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

Background Estimating key infectious disease parameters from the coronavirus disease (COVID-19) outbreak is essential for modelling studies and guiding intervention strategies. Aim We 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. Methods We 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. Results The 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. Conclusion High 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.

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Estimating the generation interval for COVID-19 based on symptom onset data

10.1101/2020.03.05.20031815 ◽

2020 ◽

Cited By ~ 36

Author(s):

Ganyani Tapiwa ◽

Kremer Cécile ◽

Chen Dongxuan ◽

Torneri Andrea ◽

Faes Christel ◽

...

Keyword(s):

Incubation Period ◽

Symptom Onset ◽

Contact Tracing ◽

Transmission Network ◽

Generation Interval ◽

Period Distribution ◽

Reproduction Numbers ◽

Serial Interval ◽

Modelling Studies ◽

Interval Distribution

AbstractBackgroundEstimating key infectious disease parameters from the COVID-19 outbreak is quintessential for modelling studies and guiding intervention strategies. Whereas different estimates for the incubation period distribution and the serial interval distribution have been reported, estimates of the generation interval for COVID-19 have not been provided.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 proportions pre-symptomatic transmission and reproduction numbers.ResultsThe mean generation interval was 5.20 (95%CI 3.78-6.78) days for Singapore and 3.95 (95%CI 3.01-4.91) days for Tianjin, China when relying on a previously reported incubation period with mean 5.2 and SD 2.8 days. The proportion of pre-symptomatic transmission was 48% (95%CI 32-67%) for Singapore and 62% (95%CI 50-76%) for Tianjin, China. Estimates of the reproduction number based on the generation interval distribution were slightly higher than those based on the serial interval distribution.ConclusionsEstimating generation and serial interval distributions from outbreak data requires careful investigation of the underlying transmission network. Detailed contact tracing information is essential for correctly estimating these quantities.

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

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2011548118 ◽

2020 ◽

Vol 118 (2) ◽

pp. e2011548118

Author(s):

Sang Woo Park ◽

Kaiyuan Sun ◽

David Champredon ◽

Michael Li ◽

Benjamin M. Bolker ◽

...

Keyword(s):

Symptom Onset ◽

Reproduction Number ◽

Heuristic Method ◽

Population Level ◽

Contact Tracing ◽

Epidemic Dynamics ◽

Transmission Chain ◽

Reproduction Numbers ◽

Serial Interval ◽

Forward Looking

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.

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Transmission onset distribution of COVID-19

10.1101/2020.05.13.20101246 ◽

2020 ◽

Cited By ~ 1

Author(s):

June Young Chun ◽

Gyuseung Baek ◽

Yongdai Kim

Keyword(s):

Standard Deviation ◽

Incubation Period ◽

Bayesian Methods ◽

Symptom Onset ◽

Onset Time ◽

Preventive Measure ◽

Credible Interval ◽

Serial Interval ◽

Interval Distribution ◽

Key Parameter

AbstractObjectivesThe distribution of the transmission onset of COVID-19 relative to the symptom onset is a key parameter for infection control. It is often not easy to study the transmission onset time, as is difficult to know who infected whom exactly when.MethodsWe inferred transmission onset time from 72 infector-infectee pairs in South Korea, either with known or inferred contact dates by means of incubation period. Combining this data with known information of infector’s symptom onset, we could generate the transmission onset distribution of COVID-19, using Bayesian methods. Serial interval distribution could be automatically estimated from our data.ResultsWe estimated the median transmission onset to be 1.31 days (standard deviation, 2.64 days) after symptom onset with peak at 0.72 days before symptom onset. The pre-symptomatic transmission proportion was 37% (95% credible interval [CI], 16–52%). The median incubation period was estimated to be 2.87 days (95% CI, 2.33–3.50 days) and the median serial interval to be 3.56 days (95% CI, 2.72–4.44 days).ConclusionsConsidering the transmission onset distribution peaked with the symptom onset and the pre-symptomatic transmission proportion is substantial, the usual preventive measure might be too late to prevent SARS-CoV-2 transmission.

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Estimation of COVID-19 transmission rates in California and the U.S. with reporting delays

10.1101/2020.05.14.20101162 ◽

2020 ◽

Author(s):

Lee Worden ◽

Rae Wannier ◽

Micaela Neus ◽

Jennifer C. Kwan ◽

Alex Y. Ge ◽

...

Keyword(s):

United States ◽

Symptom Onset ◽

The United States ◽

Time Varying ◽

Transmission Rates ◽

Reproduction Numbers ◽

Serial Interval ◽

Reporting Delays ◽

Interval Distribution ◽

The U.S

We estimated time-varying reproduction numbers of COVID-19 transmission in counties and regions of California and in states of the United States, using the Wallinga-Teunis method of estimations applied to publicly available data. The serial interval distribution assumed incorporates wide uncertainty in delays from symptom onset to case reporting. This assumption contributes smoothing and a small but meaningful increase in numerical estimates of reproduction numbers due to the likely existence of secondary cases not yet reported. Transmission in many areas of the U.S. may not yet be controlled, including areas in which case counts appear to be stable or slowly declining.

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

10.1101/2020.09.18.20197210 ◽

2020 ◽

Cited By ~ 2

Author(s):

Sonja Lehtinen ◽

Peter Ashcroft ◽

Sebastian Bonhoeffer

Keyword(s):

Symptom Onset ◽

Generation Time ◽

Time Distribution ◽

Contact Tracing ◽

Time Interval ◽

Single Individual ◽

Serial Interval ◽

The Impact ◽

The Relationship ◽

Interval Distribution

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.

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Estimating the protective effect of case isolation with transmission tree reconstruction during the Ebola outbreak in Nigeria, 2014

Journal of The Royal Society Interface ◽

10.1098/rsif.2020.0498 ◽

2020 ◽

Vol 17 (169) ◽

pp. 20200498

Author(s):

Yat Hin Chan ◽

Hiroshi Nishiura

Keyword(s):

Protective Effect ◽

Reproduction Number ◽

Credible Interval ◽

Hospitalization Rate ◽

Contact Tracing ◽

Transmission Network ◽

Tree Reconstruction ◽

Serial Interval ◽

Formed Part ◽

The Individual

The mainstream interventions used during the 2014–2016 Ebola epidemic were contact tracing and case isolation. The Ebola outbreak in Nigeria that formed part of the 2014–2016 epidemic demonstrated the effectiveness of control interventions with a 100% hospitalization rate. Here, we aim to explicitly estimate the protective effect of case isolation, reconstructing the time events of onset of illness and hospitalization as well as the transmission network. We show that case isolation reduced the reproduction number and shortened the serial interval. Employing Bayesian inference with the Markov chain Monte Carlo method for parameter estimation and assuming that the reproduction number exponentially declines over time, the protective effect of case isolation was estimated to be 39.7% (95% credible interval: 2.4%–82.1%). The individual protective effect of case isolation was also estimated, showing that the effectiveness was dependent on the speed, i.e. the time from onset of illness to hospitalization.

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Cohort-based approach to understanding the roles of generation and serial intervals in shaping epidemiological dynamics

10.1101/2020.06.04.20122713 ◽

2020 ◽

Author(s):

Sang Woo Park ◽

Kaiyuan Sun ◽

David Champredon ◽

Michael Li ◽

Benjamin M. Bolker ◽

...

Keyword(s):

Growth Rate ◽

Disease Transmission ◽

Reproduction Number ◽

Heuristic Method ◽

Interval Data ◽

Contact Tracing ◽

Individual Level ◽

Event Time ◽

Serial Interval ◽

Interval Distribution

AbstractGeneration intervals and serial intervals are critical quantities for characterizing outbreak dynamics. Generation intervals characterize the time between infection and transmission, while serial intervals characterize the time between the onset of symptoms in a chain of transmission. They are often used interchangeably, leading to misunderstanding of how these intervals link the epidemic growth rate r and the reproduction number ℛ. Generation intervals provide a mechanistic link between r and ℛ but are harder to measure via contact tracing. While serial intervals are easier to measure from contact tracing, recent studies suggest that the two intervals give different estimates of ℛ from r. We present a general framework for characterizing epidemiological delays based on cohorts (i.e., a group of individuals that share the same event time, such as symptom onset) and show that forward-looking serial intervals, which correctly link ℛ with r, are not the same as “intrinsic” serial intervals, but instead change with r. We provide a heuristic method for addressing potential biases that can arise from not accounting for changes in serial intervals across cohorts and apply the method to estimating ℛ for the COVID-19 outbreak in China using serial-interval data — our analysis shows that using incorrectly defined serial intervals can severely bias estimates. This study demonstrates the importance of early epidemiological investigation through contact tracing and provides a rationale for reassessing generation intervals, serial intervals, and ℛ estimates, for COVID-19.Significance StatementThe generation- and serial-interval distributions are key, but different, quantities in outbreak analyses. Recent theoretical studies suggest that two distributions give different estimates of the reproduction number ℛ from the exponential growth rate r; however, both intervals, by definition, describe disease transmission at the individual level. Here, we show that the serial-interval distribution, defined from the correct reference time and cohort, gives the same estimate of ℛ as the generation-interval distribution. We then apply our framework to serial-interval data from the COVID-19 outbreak in China. While our study supports the use of serial-interval distributions in estimating ℛ, it also reveals necessary changes to the current understanding and applications of serial-interval distribution.

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First Consistent Determination of the Basic Reproduction Number for the First Covid-19 Wave in 71 Countries from the SIR-Epidemics Model with a Constant Ratio of Recovery to Infection Rate

Global Journal of Science Frontier Research ◽

10.34257/gjsfrfvol20is8pg37 ◽

2020 ◽

pp. 37-43

Author(s):

R. Schlickeiser ◽

M. Kröger

Keyword(s):

Infection Rate ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Simple Relation ◽

Reproduction Numbers ◽

Serial Interval ◽

Reproduction Factor ◽

Interval Distribution ◽

The Basic Reproduction Number

The box-shaped serial interval distribution and the analytical solution of the Susceptible Infectious-Recovered (SIR)-epidemics model with a constant time-independent ratio of the recovery (μ0) to infection rate (a0) are used to calculate the effective reproduction factor and the basic reproduction number R0. The latter depends on the positively valued net infection number x = 13.5(a0 − μ0) as R0(x) = x(1 − e−x)−1 which for all values of x is greater unity. This dependence differs from the simple relation R0 = a0/μ0. With the earlier determination of the values of k and a0 of the Covid-19 pandemic waves in 71 countries the net infection rates and the basic reproduction numbers for these countries are calculated.

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Serial interval and generation interval for respectively the imported and local infectors estimated using reported contact-tracing data of COVID-19 in China

10.1101/2020.04.15.20065946 ◽

2020 ◽

Cited By ~ 3

Author(s):

Menghui Li ◽

Kai Liu ◽

Yukun Song ◽

Ming Wang ◽

Jinshan Wu

Keyword(s):

Reproduction Number ◽

Contact Tracing ◽

Time Varying ◽

Generation Interval ◽

2Nd Generation ◽

Serial Interval ◽

Interval Censored ◽

Imported Cases ◽

Emerging Virus ◽

Censored Likelihood

AbstractBackgroundsThe emerging virus, COVID-19, has caused a massive out-break worldwide. Based on the publicly available contact-tracing data, we identified 337 transmission chains from 10 provinces in China and estimated the serial interval (SI) and generation interval (GI) of COVID-19 in China.MethodsInspired by possibly different 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 others transmissions among 2+ generations. The corresponding SI (GI) is respec-tively denoted as , and . A Bayesian approach with doubly interval-censored likelihood is employed to fit the lognormal, gamma, and Weibull distribution function of the SI and GI using the identified 337 transmission chains.FindingsIt is found that the estimated , and , thus overall both SI and GI decrease when generation increases.

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Transmission dynamics of the delta variant of SARS-CoV-2 infections in Daejeon, South Korea

10.21203/rs.3.rs-934350/v1 ◽

2021 ◽

Author(s):

Hari Hwang ◽

Jun-Sik Lim ◽

Sun-Ah Song ◽

Chiara Achangwa ◽

Woobeom Sim ◽

...

Keyword(s):

South Korea ◽

Symptom Onset ◽

Credible Interval ◽

Transmission Dynamics ◽

Contact Tracing ◽

Nasopharyngeal Swab ◽

Strict Adherence ◽

Virus Shedding ◽

Viral Shedding ◽

Asymptomatic Patients

Abstract Background The delta variant of SARS-CoV-2 is now the predominant variant worldwide. However, its transmission dynamics remain unclear. Methods We analyzed all case patients in local clusters and temporal patterns of viral shedding using contact tracing data from 405 cases associated with the delta variant of SARS-CoV-2 between 22 June and 31 July 2021 in Daejeon, South Korea. Results Overall, half of the cases were aged under 19 years, and 20% were asymptomatic at the time of epidemiological investigation. We estimated the mean serial interval as 3.26 days (95% credible interval 2.92, 3.60), and 12% of the transmission occurred before symptom onset of the infector. We identified six clustered outbreaks, and all were associated with indoor facilities. In 23 household contacts, the secondary attack rate was 63% (52/82). We estimated that 15% (95% confidence interval, 13–18%) of cases seeded 80% of all local transmission. Analysis of the nasopharyngeal swab samples identified virus shedding from asymptomatic patients, and the highest viral load was observed two days after symptom onset. The temporal pattern of viral shedding did not differ between children and adults (P = 0.48). Conclusions Our findings suggest that the delta variant is highly transmissible in indoor settings and households. Rapid contact tracing, isolation of the asymptomatic contacts, and strict adherence to public health measures are needed to mitigate the community transmission of the delta variant.

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