and for evaluating the effectiveness of mitigation strategies. Many studies have estimated the infectiousness profile using observed serial intervals. However, statistical and epidemiological biases could lead to underestimation of the duration of infectiousness. We correct for these biases by curating data from the initial outbreak of the pandemic in China (when mitigation was minimal), and find that the infectiousness profile of the original strain is longer than previously thought. Sensitivity analysis shows our results are robust to model structure, assumed growth rate and potential observational biases. Although unmitigated transmission data is lacking for variants of concern (VOCs), previous analyses suggest that the alpha and delta variants have faster within-host kinetics, which we extrapolate to crude estimates of variant-specific unmitigated generation intervals. Knowing the unmitigated infectiousness profile of infected individuals can inform estimates of the effectiveness of isolation and quarantine measures. The framework presented here can help design better quarantine policies in early stages of future epidemics.

The importance of the generation interval in investigating dynamics and control of new SARS-CoV-2 variants.

Inferring the relative strength (i.e. the ratio of reproduction numbers) and relative speed (i.e. the difference between growth rates) of new SARS-CoV-2 variants is critical to predicting and controlling the course of the current pandemic. Analyses of new variants have primarily focused on characterizing changes in the proportion of new variants, implicitly or explicitly assuming that the relative speed remains fixed over the course of an invasion. We use a generation-interval-based framework to challenge this assumption and illustrate how relative strength and speed change over time under two idealized interventions: a constant-strength intervention like idealized vaccination or social distancing, which reduces transmission rates by a constant proportion, and a constant-speed intervention like idealized contact tracing, which isolates infected individuals at a constant rate. In general, constant-strength interventions change the relative speed of a new variant, while constant-speed interventions change its relative strength. Differences in the generation-interval distributions between variants can exaggerate these changes and modify the effectiveness of interventions. Finally, neglecting differences in generation-interval distributions can bias estimates of relative strength.

Inference of the SARS-CoV-2 generation time using UK household data.

The distribution of the generation time (the interval between individuals becoming infected and transmitting the virus) characterises changes in the transmission risk during SARS-CoV-2 infections. Inferring the generation time distribution is essential to plan and assess public health measures. We previously developed a mechanistic approach for estimating the generation time, which provided an improved fit to data from the early months of the COVID-19 pandemic (December 2019-March 2020) compared to existing models (Hart et al., 2021). However, few estimates of the generation time exist based on data from later in the pandemic. Here, using data from a household study conducted from March to November 2020 in the UK, we provide updated estimates of the generation time. We considered both a commonly used approach in which the transmission risk is assumed to be independent of when symptoms develop, and our mechanistic model in which transmission and symptoms are linked explicitly. Assuming independent transmission and symptoms, we estimated a mean generation time (4.2 days, 95% credible interval 3.3-5.3 days) similar to previous estimates from other countries, but with a higher standard deviation (4.9 days, 3.0-8.3 days). Using our mechanistic approach, we estimated a longer mean generation time (5.9 days, 5.2-7.0 days) and a similar standard deviation (4.8 days, 4.0-6.3 days). As well as estimating the generation time using data from the entire study period, we also considered whether the generation time varied temporally. Both models suggest a shorter mean generation time in September-November 2020 compared to earlier months. Since the SARS-CoV-2 generation time appears to be changing, further data collection and analysis is necessary to continue to monitor ongoing transmission and inform future public health policy decisions.

Meta-analysis of the severe acute respiratory syndrome coronavirus 2 serial intervals and the impact of parameter uncertainty on the coronavirus disease 2019 reproduction number.

The serial interval of an infectious disease, commonly interpreted as the time between the onset of symptoms in sequentially infected individuals within a chain of transmission, is a key epidemiological quantity involved in estimating the reproduction number. The serial interval is closely related to other key quantities, including the incubation period, the generation interval (the time between sequential infections), and time delays between infection and the observations associated with monitoring an outbreak such as confirmed cases, hospital admissions, and deaths. Estimates of these quantities are often based on small data sets from early contact tracing and are subject to considerable uncertainty, which is especially true for early coronavirus disease 2019 data. In this paper, we estimate these key quantities in the context of coronavirus disease 2019 for the UK, including a meta-analysis of early estimates of the serial interval. We estimate distributions for the serial interval with a mean of 5.9 (95% CI 5.2; 6.7) and SD 4.1 (95% CI 3.8; 4.7) days (empirical distribution), the generation interval with a mean of 4.9 (95% CI 4.2; 5.5) and SD 2.0 (95% CI 0.5; 3.2) days (fitted gamma distribution), and the incubation period with a mean 5.2 (95% CI 4.9; 5.5) and SD 5.5 (95% CI 5.1; 5.9) days (fitted log-normal distribution). We quantify the impact of the uncertainty surrounding the serial interval, generation interval, incubation period, and time delays, on the subsequent estimation of the reproduction number, when pragmatic and more formal approaches are taken. These estimates place empirical bounds on the estimates of most relevant model parameters and are expected to contribute to modeling coronavirus disease 2019 transmission.

Using Proper Mean Generation Intervals in Modeling of COVID-19.

In susceptible-exposed-infectious-recovered (SEIR) epidemic models, with the exponentially distributed duration of exposed/infectious statuses, the mean generation interval (GI, time lag between infections of a primary case and its secondary case) equals the mean latent period (LP) plus the mean infectious period (IP). It was widely reported that the GI for COVID-19 is as short as 5 days. However, many works in top journals used longer LP or IP with the sum (i.e., GI), e.g., >7 days. This discrepancy will lead to overestimated basic reproductive number and exaggerated expectation of infection attack rate (AR) and control efficacy. We argue that it is important to use suitable epidemiological parameter values for proper estimation/prediction. Furthermore, we propose an epidemic model to assess the transmission dynamics of COVID-19 for Belgium, Israel, and the United Arab Emirates (UAE). We estimated a time-varying reproductive number [R0(t)] based on the COVID-19 deaths data and we found that Belgium has the highest AR followed by Israel and the UAE.

Estimating the generation interval and inferring the latent period of COVID-19 from the contact tracing data.

The coronavirus disease 2019 (COVID-19) emerged by end of 2019, and became a serious public health threat globally in less than half a year. The generation interval and latent period, though both are of importance in understanding the features of COVID-19 transmission, are difficult to observe, and thus they can rarely be learnt from surveillance data empirically. In this study, we develop a likelihood framework to estimate the generation interval and incubation period simultaneously by using the contact tracing data of COVID-19 cases, and infer the pre-symptomatic transmission proportion and latent period thereafter. We estimate the mean of incubation period at 6.8 days (95 %CI: 6.2, 7.5) and SD at 4.1 days (95 %CI: 3.7, 4.8), and the mean of generation interval at 6.7 days (95 %CI: 5.4, 7.6) and SD at 1.8 days (95 %CI: 0.3, 3.8). The basic reproduction number is estimated ranging from 1.9 to 3.6, and there are 49.8 % (95 %CI: 33.3, 71.5) of the secondary COVID-19 infections likely due to pre-symptomatic transmission. Using the best estimates of model parameters, we further infer the mean latent period at 3.3 days (95 %CI: 0.2, 7.9). Our findings highlight the importance of both isolation for symptomatic cases, and for the pre-symptomatic and asymptomatic cases.

Serial Interval and Generation Interval for Imported and Local Infectors, Respectively, Estimated Using Reported Contact-Tracing Data of COVID-19 in China.

The emerging virus, COVID-19, has caused a massive outbreak worldwide. Based on the publicly available contact-tracing data, we identified 509 transmission chains from 20 provinces in China and estimated the serial interval (SI) and generation interval (GI) of COVID-19 in China. Inspired by different possible values of the time-varying reproduction number for the imported cases and the local cases in China, we divided all transmission events into three subsets: imported (the zeroth generation) infecting 1st-generation locals, 1st-generation locals infecting 2nd-generation locals, and other transmissions among 2+. The corresponding SI (GI) is respectively denoted as SI10 ( GI10 ), SI21 ( GI21 ), and SI3+2+ ( GI3+2+ ). A Bayesian approach with doubly interval-censored likelihood is employed to fit the distribution function of the SI and GI. It was found that the estimated SI10=6.52 (95% CI:5.96-7.13) , SI21=6.01 (95%CI:5.44-6.64) , SI3+2+=4.39 (95% CI:3.74-5.15) , and GI10=5.47 (95% CI:4.57-6.45) , GI21=5.01 (95% CI:3.58-7.06) , GI3+2+=4.25 (95% CI:2.82-6.23) . Thus, overall both SI and GI decrease when generation increases.

Forward-looking serial intervals correctly link epidemic growth to reproduction numbers.

The reproduction number R and the growth rate r are critical epidemiological quantities. They are linked by generation intervals, the time between infection and onward transmission. Because generation intervals are difficult to observe, epidemiologists often substitute serial intervals, the time between symptom onset in successive links in a transmission chain. Recent studies suggest that such substitution biases estimates of R based on r. Here we explore how these intervals vary over the course of an epidemic, and the implications for R estimation. Forward-looking serial intervals, measuring time forward from symptom onset of an infector, correctly describe the renewal process of symptomatic cases and therefore reliably link R with r. In contrast, backward-looking intervals, which measure time backward, and intrinsic intervals, which neglect population-level dynamics, give incorrect R estimates. Forward-looking intervals are affected both by epidemic dynamics and by censoring, changing in complex ways over the course of an epidemic. We present a heuristic method for addressing biases that arise from neglecting changes in serial intervals. We apply the method to early (21 January to February 8, 2020) serial interval-based estimates of R for the COVID-19 outbreak in China outside Hubei province; using improperly defined serial intervals in this context biases estimates of initial R by up to a factor of 2.6. This study demonstrates the importance of early contact tracing efforts and provides a framework for reassessing generation intervals, serial intervals, and R estimates for COVID-19.

Epidemiological parameters of COVID-19 and its implication for infectivity among patients in China, 1 January to 11 February 2020.

BackgroundThe natural history of disease in patients infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) remained obscure during the early pandemic.AimOur objective was to estimate epidemiological parameters of coronavirus disease (COVID-19) and assess the relative infectivity of the incubation period.MethodsWe estimated the distributions of four epidemiological parameters of SARS-CoV-2 transmission using a large database of COVID-19 cases and potential transmission pairs of cases, and assessed their heterogeneity by demographics, epidemic phase and geographical region. We further calculated the time of peak infectivity and quantified the proportion of secondary infections during the incubation period.ResultsThe median incubation period was 7.2 (95% confidence interval (CI): 6.9‒7.5) days. The median serial and generation intervals were similar, 4.7 (95% CI: 4.2‒5.3) and 4.6 (95% CI: 4.2‒5.1) days, respectively. Paediatric cases < 18 years had a longer incubation period than adult age groups (p = 0.007). The median incubation period increased from 4.4 days before 25 January to 11.5 days after 31 January (p < 0.001), whereas the median serial (generation) interval contracted from 5.9 (4.8) days before 25 January to 3.4 (3.7) days after. The median time from symptom onset to discharge was also shortened from 18.3 before 22 January to 14.1 days after. Peak infectivity occurred 1 day before symptom onset on average, and the incubation period accounted for 70% of transmission.ConclusionThe high infectivity during the incubation period led to short generation and serial intervals, necessitating aggressive control measures such as early case finding and quarantine of close contacts.

Reconciling early-outbreak estimates of the basic reproductive number and its uncertainty: framework and applications to the novel coronavirus (SARS-CoV-2) outbreak.

A novel coronavirus (SARS-CoV-2) emerged as a global threat in December 2019. As the epidemic progresses, disease modellers continue to focus on estimating the basic reproductive number [Formula: see text]-the average number of secondary cases caused by a primary case in an otherwise susceptible population. The modelling approaches and resulting estimates of [Formula: see text] during the beginning of the outbreak vary widely, despite relying on similar data sources. Here, we present a statistical framework for comparing and combining different estimates of [Formula: see text] across a wide range of models by decomposing the basic reproductive number into three key quantities: the exponential growth rate, the mean generation interval and the generation-interval dispersion. We apply our framework to early estimates of [Formula: see text] for the SARS-CoV-2 outbreak, showing that many [Formula: see text] estimates are overly confident. Our results emphasize the importance of propagating uncertainties in all components of [Formula: see text], including the shape of the generation-interval distribution, in efforts to estimate [Formula: see text] at the outset of an epidemic.

[Study on assessing early epidemiological parameters of COVID-19 epidemic in China].

Objective: To study the early dynamics of the epidemic of coronavirus disease (COVID-19) in China from 15 to 31 January, 2020, and estimate the corresponding epidemiological parameters (incubation period, generation interval and basic reproduction number) of the epidemic. Methods: By means of Weibull, Gamma and Lognormal distributions methods, we estimated the probability distribution of the incubation period and generation interval data obtained from the reported COVID-19 cases. Moreover, the AIC criterion was used to determine the optimal distribution. Considering the epidemic is ongoing, the exponential growth model was used to fit the incidence data of COVID-19 from 10 to 31 January, 2020, and exponential growth method, maximum likelihood method and SEIR model were used to estimate the basic reproduction number. Results: Early COVID-19 cases kept an increase in exponential growth manner before 26 January, 2020, then the increase trend became slower. The average incubation period was 5.01 (95%CI: 4.31-5.69) days; the average generation interval was 6.03 (95%CI: 5.20-6.91) days. The basic reproduction number was estimated to be 3.74 (95%CI: 3.63-3.87), 3.16 (95%CI: 2.90-3.43), and 3.91 (95%CI: 3.71-4.11) by three methods, respectively. Conclusions: The Gamma distribution fits both the generation interval and incubation period best, and the mean value of generation interval is 1.02 day longer than that of incubation period. The relatively high basic reproduction number indicates that the epidemic is still serious; Based on our analysis, the turning point of the epidemic would be seen on 26 January, the growth rate would be lower afterwards.

Estimating the generation interval for coronavirus disease (COVID-19) based on symptom onset data, March 2020.

BackgroundEstimating key infectious disease parameters from the coronavirus disease (COVID-19) outbreak is essential for modelling studies and guiding intervention strategies.AimWe estimate the generation interval, serial interval, proportion of pre-symptomatic transmission and effective reproduction number of COVID-19. We illustrate that reproduction numbers calculated based on serial interval estimates can be biased.MethodsWe used outbreak data from clusters in Singapore and Tianjin, China to estimate the generation interval from symptom onset data while acknowledging uncertainty about the incubation period distribution and the underlying transmission network. From those estimates, we obtained the serial interval, proportions of pre-symptomatic transmission and reproduction numbers.ResultsThe mean generation interval was 5.20 days (95% credible interval (CrI): 3.78-6.78) for Singapore and 3.95 days (95% CrI: 3.01-4.91) for Tianjin. The proportion of pre-symptomatic transmission was 48% (95% CrI: 32-67) for Singapore and 62% (95% CrI: 50-76) for Tianjin. Reproduction number estimates based on the generation interval distribution were slightly higher than those based on the serial interval distribution. Sensitivity analyses showed that estimating these quantities from outbreak data requires detailed contact tracing information.ConclusionHigh estimates of the proportion of pre-symptomatic transmission imply that case finding and contact tracing need to be supplemented by physical distancing measures in order to control the COVID-19 outbreak. Notably, quarantine and other containment measures were already in place at the time of data collection, which may inflate the proportion of infections from pre-symptomatic individuals.