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.

A fast look-up method for Bayesian mean-parameterised Conway-Maxwell-Poisson regression models.

Count data that are subject to both under and overdispersion at some hierarchical level cannot be readily accommodated by classic models such as Poisson or negative binomial regression models. The mean-parameterised Conway-Maxwell-Poisson distribution allows for both types of dispersion within the same model, but is doubly intractable with an embedded normalising constant. We propose a look-up method where pre-computing values of the rate parameter dramatically reduces computing times and renders the proposed model a practicable alternative when faced with such bidispersed data. The approach is demonstrated and verified using a simulation study and applied to three datasets: an underdispersed small dataset on takeover bids, a medium dataset on yellow cards issued by referees in the English Premier League prior to and during the Covid-19 pandemic, and a large Test match cricket bowling dataset, the latter two of which each exhibit over and underdispersion at the individual level.

Bayesian model averaging for mortality forecasting using leave-future-out validation

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Various stochastic frameworks have been developed to model mortality patterns by taking into account the main stylized facts driving these patterns. However, relying on the prediction of one specific model can be too restrictive and can lead to some well-documented drawbacks, including model misspecification, parameter uncer-tainty, and overfitting. To address these issues we first consider mortality modeling in a Bayesian negative-binomial framework to account for overdispersion and the uncer-tainty about the parameter estimates in a natural and coherent way. Model averaging techniques are then considered as a response to model misspecifications. In this paper, we propose two methods based on leave-future-out validation and compare them to standard Bayesian model averaging (BMA) based on marginal likelihood. An intensive numerical study is carried out over a large range of simulation setups to compare the performances of the proposed methodologies. An illustration is then proposed on real-life mortality datasets, along with a sensitivity analysis to a Covid-type scenario. Overall, we found that both methods based on an out-of-sample criterion outperform the standard BMA approach in terms of prediction performance and robustness.(c) 2022 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

A flexible integer-valued AR(1) process: estimation, forecasting and modeling COVID-19 data

In the present paper, we concentrate on an INAR(1) model with flexible binomial-discrete Poisson Lindley innovations (BDPLINAR(1)), which describes several attractive properties. The applicability of the proposed process is evaluated by the daily counts of the COVID-19 data sets that indicate the superiority of the BDPLINAR(1) model among some competitor models. The model adequacy checking using Pearson residuals indicates that the BDPLINAR(1) model is appropriate for modeling the COVID-19 data. Several forecasting approaches, such as the classic, mode, probability function, and modified Sieve Bootstrap methods, are considered for the COVID-19 data under the BDPLINAR(1) model. © 2023 Informa UK Limited, trading as Taylor & Francis Group.

Quantifying the Effects of Contact Tracing, Testing, and Containment Measures in the Presence of Infection Hotspots

Multiple lines of evidence strongly suggest that infection hotspots, where a single individual infects many others, play a key role in the transmission dynamics of COVID-19. However, most of the existing epidemiological models fail to capture this aspect by neither representing the sites visited by individuals explicitly nor characterizing disease transmission as a function of individual mobility patterns. In this work, we introduce a temporal point process modeling framework that specifically represents visits to the sites where individuals get in contact and infect each other. Under our model, the number of infections caused by an infectious individual naturally emerges to be overdispersed. Using an efficient sampling algorithm, we demonstrate how to estimate the transmission rate of infectious individuals at the sites they visit and in their households using Bayesian optimization (BO) and longitudinal case data. Simulations using fine-grained and publicly available demographic data and site locations from Bern, Switzerland showcase the flexibility of our framework. To facilitate research and analyses of other cities and regions, we release an open-source implementation of our framework.

COVID-19 hospitalizations and patients' age at admission: The neglected importance of data variability for containment policies.

Introduction: An excess in the daily fluctuation of COVID-19 in hospital admissions could cause uncertainty and delays in the implementation of care interventions. This study aims to characterize a possible source of extravariability in the number of hospitalizations for COVID-19 by considering age at admission as a potential explanatory factor. Age at hospitalization provides a clear idea of the epidemiological impact of the disease, as the elderly population is more at risk of severe COVID-19 outcomes. Administrative data for the Veneto region, Northern Italy from February 1, 2020, to November 20, 2021, were considered. Methods: An inferential approach based on quasi-likelihood estimates through the generalized estimation equation (GEE) Poisson link function was used to quantify the overdispersion. The daily variation in the number of hospitalizations in the Veneto region that lagged at 3, 7, 10, and 15 days was associated with the number of news items retrieved from Global Database of Events, Language, and Tone (GDELT) regarding containment interventions to determine whether the magnitude of the past variation in daily hospitalizations could impact the number of preventive policies. Results: This study demonstrated a significant increase in the pattern of hospitalizations for COVID-19 in Veneto beginning in December 2020. Age at admission affected the excess variability in the number of admissions. This effect increased as age increased. Specifically, the dispersion was significantly lower in people under 30 years of age. From an epidemiological point of view, controlling the overdispersion of hospitalizations and the variables characterizing this phenomenon is crucial. In this context, the policies should prevent the spread of the virus in particular in the elderly, as the uncontrolled diffusion in this age group would result in an extra variability in daily hospitalizations. Discussion: This study demonstrated that the overdispersion, together with the increase in hospitalizations, results in a lagged inflation of the containment policies. However, all these interventions represent strategies designed to contain a mechanism that has already been triggered. Further efforts should be directed toward preventive policies aimed at protecting the most fragile subjects, such as the elderly. Therefore, it is essential to implement containment strategies before the occurrence of potentially out-of-control situations, resulting in congestion in hospitals and health services.

SARS-CoV-2 Transmission and Prevention in the Era of the Delta Variant.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) delta variant transmits much more rapidly than prior SARS-CoV-2 viruses. The primary mode of transmission is via short range aerosols that are emitted from the respiratory tract of an index case. There is marked heterogeneity in the spread of this virus, with 10% to 20% of index cases contributing to 80% of secondary cases, while most index cases have no subsequent transmissions. Vaccination, ventilation, masking, eye protection, and rapid case identification with contact tracing and isolation can all decrease the transmission of this virus.

Bayesian negative binomial regression with spatially varying dispersion: Modeling COVID-19 incidence in Georgia.

Overdispersed count data arise commonly in disease mapping and infectious disease studies. Typically, the level of overdispersion is assumed to be constant over time and space. In some applications, however, this assumption is violated, and in such cases, it is necessary to model the dispersion as a function of time and space in order to obtain valid inferences. Motivated by a study examining spatiotemporal patterns in COVID-19 incidence, we develop a Bayesian negative binomial model that accounts for heterogeneity in both the incidence rate and degree of overdispersion. To fully capture the heterogeneity in the data, we introduce region-level covariates, smooth temporal effects, and spatially correlated random effects in both the mean and dispersion components of the model. The random effects are assigned bivariate intrinsic conditionally autoregressive priors that promote spatial smoothing and permit the model components to borrow information, which is appealing when the mean and dispersion are spatially correlated. Through simulation studies, we show that ignoring heterogeneity in the dispersion can lead to biased and imprecise estimates. For estimation, we adopt a Bayesian approach that combines full-conditional Gibbs sampling and Metropolis-Hastings steps. We apply the model to a study of COVID-19 incidence in the state of Georgia, USA from March 15 to December 31, 2020.

Lockdowns exert selection pressure on overdispersion of SARS-CoV-2 variants.

The SARS-CoV-2 ancestral strain has caused pronounced superspreading events, reflecting a disease characterized by overdispersion, where about 10% of infected people cause 80% of infections. New variants of the disease have different person-to-person variability in viral load, suggesting for example that the Alpha (B.1.1.7) variant is more infectious but relatively less prone to superspreading. Meanwhile, non-pharmaceutical mitigation of the pandemic has focused on limiting social contacts (lockdowns, regulations on gatherings) and decreasing transmission risk through mask wearing and social distancing. Using a mathematical model, we show that the competitive advantage of disease variants may heavily depend on the restrictions imposed. In particular, we find that lockdowns exert an evolutionary pressure which favours variants with lower levels of overdispersion. Our results suggest that overdispersion is an evolutionarily unstable trait, with a tendency for more homogeneously spreading variants to eventually dominate.

Analysis of overdispersion in airborne transmission of COVID-19

Superspreading events and overdispersion are hallmarks of the COVID-19 pandemic. However, the specific roles and influence of established viral and physical factors related to the mechanisms of transmission, on overdispersion, remain unresolved. We, therefore, conducted mechanistic modeling of SARS-CoV-2 point-source transmission by infectious aerosols using real-world occupancy data from more than 100 000 social contact settings in ten US metropolises. We found that 80% of secondary infections are predicted to arise from approximately 4% of index cases, which show up as a stretched tail in the probability density function of secondary infections per infectious case. Individual-level variability in viral load emerges as the dominant driver of overdispersion, followed by occupancy. We then derived an analytical function, which replicates the simulated overdispersion, and with which we demonstrate the effectiveness of potential mitigation strategies. Our analysis, connecting the mechanistic understanding of SARS-CoV-2 transmission by aerosols with observed large-scale epidemiological characteristics of COVID-19 outbreaks, adds an important dimension to the mounting body of evidence with regard to airborne transmission of SARS-CoV-2 and thereby emerges as a powerful tool toward assessing the probability of outbreaks and the potential impact of mitigation strategies on large scale disease dynamics. © 2022 Author(s).

Distributed Quasi-Poisson regression algorithm for modeling multi-site count outcomes in distributed data networks.

BACKGROUND: Observational studies incorporating real-world data from multiple institutions facilitate study of rare outcomes or exposures and improve generalizability of results. Due to privacy concerns surrounding patient-level data sharing across institutions, methods for performing regression analyses distributively are desirable. Meta-analysis of institution-specific estimates is commonly used, but has been shown to produce biased estimates in certain settings. While distributed regression methods are increasingly available, methods for analyzing count outcomes are currently limited. Count data in practice are commonly subject to overdispersion, exhibiting greater variability than expected under a given statistical model. OBJECTIVE: We propose a novel computational method, a one-shot distributed algorithm for quasi-Poisson regression (ODAP), to distributively model count outcomes while accounting for overdispersion. METHODS: ODAP incorporates a surrogate likelihood approach to perform distributed quasi-Poisson regression without requiring patient-level data sharing, only requiring sharing of aggregate data from each participating institution. ODAP requires at most three rounds of non-iterative communication among institutions to generate coefficient estimates and corresponding standard errors. In simulations, we evaluate ODAP under several data scenarios possible in multi-site analyses, comparing ODAP and meta-analysis estimates in terms of error relative to pooled regression estimates, considered the gold standard. In a proof-of-concept real-world data analysis, we similarly compare ODAP and meta-analysis in terms of relative error to pooled estimatation using data from the OneFlorida Clinical Research Consortium, modeling length of stay in COVID-19 patients as a function of various patient characteristics. In a second proof-of-concept analysis, using the same outcome and covariates, we incorporate data from the UnitedHealth Group Clinical Discovery Database together with the OneFlorida data in a distributed analysis to compare estimates produced by ODAP and meta-analysis. RESULTS: In simulations, ODAP exhibited negligible error relative to pooled regression estimates across all settings explored. Meta-analysis estimates, while largely unbiased, were increasingly variable as heterogeneity in the outcome increased across institutions. When baseline expected count was 0.2, relative error for meta-analysis was above 5% in 25% of iterations (250/1000), while the largest relative error for ODAP in any iteration was 3.59%. In our proof-of-concept analysis using only OneFlorida data, ODAP estimates were closer to pooled regression estimates than those produced by meta-analysis for all 15 covariates. In our distributed analysis incorporating data from both OneFlorida and the UnitedHealth Group Clinical Discovery Database, ODAP and meta-analysis estimates were largely similar, while some differences in estimates (as large as 13.8%) could be indicative of bias in meta-analytic estimates. CONCLUSIONS: ODAP performs privacy-preserving, communication-efficient distributed quasi-Poisson regression to analyze count outcomes using data stored within multiple institutions. Our method produces estimates nearly matching pooled regression estimates and sometimes more accurate than meta-analysis estimates, most notably in settings with relatively low counts and high outcome heterogeneity across institutions.

Analysis of Factors Influencing the COVID-19 Mortality Rate in Indonesia using Zero Inflated Negative Binomial Model

This research aims to create a model, analyze the factors that influence the COVID-19 mortality rate in Indonesia. There are five independent variables and one dependent variable used in the research. The independent variables used are the percentage of poor people, the percentage of households using shared toilet facilities, the percentage of households using wood as the main fuel for cooking, the percentage of the population whose drinking water source comes from pumped water and the percentage of population who have health insurance from private insurance. While the dependent variable used is the Annual Parasite incidence COVID-19. The results obtained are as follows. First, a Zero-Inflated Negative Binomial regression model was obtained for the case of COVID-19 morbidity where this model could overcome overdispersion and excess zero values in observations. Second, there are 4 independent variables that have a significant effect on the count model and there is no independent variable that has a significant effect on the Zero inflation model. Third, a web application is produced that can display the Zero-Inflated Negative Binomial regression model (ZINB). © 2022. All Rights Reserved.

On Discrete Poisson–Mirra Distribution: Regression, INAR(1) Process and Applications

Several pieces of research have spotlighted the importance of count data modelling and its applications in real-world phenomena. In light of this, a novel two-parameter compound-Poisson distribution is developed in this paper. Its mathematical functionalities are investigated. The two unknown parameters are estimated using both maximum likelihood and Bayesian approaches. We also offer a parametric regression model for the count datasets based on the proposed distribution. Furthermore, the first-order integer-valued autoregressive process, or INAR(1) process, is also used to demonstrate the utility of the suggested distribution in time series analysis. The unknown parameters of the proposed INAR(1) model are estimated using the conditional maximum likelihood, conditional least squares, and Yule–Walker techniques. Simulation studies for the suggested distribution and the INAR(1) model based on this innovative distribution are also undertaken as an assessment of the long-term performance of the estimators. Finally, we utilized three real datasets to depict the new model’s real-world applicability. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

The Geographically Weighted Multivariate Poisson Inverse Gaussian Regression Model and Its Applications

This study aims to develop a method for multivariate spatial overdispersion count data with mixed Poisson distribution, namely the Geographically Weighted Multivariate Poisson Inverse Gaussian Regression (GWMPIGR) model. The parameters of the GWMPIGR model are estimated locally using the maximum likelihood estimation (MLE) method by considering spatial effects. Therefore, the significance of the regression parameter differs for each location. In this study, four GWMPIGR models are evaluated based on the exposure variable and the spatial weighting function. We compare the performance of those four models in real-world application using data on the number of infant, under-5 and maternal deaths in East Java in 2019 using five predictor variables. In this study, the GWMPIGR model uses one exposure variable and three exposure variables. Compared to the fixed kernel Gaussian weighting function, the GWMPIGR model with the fixed kernel bisquare weighting function and one exposure variable has a better fit based on the AICc value. Furthermore, according to the best GWMPIGR model, there are several regional groups formed based on predictors that significantly affected each event in East Java in 2019.

Bayesian model averaging for mortality forecasting using leave-future-out validation

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Various stochastic frameworks have been developed to model mortality patterns by taking into account the main stylized facts driving these patterns. However, relying on the prediction of one specific model can be too restrictive and can lead to some well-documented drawbacks, including model misspecification, parameter uncertainty, and overfitting. To address these issues we first consider mortality modeling in a Bayesian negative-binomial framework to account for overdispersion and the uncertainty about the parameter estimates in a natural and coherent way. Model averaging techniques are then considered as a response to model misspecifications. In this paper, we propose two methods based on leave-future-out validation and compare them to standard Bayesian model averaging (BMA) based on marginal likelihood. An intensive numerical study is carried out over a large range of simulation setups to compare the performances of the proposed methodologies. An illustration is then proposed on real-life mortality datasets, along with a sensitivity analysis to a Covid-type scenario. Overall, we found that both methods based on an out-of-sample criterion outperform the standard BMA approach in terms of prediction performance and robustness.

Secondary transmission of SARS-CoV-2 during the first two waves in Japan: Demographic characteristics and overdispersion.

OBJECTIVES: Super-spreading events caused by overdispersed secondary transmission are crucial in the transmission of COVID-19. However, the exact level of overdispersion, demographics, and other factors associated with secondary transmission remain elusive. In this study, we aimed to elucidate the frequency and patterns of secondary transmission of SARS-CoV-2 in Japan. METHODS: We analyzed 16,471 cases between January 2020 and August 2020. We generated the number of secondary cases distribution and estimated the dispersion parameter (k) by fitting the negative binomial distribution in each phase. The frequencies of the secondary transmission were compared by demographic and clinical characteristics, calculating the odds ratio using logistic regression models. RESULTS: We observed that 76.7% of the primary cases did not generate secondary cases with an estimated dispersion parameter k of 0.23. The demographic patterns of primary-secondary cases differed between phases, with 20-69 years being the predominant age group. There were higher proportions of secondary transmissions among older individuals, symptomatic patients, and patients with 2 days or more between onset and confirmation. CONCLUSIONS: The study showed the estimation of the frequency of secondary transmission of SARS-CoV-2 and the characteristics of people who generated the secondary transmission.

Misspecified modeling of subsequent waves during COVID-19 outbreak: A change-point growth model.

In the analysis of cumulative counts of SARS-CoV-2 infections, such as deaths or cases, common parametric models based on log-logistic growth curves adapt well to describe a single wave at a time. Unfortunately, in Italy, as well as all over the globe, from February 2020 to March 2021 more than one wave has been observed. In this paper, we propose a method to fit more than one wave in the same model. In particular, we discuss an approach based on a change-point model in a pseudo-likelihood framework that takes into account some model misspecification issues, such as those concerning the assumption of Poisson marginals and those relating to overdispersion and autocorrelation. An application to data collected in Italy is discussed.

Type I multivariate zero-inflated COM-Poisson regression model.

In this paper, we present the Type I multivariate zero-inflated Conway-Maxwell-Poisson distribution, whose development is based on the extension of the Type I multivariate zero-inflated Poisson distribution. We developed important properties of the distribution and present a regression model. The AIC and BIC criteria are used to select the best fitted model. Two real data sets have been used to illustrate the proposed model. Moreover, we conclude by stating that the Type I multivariate zero-inflated Conway-Maxwell-Poisson distribution produces a better fitted model for multivariate count data with excess of zeros.

Increased close proximity airborne transmission of the SARS-CoV-2 Delta variant.

The Delta variant of SARS-CoV-2 causes higher viral loads in infected hosts, increasing the risk of close proximity airborne transmission through breathing, speaking and coughing. We performed a Monte Carlo simulation using a social contact network and exponential dose-response model to quantify the close proximity reproduction number of both wild-type SARS-CoV-2 and the Delta variant. We estimate more than twice as many Delta variant cases will reproduce infection in their close proximity contacts (64%) versus the wild-type SARS-CoV-2 (29%). Occupational health guidelines must consider close proximity airborne transmission and recommend improved personal respiratory protection for high-risk workers.

[SARS-CoV-2 transmission routes and implications for self- and non-self-protection]. / SARS-CoV-2-Übertragungswege und Implikationen für den Selbst- und Fremdschutz.

The global spread of the coronavirus SARS-CoV­2 has massively impacted health, economic, and social systems. Although effective vaccines are now available, it is likely that this pathogen will become endemic and stay with us for years. In order to most effectively protect others and oneself from SARS-CoV­2 infection, an understanding of how SARS-CoV­2 is transmitted is of utmost importance.In this review paper, we explain transmission routes with an eye towards protecting others and oneself. We also address characteristics of SARS-CoV­2 transmission in the community. This work will help to clarify the following questions based on the available literature: When and for how long is an infected person contagious? How is the virus excreted? How is the virus taken up? How does the virus spread in society?Human-to-human transmission of SARS-CoV­2 is strongly determined by pathogen molecular characteristics as well as the kinetics of replication, shedding, and infection. SARS-CoV­2 is transmitted primarily via human aerosols, which infected persons can excrete even if symptoms of the disease are not (yet) present. Most infected people cause only a few secondary cases, whereas a few cases (so-called super-spreaders) cause a high number of secondary infections - at the population level one speaks of a so-called "overdispersion." These special characteristics of SARS-CoV­2 (asymptomatic aerosol transmission and overdispersion) make the pandemic difficult to control.