Low dispersion in the infectiousness of COVID-19 cases implies difficulty in control

Estimating the reproduction number and transmission heterogeneity from the size distribution of clusters of identical pathogen sequences

Quantifying transmission intensity and heterogeneity is crucial to ascertain the threat posed by infectious diseases and inform the design of interventions. Methods that jointly estimate the reproduction number R and the dispersion parameter k have however mainly remained limited to the analysis of epidemiological clusters or contact tracing data, whose collection often proves difficult. Here, we show that clusters of identical sequences are imprinted by the pathogen offspring distribution, and we derive an analytical formula for the distribution of the size of these clusters. We develop and evaluate an inference framework to jointly estimate the reproduction number and the dispersion parameter from the size distribution of clusters of identical sequences. We then illustrate its application across a range of epidemiological situations. Finally, we develop a hypothesis testing framework relying on clusters of identical sequences to determine whether a given pathogen genetic subpopulation is associated with increased or reduced transmissibility. Our work provides tools to estimate the reproduction number and transmission heterogeneity from pathogen sequences without building a phylogenetic tree, thus making it easily scalable to large pathogen genome datasets.

Quantitatively assessing early detection strategies for mitigating COVID-19 and future pandemics

Researchers and policymakers have proposed systems to detect novel pathogens earlier than existing surveillance systems by monitoring samples from hospital patients, wastewater, and air travel, in order to mitigate future pandemics. How much benefit would such systems offer? We developed, empirically validated, and mathematically characterized a quantitative model that simulates disease spread and detection time for any given disease and detection system. We find that hospital monitoring could have detected COVID-19 in Wuhan 0.4 weeks earlier than it was actually discovered, at 2,300 cases (standard error: 76 cases) compared to 3,400 (standard error: 161 cases). Wastewater monitoring would not have accelerated COVID-19 detection in Wuhan, but provides benefit in smaller catchments and for asymptomatic or long-incubation diseases like polio or HIV/AIDS. Monitoring of air travel provides little benefit in most scenarios we evaluated. In sum, early detection systems can substantially mitigate some future pandemics, but would not have changed the course of COVID-19.

Superspreading, overdispersion and their implications in the SARS-CoV-2 (COVID-19) pandemic: a systematic review and meta-analysis of the literature

BACKGROUND

A recurrent feature of infectious diseases is the observation that different individuals show different levels of secondary transmission. This inter-individual variation in transmission potential is often quantified by the dispersion parameter k. Low values of k indicate a high degree of variability and a greater probability of superspreading events. Understanding k for COVID-19 across contexts can assist policy makers prepare for future pandemics.

METHODS

A literature search following a systematic approach was carried out in PubMed, Embase, Web of Science, Cochrane Library, medRxiv, bioRxiv and arXiv to identify publications containing epidemiological findings on superspreading in COVID-19. Study characteristics, epidemiological data, including estimates for k and R0, and public health recommendations were extracted from relevant records.

RESULTS

The literature search yielded 28 peer-reviewed studies. The mean k estimates ranged from 0.04 to 2.97. Among the 28 studies, 93% reported mean k estimates lower than one, which is considered as marked heterogeneity in inter-individual transmission potential. Recommended control measures were specifically aimed at preventing superspreading events. The combination of forward and backward contact tracing, timely confirmation of cases, rapid case isolation, vaccination and preventive measures were suggested as important components to suppress superspreading.

CONCLUSIONS

Superspreading events were a major feature in the pandemic of SARS-CoV-2. On the one hand, this made outbreaks potentially more explosive but on the other hand also more responsive to public health interventions. Going forward, understanding k is critical for tailoring public health measures to high-risk groups and settings where superspreading events occur.

Systematic review and meta-analyses of superspreading of SARS-CoV-2 infections

Superspreading, or overdispersion in transmission, is a feature of SARS-CoV-2 transmission which results in surging epidemics and large clusters of infection. The dispersion parameter is a statistical parameter used to characterize and quantify heterogeneity. In the context of measuring transmissibility, it is analogous to measures of superspreading potential among populations by assuming that collective offspring distribution follows a negative-binomial distribution. We conducted a systematic review and meta-analysis on globally reported dispersion parameters of SARS-CoV-2 infection. All searches were carried out on 10 September 2021 in PubMed for articles published from 1 January 2020 to 10 September 2021. Multiple estimates of the dispersion parameter have been published for 17 studies, which could be related to where and when the data were obtained, in 8 countries (e.g. China, the United States, India, Indonesia, Israel, Japan, New Zealand and Singapore). High heterogeneity was reported among the included studies. The mean estimates of dispersion parameters range from 0.06 to 2.97 over eight countries, the pooled estimate was 0.55 (95% CI: 0.30, 0.79), with changing means over countries and decreasing slightly with the increasing reproduction number. The expected proportion of cases accounting for 80% of all transmissions is 19% (95% CrI: 7, 34) globally. The study location and method were found to be important drivers for diversity in estimates of dispersion parameters. While under high potential of superspreading, larger outbreaks could still occur with the import of the COVID-19 virus by traveling even when an epidemic seems to be under control.

A quantitative method to project the probability of the end of an epidemic: Application to the COVID-19 outbreak in Wuhan, 2020

The end-of-outbreak declaration is an important part of epidemic control, marking the relaxation or cancellation of prevention and control measures. We propose a probability model to retrospectively quantify the confidence of giving the end-of-outbreak declaration during the COVID-19 epidemic in early 2020 in Wuhan. By using the linear spline, we firstly estimates the time-varying proportion of cases who miss the nonpharmaceutical interventions (NPIs) among all reported cases. Assuming the reproduction numbers being 1.5, 2.0, 3.0, 4.0, 5.0 and 6.0, the respective probability of the end of the COVID-19 outbreak with time after the last reported case can be iteratively computed. Consequently, the varying reproduction numbers produce slightly different increasing patterns of NPI effectiveness, and the end-of-outbreak declarations with 95% confidence are projected consistently earlier than the day when the lockdown was actually lifted. The reason for the timing discrepancy is discussed as well.

Characterizing superspreading potential of infectious disease: Decomposition of individual transmissibility

In the context of infectious disease transmission, high heterogeneity in individual infectiousness indicates that a few index cases can generate large numbers of secondary cases, a phenomenon commonly known as superspreading. The potential of disease superspreading can be characterized by describing the distribution of secondary cases (of each seed case) as a negative binomial (NB) distribution with the dispersion parameter, k. Based on the feature of NB distribution, there must be a proportion of individuals with individual reproduction number of almost 0, which appears restricted and unrealistic. To overcome this limitation, we generalized the compound structure of a Poisson rate and included an additional parameter, and divided the reproduction number into independent and additive fixed and variable components. Then, the secondary cases followed a Delaporte distribution. We demonstrated that the Delaporte distribution was important for understanding the characteristics of disease transmission, which generated new insights distinct from the NB model. By using real-world dataset, the Delaporte distribution provides improvements in describing the distributions of COVID-19 and SARS cases compared to the NB distribution. The model selection yielded increasing statistical power with larger sample sizes as well as conservative type I error in detecting the improvement in fitting with the likelihood ratio (LR) test. Numerical simulation revealed that the control strategy-making process may benefit from monitoring the transmission characteristics under the Delaporte framework. Our findings highlighted that for the COVID-19 pandemic, population-wide interventions may control disease transmission on a general scale before recommending the high-risk-specific control strategies.

Superspreading is one of the key transmission features of many infectious diseases and is considered a consequence of the heterogeneity in infectiousness of individual cases. To characterize the superspreading potential, we divided individual infectiousness into two independent and additive components, including a fixed baseline and a variable part. Such decomposition produced an improvement in the fit of the model explaining the distribution of real-world datasets of COVID-19 and SARS that can be captured by the classic statistical tests. Disease control strategies may be developed by monitoring the characteristics of superspreading. For the COVID-19 pandemic, population-wide interventions are suggested first to limit the transmission at a scale of general population, and then high-risk-specific control strategies are recommended subsequently to lower the risk of superspreading.

The co-circulating transmission dynamics of SARS-CoV-2 Alpha and Eta variants in Nigeria: A retrospective modeling study of COVID-19

BACKGROUND

The COVID-19 pandemic poses serious threats to public health globally, and the emerging mutations in SARS-CoV-2 genomes has become one of the major challenges of disease control. In the second epidemic wave in Nigeria, the roles of co-circulating SARS-CoV-2 Alpha (ie, B.1.1.7) and Eta (ie, B.1.525) variants in contributing to the epidemiological outcomes were of public health concerns for investigation.

METHODS

We developed a mathematical model to capture the transmission dynamics of different types of strains in Nigeria. By fitting to the national-wide COVID-19 surveillance data, the transmission advantages of SARS-CoV-2 variants were estimated by likelihood-based inference framework.

RESULTS

The reproduction numbers were estimated to decrease steadily from 1.5 to 0.8 in the second epidemic wave. In December 2020, when both Alpha and Eta variants were at low prevalent levels, their transmission advantages (against the wild type) were estimated at 1.51 (95% credible intervals (CrI) = 1.48, 1.54), and 1.56 (95% CrI = 1.54, 1.59), respectively. In January 2021, when the original variants almost vanished, we estimated a weak but significant transmission advantage of Eta against Alpha variants with 1.14 (95% CrI = 1.11, 1.16).

CONCLUSIONS

Our findings suggested evidence of the transmission advantages for both Alpha and Eta variants, of which Eta appeared slightly more infectious than Alpha. We highlighted the critical importance of COVID-19 control measures in mitigating the outbreak size and relaxing the burdens to health care systems in Nigeria.

Characterization of Unlinked Cases of COVID-19 and Implications for Contact Tracing Measures: Retrospective Analysis of Surveillance Data

BACKGROUND

Contact tracing and intensive testing programs are essential for controlling the spread of COVID-19. However, conventional contact tracing is resource intensive and may not result in the tracing of all cases due to recall bias and cases not knowing the identity of some close contacts. Few studies have reported the epidemiological features of cases not identified by contact tracing ("unlinked cases") or described their potential roles in seeding community outbreaks.

OBJECTIVE

For this study, we characterized the role of unlinked cases in the epidemic by comparing their epidemiological profile with the linked cases; we also estimated their transmission potential across different settings.

METHODS

We obtained rapid surveillance data from the government, which contained the line listing of COVID-19 confirmed cases during the first three waves in Hong Kong. We compared the demographics, history of chronic illnesses, epidemiological characteristics, clinical characteristics, and outcomes of linked and unlinked cases. Transmission potentials in different settings were assessed by fitting a negative binomial distribution to the observed offspring distribution.

RESULTS

Time interval from illness onset to hospital admission was longer among unlinked cases than linked cases (median 5.00 days versus 3.78 days; P<.001), with a higher proportion of cases whose condition was critical or serious (13.0% versus 8.2%; P<.001). The proportion of unlinked cases was associated with an increase in the weekly number of local cases (P=.049). Cluster transmissions from the unlinked cases were most frequently identified in household settings, followed by eateries and workplaces, with the estimated probability of cluster transmissions being around 0.4 for households and 0.1-0.3 for the latter two settings.

CONCLUSIONS

The unlinked cases were positively associated with time to hospital admission, severity of infection, and epidemic size-implying a need to design and implement digital tracing methods to complement current conventional testing and tracing. To minimize the risk of cluster transmissions from unlinked cases, digital tracing approaches should be effectively applied in high-risk socioeconomic settings, and risk assessments should be conducted to review and adjust the policies.

Contact tracing is an imperfect tool for controlling COVID-19 transmission and relies on population adherence

Emerging evidence suggests that contact tracing has had limited success in the UK in reducing the R number across the COVID-19 pandemic. We investigate potential pitfalls and areas for improvement by extending an existing branching process contact tracing model, adding diagnostic testing and refining parameter estimates. Our results demonstrate that reporting and adherence are the most important predictors of programme impact but tracing coverage and speed plus diagnostic sensitivity also play an important role. We conclude that well-implemented contact tracing could bring small but potentially important benefits to controlling and preventing outbreaks, providing up to a 15% reduction in R. We reaffirm that contact tracing is not currently appropriate as the sole control measure.

Superspreading and heterogeneity in transmission of SARS, MERS, and COVID-19: A systematic review

BACKGROUND

Severe acute respiratory syndrome (SARS), Middle East respiratory syndrome (MERS), and coronavirus disease 2019 (COVID-19) have caused substantial public health burdens and global health threats. Understanding the superspreading potentials of these viruses are important for characterizing transmission patterns and informing strategic decision-making in disease control. This systematic review aimed to summarize the existing evidence on superspreading features and to compare the heterogeneity in transmission within and among various betacoronavirus epidemics of SARS, MERS and COVID-19.

METHODS

PubMed, MEDLINE, and Embase databases were extensively searched for original studies on the transmission heterogeneity of SARS, MERS, and COVID-19 published in English between January 1, 2003, and February 10, 2021. After screening the articles, we extracted data pertaining to the estimated dispersion parameter (k) which has been a commonly-used measurement for superspreading potential.

FINDINGS

We included a total of 60 estimates of transmission heterogeneity from 26 studies on outbreaks in 22 regions. The majority (90%) of the k estimates were small, with values less than 1, indicating an over-dispersed transmission pattern. The point estimates of k for SARS and MERS ranged from 0.12 to 0.20 and from 0.06 to 2.94, respectively. Among 45 estimates of individual-level transmission heterogeneity for COVID-19 from 17 articles, 91% were derived from Asian regions. The point estimates of k for COVID-19 ranged between 0.1 and 5.0.

CONCLUSIONS

We detected a substantial over-dispersed transmission pattern in all three coronaviruses, while the k estimates varied by differences in study design and public health capacity. Our findings suggested that even with a reduced R value, the epidemic still has a high resurgence potential due to transmission heterogeneity.

Anti-clustering in the national SARS-CoV-2 daily infection counts

The noise in daily infection counts of an epidemic should be super-Poissonian due to intrinsic epidemiological and administrative clustering. Here, we use this clustering to classify the official national SARS-CoV-2 daily infection counts and check for infection counts that are unusually anti-clustered. We adopt a one-parameter model of ϕ i ' infections per cluster, dividing any daily count n i into n i / ϕ i ' 'clusters', for 'country' i. We assume thatn i / ϕ i ' on a given day j is drawn from a Poisson distribution whose mean is robustly estimated from the four neighbouring days, and calculate the inferred Poisson probability P i j ' of the observation. The P i j ' values should be uniformly distributed. We find the value ϕ i that minimises the Kolmogorov-Smirnov distance from a uniform distribution. We investigate the (ϕ i , N i ) distribution, for total infection count N i . We consider consecutive count sequences above a threshold of 50 daily infections. We find that most of the daily infection count sequences are inconsistent with a Poissonian model. Most are found to be consistent with the ϕ i model. The 28-, 14- and 7-day least noisy sequences for several countries are best modelled as sub-Poissonian, suggesting a distinct epidemiological family. The 28-day least noisy sequence of Algeria has a preferred model that is strongly sub-Poissonian, with ϕ i 28 < 0.1 . Tajikistan, Turkey, Russia, Belarus, Albania, United Arab Emirates and Nicaragua have preferred models that are also sub-Poissonian, with ϕ i 28 < 0.5 . A statistically significant (P τ < 0.05) correlation was found between the lack of media freedom in a country, as represented by a high Reporters sans frontieres Press Freedom Index (PFI2020), and the lack of statistical noise in the country's daily counts. The ϕ i model appears to be an effective detector of suspiciously low statistical noise in the national SARS-CoV-2 daily infection counts.

Ambient temperature and subsequent COVID-19 mortality in the OECD countries and individual United States

Epidemiological studies have yielded conflicting results regarding climate and incident SARS-CoV-2 infection, and seasonality of infection rates is debated. Moreover, few studies have focused on COVD-19 deaths. We studied the association of average ambient temperature with subsequent COVID-19 mortality in the OECD countries and the individual United States (US), while accounting for other important meteorological and non-meteorological co-variates. The exposure of interest was average temperature and other weather conditions, measured at 25 days prior and 25 days after the first reported COVID-19 death was collected in the OECD countries and US states. The outcome of interest was cumulative COVID-19 mortality, assessed for each region at 25, 30, 35, and 40 days after the first reported death. Analyses were performed with negative binomial regression and adjusted for other weather conditions, particulate matter, sociodemographic factors, smoking, obesity, ICU beds, and social distancing. A 1 °C increase in ambient temperature was associated with 6% lower COVID-19 mortality at 30 days following the first reported death (multivariate-adjusted mortality rate ratio: 0.94, 95% CI 0.90, 0.99, p = 0.016). The results were robust for COVID-19 mortality at 25, 35 and 40 days after the first death, as well as other sensitivity analyses. The results provide consistent evidence across various models of an inverse association between higher average temperatures and subsequent COVID-19 mortality rates after accounting for other meteorological variables and predictors of SARS-CoV-2 infection or death. This suggests potentially decreased viral transmission in warmer regions and during the summer season.

Modeling of suppression and mitigation interventions in the COVID-19 epidemics

Background

The global spread of the COVID-19 pandemic has become the most fundamental threat to human health. In the absence of vaccines and effective therapeutical solutions, non-pharmaceutic intervention has become a major way for controlling the epidemic. Gentle mitigation interventions are able to slow down the epidemic but not to halt it well. While strict suppression interventions are efficient for controlling the epidemic, long-term measures are likely to have negative impacts on economics and people’s daily live. Hence, dynamically balancing suppression and mitigation interventions plays a fundamental role in manipulating the epidemic curve.

Methods

We collected data of the number of infections for several countries during the COVID-19 pandemics and found a clear phenomenon of periodic waves of infection. Based on the observation, by connecting the infection level with the medical resources and a tolerance parameter, we propose a mathematical model to understand impacts of combining intervention measures on the epidemic dynamics.

Results

Depending on the parameters of the medical resources, tolerance level, and the starting time of interventions, the combined intervention measure dynamically changes with the infection level, resulting in a periodic wave of infections controlled below an accepted level. The study reveals that, (a) with an immediate, strict suppression, the numbers of infections and deaths are well controlled with a significant reduction in a very short time period; (b) an appropriate, dynamical combination of suppression and mitigation may find a feasible way in reducing the impacts of epidemic on people’s live and economics.

Conclusions

While the assumption of interventions deployed with a cycle of period in the model is limited and unrealistic, the phenomenon of periodic waves of infections in reality is captured by our model. These results provide helpful insights for policy-makers to dynamically deploy an appropriate intervention strategy to effectively battle against the COVID-19.

Long, thin transmission chains of Severe Acute Respiratory Syndrome Coronavirus 2 may go undetected for several weeks at low to moderate reproduction numbers: Implications for containment and elimination strategy

Severe Acute Respiratory Syndrome Coronavirus 1 (SARS-CoV-1) infections almost always caused overt symptoms, so effective case and contact management enabled its effective eradication within months. However, Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) usually causes only mild symptoms, so transmission chains may grow to include several individuals before at least one index case becomes ill enough to self-report for diagnosis and care. Here, simple mathematical models were developed to evaluate the implications of delayed index case detection for retrospective contact tracing and management responses. Specifically, these simulations illustrate how: (1) Contact tracing and management may effectively contain most but not all large SARS-CoV-2 clusters arising at foci with high reproduction numbers because rapidly expanding transmission chains ensure at least one overtly symptomatic index case occurs within two viral generations a week or less apart. (2) However, lower reproduction numbers give rise to thinner transmission chains extending through longer sequences of non-reporting asymptomatic and paucisymptomatic individuals, often spanning three or more viral generations (≥2 weeks of transmission) before an overtly symptomatic index case occurs. (3) Consequently, it is not always possible to fully trace and contain such long, thin transmission chains, so the community transmission they give rise to is underrepresented in surveillance data. (4) Wherever surveillance systems are weak and/or transmission proceeds within population groups with lower rates of overt clinical symptoms and/or self-reporting, case and contact management effectiveness may be more severely limited, even at the higher reproduction numbers associated with larger outbreaks. (5) Because passive surveillance platforms may be especially slow to detect the thinner transmission chains that occur at low reproduction numbers, establishing satisfactory confidence of elimination may require that no confirmed cases are detected for two full months, throughout which presumptive preventative measures must be maintained to ensure complete collapse of undetected residual transmission. (6) Greater scope exists for overcoming these limitations by enhancing field surveillance for new suspected cases than by improving diagnostic test sensitivity. (7) While population-wide active surveillance may enable complete traceability and containment, this goal may also be achievable through enhanced passive surveillance for paucisymptomatic infections, combining readily accessible decentralized testing with population hypersensitization to self-reporting with mild symptoms. Containment and elimination of SARS-CoV-2 will rely far more upon presumptive, population-wide prevention measures than was necessary for SARS-CoV-1, necessitating greater ambition, political will, investment, public support, persistence and patience. Nevertheless, case and contact management may be invaluable for at least partially containing SARS-CoV-2 transmission, especially larger outbreaks, but only if enabled by sufficiently sensitive surveillance. Furthermore, consistently complete transmission chain containment may be enabled by focally enhanced surveillance around manageably small numbers of outbreaks in the end stages of successful elimination campaigns, so that their endpoints may be accelerated and sustained.

Inferencing superspreading potential using zero-truncated negative binomial model: exemplification with COVID-19

Background

In infectious disease transmission dynamics, the high heterogeneity in individual infectiousness indicates that few index cases generate large numbers of secondary cases, which is commonly known as superspreading events. The heterogeneity in transmission can be measured by describing the distribution of the number of secondary cases as a negative binomial (NB) distribution with dispersion parameter, k. However, such inference framework usually neglects the under-ascertainment of sporadic cases, which are those without known epidemiological link and considered as independent clusters of size one, and this may potentially bias the estimates.

Methods

In this study, we adopt a zero-truncated likelihood-based framework to estimate k. We evaluate the estimation performance by using stochastic simulations, and compare it with the baseline non-truncated version. We exemplify the analytical framework with three contact tracing datasets of COVID-19.

Results

We demonstrate that the estimation bias exists when the under-ascertainment of index cases with 0 secondary case occurs, and the zero-truncated inference overcomes this problem and yields a less biased estimator of k. We find that the k of COVID-19 is inferred at 0.32 (95%CI: 0.15, 0.64), which appears slightly smaller than many previous estimates. We provide the simulation codes applying the inference framework in this study.

Conclusions

The zero-truncated framework is recommended for less biased transmission heterogeneity estimates. These findings highlight the importance of individual-specific case management strategies to mitigate COVID-19 pandemic by lowering the transmission risks of potential super-spreaders with priority.

A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic

In this paper, we propose a mathematical model to assess the impacts of using face masks, hospitalization of symptomatic individuals and quarantine of asymptomatic individuals in combating the COVID-19 pandemic in India. We calibrate the proposed model to fit the four data sets, viz. data for the states of Maharashtra, Delhi, Tamil Nadu and overall India, and estimate the rate of infection of susceptible with symptomatic population and recovery rate of quarantined individuals. We also estimate basic reproduction number to illustrate the epidemiological status of the regions under study. Our simulations infer that the infective population will be on increasing curve for Maharashtra and India, and settling for Tamil Nadu and Delhi. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected individuals. Our results reveal that to curtail the disease burden in India, specific control strategies should be implemented effectively so that the basic reproduction number is decreased below unity. The three control strategies are shown to be important preventive measures to lower disease transmission rate. The model is further extended to its stochastic counterpart to encapsulate the variation or uncertainty observed in the disease transmissibility. We observe the variability in the infective population and found their distribution at certain fixed time, which shows that for small populations, the stochasticity will play an important role.