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

2020 ◽  
Vol 118 (2) ◽  
pp. e2011548118
Author(s):  
Sang Woo Park ◽  
Kaiyuan Sun ◽  
David Champredon ◽  
Michael Li ◽  
Benjamin M. Bolker ◽  
...  

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.

2020 ◽  
Vol 25 (17) ◽  
Author(s):  
Tapiwa Ganyani ◽  
Cécile Kremer ◽  
Dongxuan Chen ◽  
Andrea Torneri ◽  
Christel Faes ◽  
...  

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.


Author(s):  
Ganyani Tapiwa ◽  
Kremer Cécile ◽  
Chen Dongxuan ◽  
Torneri Andrea ◽  
Faes Christel ◽  
...  

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.


2020 ◽  
Author(s):  
Mary Bushman ◽  
Colin Worby ◽  
Hsiao-Han Chang ◽  
Moritz Kraemer ◽  
William P. Hanage

AbstractNonpharmaceutical interventions, such as contact tracing and quarantine, are currently the primary means of controlling the spread of SARS-CoV-2; however, it remains uncertain which interventions are most effective at reducing transmission at the population level. Using serial interval data from before and after the rollout of nonpharmaceutical interventions in China, we estimate that the relative frequency of presymptomatic transmission increased from 34% before the rollout to 71% afterward. The shift touward earlier transmission indicates a disproportionate reduction in transmission post-symptom onset. We estimate that, following the rollout of nonpharmaceutical interventions, transmission post-symptom onset was reduced by 82% whereas presymptomatic transmission decreased by only 16%. These findings suggest that interventions which limit opportunities for transmission in the later stages of infection, such as contact tracing and isolation, may have been particularly effective at reducing transmission of SARS-CoV-2.


Author(s):  
Mary Bushman ◽  
Colin Worby ◽  
Hsiao-Han Chang ◽  
Moritz U. G. Kraemer ◽  
William P. Hanage

AbstractNonpharmaceutical interventions, such as contact tracing and quarantine, have been the primary means of controlling the spread of SARS-CoV-2; however, it remains uncertain which interventions are most effective at reducing transmission at the population level. Using serial interval data from before and after the rollout of nonpharmaceutical interventions in China, we estimate that the relative frequency of presymptomatic transmission increased from 34% before the rollout to 71% afterward. The shift toward earlier transmission indicates a disproportionate reduction in transmission post-symptom onset. We estimate that, following the rollout of nonpharmaceutical interventions, transmission post-symptom onset was reduced by 82% whereas presymptomatic transmission decreased by only 16%. The observation that only one-third of transmission was presymptomatic at baseline, combined with the finding that NPIs reduced presymptomatic transmission by less than 20%, suggests that the overall impact of NPIs was driven in large part by reductions in transmission following symptom onset. This implies that interventions which limit opportunities for transmission in the later stages of infection, such as contact tracing and isolation, are particularly important for control of SARS-CoV-2. Interventions which specifically reduce opportunities for presymptomatic transmission, such as quarantine of asymptomatic contacts, are likely to have smaller, but non-negligible, effects on overall transmission.


2020 ◽  
Author(s):  
Sang Woo Park ◽  
Kaiyuan Sun ◽  
David Champredon ◽  
Michael Li ◽  
Benjamin M. Bolker ◽  
...  

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.


2020 ◽  
Author(s):  
Mohak Gupta ◽  
Giridara G Parameswaran ◽  
Manraj S Sra ◽  
Rishika Mohanta ◽  
Devarsh Patel ◽  
...  

Brief AbstractWe analysed SARS-CoV-2 surveillance and contact tracing data from Karnataka, India up to 21 July 2020. We estimated metrics of infectiousness and the tendency for superspreading (overdispersion), and evaluated potential determinants of infectiousness and symptomaticity in COVID-19 cases. Among 956 cases confirmed to be forward-traced, 8.7% of index cases had 14.4% of contacts but caused 80% of all secondary cases, suggesting significant heterogeneity in individual-level transmissibility of SARS-CoV-2 which could not be explained by the degree of heterogeneity in underlying number of contacts. Secondary attack rate was 3.6% among 16715 close contacts. Transmission was higher when index case was aged >18 years, or was symptomatic (adjusted risk ratio, aRR 3.63), or was lab-confirmed ≥4 days after symptom onset (aRR 3.01). Probability of symptomatic infection increased with age, and symptomatic infectors were 8.16 times more likely to generate symptomatic secondaries. This could potentially cause a snowballing effect on infectiousness and clinical severity across transmission generations; further studies are suggested to confirm this. Mean serial interval was 5.4 days. Adding backward contact tracing and targeting control measures to curb super-spreading may be prudent. Due to low symptomaticity and infectivity, interventions aimed at children might have a relatively small impact on reducing transmission.Structured AbstractBackgroundIndia has experienced the second largest outbreak of COVID-19 globally, yet there is a paucity of studies analysing contact tracing data in the region. Such studies can elucidate essential transmission metrics which can help optimize disease control policies.MethodsWe analysed contact tracing data collected under the Integrated Disease Surveillance Programme from Karnataka, India between 9 March and 21 July 2020. We estimated metrics of disease transmission including the reproduction number (R), overdispersion (k), secondary attack rate (SAR), and serial interval. R and k were jointly estimated using a Bayesian Markov Chain Monte Carlo approach. We evaluated the effect of age and other factors on the risk of transmitting the infection, probability of asymptomatic infection, and mortality due to COVID-19.FindingsUp to 21 July, we found 111 index cases that crossed the super-spreading threshold of ≥8 secondary cases. R and k were most reliably estimated at R 0.75 (95% CI, 0.62-0.91) and k 0.12 (0.11-0.15) for confirmed traced cases (n=956); and R 0.91 (0.72-1.15) and k 0.22 (0.17-0.27) from the three largest clusters (n=394). Among 956 confirmed traced cases, 8.7% of index cases had 14.4% of contacts but caused 80% of all secondary cases. Among 16715 contacts, overall SAR was 3.6% (3.4-3.9) and symptomatic cases were more infectious than asymptomatic cases (SAR 7.7% vs 2.0%; aRR 3.63 [3.04-4.34]). As compared to infectors aged 19-44 years, children were less infectious (aRR 0.21 [0.07-0.66] for 0-5 years and 0.47 [0.32-0.68] for 6-18 years). Infectors who were confirmed ≥4 days after symptom onset were associated with higher infectiousness (aRR 3.01 [2.11-4.31]). Probability of symptomatic infection increased with age, and symptomatic infectors were 8.16 (3.29-20.24) times more likely to generate symptomatic secondaries. Serial interval had a mean of 5.4 (4.4-6.4) days with a Weibull distribution. Overall case fatality rate was 2.5% (2.4-2.7) which increased with age.ConclusionWe found significant heterogeneity in the individual-level transmissibility of SARS-CoV-2 which could not be explained by the degree of heterogeneity in the underlying number of contacts. To strengthen contact tracing in over-dispersed outbreaks, testing and tracing delays should be minimised, retrospective contact tracing should be considered, and contact tracing performance metrics should be utilised. Targeted measures to reduce potential superspreading events should be implemented. Interventions aimed at children might have a relatively small impact on reducing SARS-CoV-2 transmission owing to their low symptomaticity and infectivity. There is some evidence that symptomatic cases produce secondary cases that are more likely to be symptomatic themselves which may potentially cause a snowballing effect on infectiousness and clinical severity across transmission generations; further studies are needed to confirm this finding.FundingGiridhara R Babu is funded by an Intermediate Fellowship by the Wellcome Trust DBT India Alliance (Clinical and Public Health Research Fellowship); grant number: IA/CPHI/14/1/501499.


2021 ◽  
Vol 18 (174) ◽  
pp. 20200756
Author(s):  
Sonja Lehtinen ◽  
Peter Ashcroft ◽  
Sebastian Bonhoeffer

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.


Author(s):  
Mirjam E. Kretzschmar ◽  
Ganna Rozhnova ◽  
Martin Bootsma ◽  
Michiel van Boven ◽  
Janneke van de Wijgert ◽  
...  

SummaryBackgroundWith confirmed cases of COVID-19 declining in many countries, lockdown measures are gradually being lifted. However, even if most social distancing measures are continued, other public health measures will be needed to control the epidemic. Contact tracing via conventional methods or mobile app technology is central to control strategies during deescalation of social distancing. We aimed to identify key factors for a contact tracing strategy (CTS) to be successful.MethodsWe evaluated the impact of timeliness and completeness in various steps of a CTS using a stochastic mathematical model with explicit time delays between time of infection and symptom onset, and between symptom onset, diagnosis by testing, and isolation (testing delay). The model also includes tracing of close contacts (e.g. household members) and casual contacts, followed by testing regardless of symptoms and isolation if positive, with different delays (tracing delay) and coverages (tracing coverage). We computed effective reproduction numbers of a CTS (Rcts) for a population with social distancing measures and various scenarios for isolation of index cases and tracing and quarantine of its contacts.FindingsFor the best-case scenario (testing and tracing delays of 0 days and tracing coverage of 80%), and assuming that around 40% of transmission occur before symptom onset, the model predicts that the effective reproduction number of 1.2 (with social distancing only) will be reduced to 0.8 by adding contact tracing. A testing delay of 2 days requires tracing delay to be at most 1 day, or tracing coverage to be at least 80% to keep Rcts below 1. With a testing/isolation delay of 3 days, even the most efficient CTS cannot reach Rcts values below 1. The effect of minimizing tracing delay (e.g., with app-based technology) declines with decreasing coverage of app use, but app-based tracing alone remains more effective than conventional tracing alone even with 20% coverage. The proportion of transmissions per index case that can be prevented depends on testing and tracing delays, and ranges from up to 80% in the best-case scenario (testing and tracing delays of 0 days) to 42% with a 3-day testing delay and 18% with a 5-day testing delay.InterpretationIn our model, minimizing testing delay had the largest impact on reducing onward transmissions. Optimizing testing and tracing coverage and minimizing tracing delays, for instance with app-based technology, further enhanced CTS effectiveness, with a potential to prevent up to 80% of all transmissions. Access to testing should therefore be optimized, and mobile app technology may reduce delays in the CTS process and optimize contact tracing coverage.Research in contextEvidence before this studyWe searched PubMed, bioRxiv, and medRxiv for articles published in English from January 1, 2020, to June 20, 2020, with the following keywords: (“2019-nCoV” OR “novel coronavirus” OR “COVID-19” OR “SARS-CoV-2”) AND “contact tracing” AND “model*”. Population-level modelling studies of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have suggested that isolation and tracing alone might not be sufficient to control outbreaks and additional measures might be required. However, few studies have focused on the effects of lifting individual measures once the first wave of the epidemic has been controlled. Lifting measures must be accompanied by effective contact tracing strategies (CTS) in order to keep the effective reproduction number below 1. A detailed analysis, with special emphasis on the effects of time delays in testing of index patients and tracing of contacts, has not been done.Added value of this studyWe performed a systematic analysis of the various steps required in the process of testing and diagnosing an index case as well as tracing and isolating possible secondary cases of the index case. We then used a stochastic transmission model which makes a distinction between close contacts (e.g. household members) and casual contacts to assess which steps and (possible) delays are crucial in determining the effectiveness of CTS. We evaluated how delays and the level of contact tracing coverage influence the effective reproduction number, and how fast CTS needs to be to keep the reproduction number below 1. We also analyzed what proportion of onward transmission can be prevented for short delays and high contact tracing coverage. Assuming that around 40% of transmission occurs before symptom onset, we found that keeping the time between symptom onset and testing and isolation of an index case short (<3 days) is imperative for a successful CTS. This implies that the process leading from symptom onset to receiving a positive test should be minimized by providing sufficient and easily accessible testing facilities. In addition, reducing contact-tracing delays also helps to keep the reproduction number below 1.Implications of all the available evidenceOur analyses highlight that CTS will only contribute to containment of COVID-19 if it can be organised in a way that time delays in the process from symptom onset to isolation of the index case and his/her contacts are very short. The process of conventional contact tracing should be reviewed and streamlined, while mobile app technology may offer a tool for gaining speed in the process. Reducing delay in testing subjects for SARS-CoV-2 should be a key objective of CTS.


Author(s):  
Chong You ◽  
Yuhao Deng ◽  
Wenjie Hu ◽  
Jiarui Sun ◽  
Qiushi Lin ◽  
...  

BackgroundThe 2019-nCoV outbreak in Wuhan, China has attracted world-wide attention. As of February 11, 2020, a total of 44730 cases of novel coronavirus-infected pneumonia associated with COVID-19 were confirmed by the National Health Commission of China.MethodsThree approaches, namely Poisson likelihood-based method (ML), exponential growth rate-based method (EGR) and stochastic Susceptible-Infected-Removed dynamic model-based method (SIR), were implemented to estimate the basic and controlled reproduction numbers.ResultsA total of 71 chains of transmission together with dates of symptoms onset and 67 dates of infections were identified among 5405 confirmed cases outside Hubei as reported by February 2, 2020. Based on this information, we find the serial interval having an average of 4.41 days with a standard deviation of 3.17 days and the infectious period having an average of 10.91 days with a standard deviation of 3.95 days.ConclusionsThe controlled reproduction number is declining. It is lower than one in most regions of China, but is still larger than one in Hubei Province. Sustained efforts are needed to further reduce the Rc to below one in order to end the current epidemic.


2020 ◽  
Author(s):  
Lee Worden ◽  
Rae Wannier ◽  
Micaela Neus ◽  
Jennifer C. Kwan ◽  
Alex Y. Ge ◽  
...  

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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