Practical considerations for measuring the effective reproductive number, Rt

Refining reproduction number estimates to account for unobserved generations of infection in emerging epidemics

Background

Estimating the transmissibility of infectious diseases is key to inform situational awareness and for response planning. Several methods tend to overestimate the basic (R₀) and effective (R_t) reproduction numbers during the initial phases of an epidemic. In this work we explore the impact of incomplete observations and underreporting of the first generations of infections during the initial epidemic phase.

Methods

We propose a debiasing procedure that utilizes a linear exponential growth model to infer unobserved initial generations of infections and apply it to EpiEstim. We assess the performance of our adjustment using simulated data, considering different levels of transmissibility and reporting rates. We also apply the proposed correction to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) incidence data reported in Italy, Sweden, the United Kingdom, and the United States.

Results

In all simulation scenarios, our adjustment outperforms the original EpiEstim method. The proposed correction reduces the systematic bias, and the quantification of uncertainty is more precise, as better coverage of the true R₀ values is achieved with tighter credible intervals. When applied to real-world data, the proposed adjustment produces basic reproduction number estimates that closely match the estimates obtained in other studies while making use of a minimal amount of data.

Conclusions

The proposed adjustment refines the reproduction number estimates obtained with the current EpiEstim implementation by producing improved, more precise estimates earlier than with the original method. This has relevant public health implications.

A semi-parametric, state-space compartmental model with time-dependent parameters for forecasting COVID-19 cases, hospitalizations and deaths

Short-term forecasts of the dynamics of coronavirus disease 2019 (COVID-19) in the period up to its decline following mass vaccination was a task that received much attention but proved difficult to do with high accuracy. However, the availability of standardized forecasts and versioned datasets from this period allows for continued work in this area. Here, we introduce the Gaussian infection state space with time dependence (GISST) forecasting model. We evaluate its performance in one to four weeks ahead forecasts of COVID-19 cases, hospital admissions and deaths in the state of California made with official reports of COVID-19, Google’s mobility reports and vaccination data available each week. Evaluation of these forecasts with a weighted interval score shows them to consistently outperform a naive baseline forecast and often score closer to or better than a high-performing ensemble forecaster. The GISST model also provides parameter estimates for a compartmental model of COVID-19 dynamics, includes a regression submodel for the transmission rate and allows for parameters to vary over time according to a random walk. GISST provides a novel, balanced combination of computational efficiency, model interpretability and applicability to large multivariate datasets that may prove useful in improving the accuracy of infectious disease forecasts.

In-Depth Correlation Analysis of SARS-CoV-2 Effective Reproduction Number and Mobility Patterns: Three Groups of Countries

Objectives

Many governments have imposed—and are still imposing—mobility restrictions to contain the coronavirus disease 2019 (COVID-19) pandemic. However, there is no consensus on whether policy-induced reductions of human mobility effectively reduce the effective reproduction number (Rt) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Several studies based on country-restricted data reported conflicting trends in the change of the SARS-CoV-2 Rt following mobility restrictions. The objective of this study was to examine, at the global scale, the existence of regional specificities in the correlations between Rt and human mobility.

Methods

We computed the Rt of SARS-CoV-2 using data on worldwide infection cases reported by the Johns Hopkins University, and analyzed the correlation between Rt and mobility indicators from the Google COVID-19 Community Mobility Reports in 125 countries, as well as states/regions within the United States, using the Pearson correlation test, linear modeling, and quadratic modeling.

Results

The correlation analysis identified countries where Rt negatively correlated with residential mobility, as expected by policymakers, but also countries where Rt positively correlated with residential mobility and countries with more complex correlation patterns. The correlations between Rt and residential mobility were non-linear in many countries, indicating an optimal level above which increasing residential mobility is counterproductive.

Conclusions

Our results indicate that, in order to effectively reduce viral circulation, mobility restriction measures must be tailored by region, considering local cultural determinants and social behaviors. We believe that our results have the potential to guide differential refinement of mobility restriction policies at a country/regional resolution.

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

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

Overlapping timescales obscure early warning signals of the second COVID-19 wave

Early warning indicators based on critical slowing down have been suggested as a model-independent and low-cost tool to anticipate the (re)emergence of infectious diseases. We studied whether such indicators could reliably have anticipated the second COVID-19 wave in European countries. Contrary to theoretical predictions, we found that characteristic early warning indicators generally decreased rather than increased prior to the second wave. A model explains this unexpected finding as a result of transient dynamics and the multiple timescales of relaxation during a non-stationary epidemic. Particularly, if an epidemic that seems initially contained after a first wave does not fully settle to its new quasi-equilibrium prior to changing circumstances or conditions that force a second wave, then indicators will show a decreasing rather than an increasing trend as a result of the persistent transient trajectory of the first wave. Our simulations show that this lack of timescale separation was to be expected during the second European epidemic wave of COVID-19. Overall, our results emphasize that the theory of critical slowing down applies only when the external forcing of the system across a critical point is slow relative to the internal system dynamics.

Genomic epidemiology of SARS-CoV-2 under an elimination strategy in Hong Kong

Hong Kong employed a strategy of intermittent public health and social measures alongside increasingly stringent travel regulations to eliminate domestic SARS-CoV-2 transmission. By analyzing 1899 genome sequences (>18% of confirmed cases) from 23-January-2020 to 26-January-2021, we reveal the effects of fluctuating control measures on the evolution and epidemiology of SARS-CoV-2 lineages in Hong Kong. Despite numerous importations, only three introductions were responsible for 90% of locally-acquired cases. Community outbreaks were caused by novel introductions rather than a resurgence of circulating strains. Thus, local outbreak prevention requires strong border control and community surveillance, especially during periods of less stringent social restriction. Non-adherence to prolonged preventative measures may explain sustained local transmission observed during wave four in late 2020 and early 2021. We also found that, due to a tight transmission bottleneck, transmission of low-frequency single nucleotide variants between hosts is rare.

Reconstruction of the transmission dynamics of the first COVID-19 epidemic wave in Thailand

Thailand was the first country reporting the first Coronavirus disease 2019 (COVID-19) infected individual outside mainland China. Here we delineated the course of the COVID-19 outbreak together with the timeline of the control measures and public health policies employed by the Thai government during the first wave of the COVID-19 outbreak in Thailand. Based on the comprehensive epidemiological data, we reconstructed the dynamics of COVID-19 transmission in Thailand using a stochastic modeling approach. Our stochastic model incorporated the effects of individual heterogeneity in infectiousness on disease transmission, which allows us to capture relevant features of superspreading events. We found that our model could accurately capture the transmission dynamics of the first COVID-19 epidemic wave in Thailand. The model predicted that at the end of the first wave, the number of cumulative confirmed cases was 3091 (95%CI: 2782-3400). We also estimated the time-varying reproduction number (R_t) during the first epidemic wave. We found that after implementing the nationwide interventions, the R_t in Thailand decreased from the peak value of 5.67 to a value below one in less than one month, indicating that the control measures employed by the Thai government during the first COVID-19 epidemic wave were effective. Finally, the effects of transmission heterogeneity and control measures on the likelihood of outbreak extinction were also investigated.

Characterizing the effective reproduction number during the COVID-19 pandemic: Insights from Qatar’s experience

Background

The effective reproduction number, R_t, is a tool to track and understand pandemic dynamics. This investigation of R_t estimations was conducted to guide the national COVID-19 response in Qatar, from the onset of the pandemic until August 18, 2021.

Methods

Real-time “empirical” R_t^Empirical was estimated using five methods, including the Robert Koch Institute, Cislaghi, Systrom-Bettencourt and Ribeiro, Wallinga and Teunis, and Cori et al. methods. R_t was also estimated using a transmission dynamics model (R_t^Model-based). Uncertainty and sensitivity analyses were conducted. Correlations between different R_t estimates were assessed by calculating correlation coefficients, and agreements between these estimates were assessed through Bland-Altman plots.

Results

R_t^Empirical captured the evolution of the pandemic through three waves, public health response landmarks, effects of major social events, transient fluctuations coinciding with significant clusters of infection, and introduction and expansion of the Alpha (B.1.1.7) variant. The various estimation methods produced consistent and overall comparable R_t^Empirical estimates with generally large correlation coefficients. The Wallinga and Teunis method was the fastest at detecting changes in pandemic dynamics. R_t^Empirical estimates were consistent whether using time series of symptomatic PCR-confirmed cases, all PCR-confirmed cases, acute-care hospital admissions, or ICU-care hospital admissions, to proxy trends in true infection incidence. R_t^Model-based correlated strongly with R_t^Empirical and provided an average R_t^Empirical.

Conclusions

R_t estimations were robust and generated consistent results regardless of the data source or the method of estimation. Findings affirmed an influential role for R_t estimations in guiding national responses to the COVID-19 pandemic, even in resource-limited settings.

Bayesian data assimilation for estimating instantaneous reproduction numbers during epidemics: Applications to COVID-19

Estimating the changes of epidemiological parameters, such as instantaneous reproduction number, Rt, is important for understanding the transmission dynamics of infectious diseases. Current estimates of time-varying epidemiological parameters often face problems such as lagging observations, averaging inference, and improper quantification of uncertainties. To address these problems, we propose a Bayesian data assimilation framework for time-varying parameter estimation. Specifically, this framework is applied to estimate the instantaneous reproduction number Rt during emerging epidemics, resulting in the state-of-the-art 'DARt' system. With DARt, time misalignment caused by lagging observations is tackled by incorporating observation delays into the joint inference of infections and Rt; the drawback of averaging is overcome by instantaneously updating upon new observations and developing a model selection mechanism that captures abrupt changes; the uncertainty is quantified and reduced by employing Bayesian smoothing. We validate the performance of DARt and demonstrate its power in describing the transmission dynamics of COVID-19. The proposed approach provides a promising solution for making accurate and timely estimation for transmission dynamics based on reported data.

Infection dynamics of COVID-19 virus under lockdown and reopening

Motivated by COVID-19, we develop and analyze a simple stochastic model for the spread of disease in human population. We track how the number of infected and critically ill people develops over time in order to estimate the demand that is imposed on the hospital system. To keep this demand under control, we consider a class of simple policies for slowing down and reopening society and we compare their efficiency in mitigating the spread of the virus from several different points of view. We find that in order to avoid overwhelming of the hospital system, a policy must impose a harsh lockdown or it must react swiftly (or both). While reacting swiftly is universally beneficial, being harsh pays off only when the country is patient about reopening and when the neighboring countries coordinate their mitigation efforts. Our work highlights the importance of acting decisively when closing down and the importance of patience and coordination between neighboring countries when reopening.

Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible.

Estimation of the Instantaneous Reproduction Number and Its Confidence Interval for Modeling the COVID-19 Pandemic

In this paper, we derive an optimal model for calculating the instantaneous reproduction number, which is an important metric to help in controlling the evolution of epidemics. Our approach, within a frequentist framework, gave us the opportunity to calculate a more realistic confidence interval, a fundamental tool for a safe interpretation of the instantaneous reproduction number value, so that health and governmental people pay more attention to it. Our reasoning begins by decoupling the incidence data in mean and Gaussian noise by using practical series analysis techniques; then, we continue with a likely relationship between the present and past incidence data. Monte Carlo simulations and numerical integrations were conducted to complement the analytical proofs, and illustrations are provided for each stage of analysis to validate the analytical results. Finally, a real case study is discussed with the incidence data of the Republic of Panama regarding the COVID-19 pandemic. We have shown that, for the calculation of the confidence interval of the instantaneous reproduction number, it is essential to include all sources of variability, not only the Poissonian processes of the incidences. This proposal is delivered with analysis tools developed with Microsoft Excel.

Analysis of the second wave of COVID-19 in India based on SEIR model

India was under a grave threat from the second wave of the COVID-19 pandemic particularly in the beginning of May 2021. The situation appeared rather gloomy as the number of infected individuals/active cases had increased alarmingly during the months of May and June 2021 compared to the first wave peak. Indian government/state governments have been implementing various control measures such as lockdowns, setting up new hospitals, and putting travel restrictions at various stages to lighten the virus spread from the initial outbreak of the pandemic. Recently, we have studied the susceptible-exposed-infectious-removed (SEIR) dynamic modeling of the epidemic evolution of COVID-19 in India with the help of appropriate parameters quantifying the various governmental actions and the intensity of individual reactions. Our analysis had predicted the scenario of the first wave quite well. In this present article, we extend our analysis to estimate and analyze the number of infected individuals during the second wave of COVID-19 in India with the help of the above SEIR model. Our findings show that the people's individual effort along with governmental actions such as implementations of curfews and accelerated vaccine strategy are the most important factors to control the pandemic in the present situation and in the future.

A COVINDEX based on a GAM beta regression model with an application to the COVID-19 pandemic in Italy

Detecting changes in COVID-19 disease transmission over time is a key indicator of epidemic growth. Near real-time monitoring of the pandemic growth is crucial for policy makers and public health officials who need to make informed decisions about whether to enforce lockdowns or allow certain activities. The effective reproduction number \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_t$$\end{document}Rt is the standard index used in many countries for this goal. However, it is known that due to the delays between infection and case registration, its use for decision making is somewhat limited. In this paper a near real-time COVINDEX is proposed for monitoring the evolution of the pandemic. The index is computed from predictions obtained from a GAM beta regression for modelling the test positive rate as a function of time. The proposal is illustrated using data on COVID-19 pandemic in Italy and compared with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_t$$\end{document}Rt. A simple chart is also proposed for monitoring local and national outbreaks by policy makers and public health officials.

Unexposed populations and potential COVID-19 hospitalisations and deaths in European countries as per data up to 21 November 2021

We estimate the potential remaining COVID-19 hospitalisation and death burdens in 19 European countries by estimating the proportion of each country's population that has acquired immunity to severe disease through infection or vaccination. Our results suggest many European countries could still face high burdens of hospitalisations and deaths, particularly those with lower vaccination coverage, less historical transmission and/or older populations. Continued non-pharmaceutical interventions and efforts to achieve high vaccination coverage are required in these countries to limit severe COVID-19 outcomes.

Fine-scale estimation of effective reproduction numbers for dengue surveillance

The effective reproduction number R_t is an epidemiological quantity that provides an instantaneous measure of transmission potential of an infectious disease. While dengue is an increasingly important vector-borne disease, few have used R_t as a measure to inform public health operations and policy for dengue. This study demonstrates the utility of R_t for real time dengue surveillance. Using nationally representative, geo-located dengue case data from Singapore over 2010–2020, we estimated R_t by modifying methods from Bayesian (EpiEstim) and filtering (EpiFilter) approaches, at both the national and local levels. We conducted model assessment of R_t from each proposed method and determined exogenous temporal and spatial drivers for R_t in relation to a wide range of environmental and anthropogenic factors. At the national level, both methods achieved satisfactory model performance (R²_EpiEstim = 0.95, R²_EpiFilter = 0.97), but disparities in performance were large at finer spatial scales when case counts are low (MASE _EpiEstim = 1.23, MASE_EpiFilter = 0.59). Impervious surfaces and vegetation with structure dominated by human management (without tree canopy) were positively associated with increased transmission intensity. Vegetation with structure dominated by human management (with tree canopy), on the other hand, was associated with lower dengue transmission intensity. We showed that dengue outbreaks were preceded by sustained periods of high transmissibility, demonstrating the potential of R_t as a dengue surveillance tool for detecting large rises in dengue cases. Real time estimation of R_t at the fine scale can assist public health agencies in identifying high transmission risk areas and facilitating localised outbreak preparedness and response.

The effective reproduction number R_t is an epidemiological quantity that provides an instantaneous measure of transmission potential of an infectious disease. While dengue is an increasingly important vector-borne disease, few have used R_t as a measure to inform public health operations and policy for dengue. This study demonstrates the utility of R_t for real time dengue surveillance. Using nationally representative, geo-located dengue case data from Singapore over 2010–2020, we estimated R_t by modifying methods from Bayesian (EpiEstim) and filtering (EpiFilter) approaches, at both the national and local levels. We conducted model assessment of R_t from each proposed method and determined exogenous temporal and spatial drivers for R_t in relation to a wide range of environmental and anthropogenic factors. At the national level, both methods achieved high accuracy, but disparities in performance were large at finer spatial scales when case counts are low. This study demonstrates the potential of R_t as a dengue surveillance tool for detecting large rises in dengue cases. Real time estimation of R_t at the fine scale can assist public health agencies in identifying high transmission risk areas and facilitating localised outbreak preparedness and response.

Plasmodium falciparum importation does not sustain malaria transmission in a semi-arid region of Kenya

Human movement impacts the spread and transmission of infectious diseases. Recently, a large reservoir of Plasmodium falciparum malaria was identified in a semi-arid region of northwestern Kenya historically considered unsuitable for malaria transmission. Understanding the sources and patterns of transmission attributable to human movement would aid in designing and targeting interventions to decrease the unexpectedly high malaria burden in the region. Toward this goal, polymorphic parasite genes (ama1, csp) in residents and passengers traveling to Central Turkana were genotyped by amplicon deep sequencing. Genotyping and epidemiological data were combined to assess parasite importation. The contribution of travel to malaria transmission was estimated by modelling case reproductive numbers inclusive and exclusive of travelers. P. falciparum was detected in 6.7% (127/1891) of inbound passengers, including new haplotypes which were later detected in locally-transmitted infections. Case reproductive numbers approximated 1 and did not change when travelers were removed from transmission networks, suggesting that transmission is not fueled by travel to the region but locally endemic. Thus, malaria is not only prevalent in Central Turkana but also sustained by local transmission. As such, interrupting importation is unlikely to be an effective malaria control strategy on its own, but targeting interventions locally has the potential to drive down transmission.

nSpatially refined time-varying reproduction numbers of SARS-CoV-2 in Arkansas and Kentucky and their relationship to population size and public health policy, March – November, 2020

Purpose

Methods

Results

Conclusions

Tracking the emergence of disparities in the subnational spread of COVID-19 in Brazil using an online application for real-time data visualisation: A longitudinal analysis

BACKGROUND

Brazil is one of the countries worst affected by the COVID-19 pandemic with over 20 million cases and 557,000 deaths reported by August 2021. Comparison of real-time local COVID-19 data between areas is essential for understanding transmission, measuring the effects of interventions, and predicting the course of the epidemic, but are often challenging due to different population sizes and structures.

METHODS

We describe the development of a new app for the real-time visualisation of COVID-19 data in Brazil at the municipality level. In the CLIC-Brazil app, daily updates of case and death data are downloaded, age standardised and used to estimate the effective reproduction number (Rt ). We show how such platforms can perform real-time regression analyses to identify factors associated with the rate of initial spread and early reproduction number. We also use survival methods to predict the likelihood of occurrence of a new peak of COVID-19 incidence.

FINDINGS

After an initial introduction in São Paulo and Rio de Janeiro states in early March 2020, the epidemic spread to northern states and then to highly populated coastal regions and the Central-West. Municipalities with higher metrics of social development experienced earlier arrival of COVID-19 (decrease of 11·1 days [95% CI:8.9,13.2] in the time to arrival for each 10% increase in the social development index). Differences in the initial epidemic intensity (mean Rt ) were largely driven by geographic location and the date of local onset.

INTERPRETATION

This study demonstrates that platforms that monitor, standardise and analyse the epidemiological data at a local level can give useful real-time insights into outbreak dynamics that can be used to better adapt responses to the current and future pandemics.

FUNDING

This project was supported by a Medical Research Council UK (MRC-UK) -São Paulo Research Foundation (FAPESP) CADDE partnership award (MR/S0195/1 and FAPESP 18/14389-0).

Spatio-temporal estimation of basic and effective reproduction number of COVID-19 and post-lockdown transmissibility in Bangladesh

The ongoing COVID-19 pandemic has caused unprecedented public health concern in Bangladesh. This study investigated the role of Non-Pharmaceutical Interventions on COVID-19 transmission and post-lockdown scenarios of 64 administrative districts and the country as a whole based on the spatiotemporal variations of effective reproduction number (R t) of COVID-19 incidences. The daily confirmed COVID-19 data of Bangladesh and its administrative districts from March 8, 2020, to March 10, 2021, were used to estimate R t. This study finds that the maximum value of R t reached 4.15 (3.43, 4.97, 95% CI) in late March 2020, which remained above 1 afterwards in most of the districts. Containment measures are moderately effective in reducing transmission by 24.03%. The R t was established below 1 from early December 2020 for overall Bangladesh and a gradual increase of R t above 1 has been seen from early February 2021. The basic reproduction number (R 0) in Bangladesh probably varied around 2.02 (1.33–3.28, 95% CI). This study finds a significant positive correlation (r = 0.75) between population density and COVID-19 incidence and explaining 56% variation in Bangladesh. The findings of this study are expected to support the policymakers to adopt appropriate measures for curbing the COVID-19 transmission effectively.

Evaluating the reliability of mobility metrics from aggregated mobile phone data as proxies for SARS-CoV-2 transmission in the USA: a population-based study

BACKGROUND

In early 2020, the response to the SARS-CoV-2 pandemic focused on non-pharmaceutical interventions, some of which aimed to reduce transmission by changing mixing patterns between people. Aggregated location data from mobile phones are an important source of real-time information about human mobility on a population level, but the degree to which these mobility metrics capture the relevant contact patterns of individuals at risk of transmitting SARS-CoV-2 is not clear. In this study we describe changes in the relationship between mobile phone data and SARS-CoV-2 transmission in the USA.

METHODS

In this population-based study, we collected epidemiological data on COVID-19 cases and deaths, as well as human mobility metrics collated by advertisement technology that was derived from global positioning systems, from 1396 counties across the USA that had at least 100 laboratory-confirmed cases of COVID-19. We grouped these counties into six ordinal categories, defined by the National Center for Health Statistics (NCHS) and graded from urban to rural, and quantified the changes in COVID-19 transmission using estimates of the effective reproduction number (Rt) between Jan 22 and July 9, 2020, to investigate the relationship between aggregated mobility metrics and epidemic trajectory. For each county, we model the time series of Rt values with mobility proxies.

FINDINGS

We show that the reproduction number is most strongly associated with mobility proxies for change in the travel into counties (0·757 [95% CI 0·689 to 0·857]), but this relationship primarily holds for counties in the three most urban categories as defined by the NCHS. This relationship weakens considerably after the initial 15 weeks of the epidemic (0·442 [-0·492 to -0·392]), consistent with the emergence of more complex local policies and behaviours, including masking.

INTERPRETATION

Our study shows that the integration of mobility metrics into retrospective modelling efforts can be useful in identifying links between these metrics and Rt. Importantly, we highlight potential issues in the data generation process for transmission indicators derived from mobile phone data, representativeness, and equity of access, which must be addressed to improve the interpretability of these data in public health.

FUNDING

There was no funding source for this study.

Superspreading quantified from bursty epidemic trajectories

The quantification of spreading heterogeneity in the COVID-19 epidemic is crucial as it affects the choice of efficient mitigating strategies irrespective of whether its origin is biological or social. We present a method to deduce temporal and individual variations in the basic reproduction number directly from epidemic trajectories at a community level. Using epidemic data from the 98 districts in Denmark we estimate an overdispersion factor k for COVID-19 to be about 0.11 (95% confidence interval 0.08-0.18), implying that 10 % of the infected cause between 70 % and 87 % of all infections.

Aiming for Zero: Reducing Transmission of Coronavirus Disease 2019 in the D.C. Department of Corrections

Background

Washington, District of Columbia lowered severe acute respiratory syndrome coronavirus 2 transmission in its large jail while community incidence was still high

Methods

Coordinated clinical and operational interventions brought new cases to near zero.

Results

Aggressive infection control and underlying jail architecture can promote correctional coronavirus disease 2019 management.

Conclusions

More intensive monitoring could help confirm that in-house transmission is truly zero.

Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique

The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures or the emergence of new viral variants. The reproduction number Rt indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of Rt is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating Rt But it estimates Rt with a significant temporal delay. Here, we propose a method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of Rt several days in advance. We show that Rt can be estimated by inverting the renewal equation linking Rt with the observed incidence curve of new cases, it Our signal-processing approach to this problem yields both Rt and a restored it corrected for the "weekend effect" by applying a deconvolution and denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open source and can be run in real time on every country in the world and every US state.

Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique

The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures or the emergence of new viral variants. The reproduction number R_t indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of R_t is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating R_t But it estimates R_t with a significant temporal delay. Here, we propose a method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of R_t several days in advance. We show that R_t can be estimated by inverting the renewal equation linking R_t with the observed incidence curve of new cases, i_t Our signal-processing approach to this problem yields both R_t and a restored i_t corrected for the "weekend effect" by applying a deconvolution and denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open source and can be run in real time on every country in the world and every US state.

Correction: Practical considerations for measuring the effective reproductive number, Rt

[This corrects the article DOI: 10.1371/journal.pcbi.1008409.].

On the use of aggregated human mobility data to estimate the reproduction number

The reproduction number of an infectious disease, such as CoViD-19, can be described through a modified version of the susceptible-infected-recovered (SIR) model with time-dependent contact rate, where mobility data are used as proxy of average movement trends and interpersonal distances. We introduce a theoretical framework to explain and predict changes in the reproduction number of SARS-CoV-2 in terms of aggregated individual mobility and interpersonal proximity (alongside other epidemiological and environmental variables) during and after the lockdown period. We use an infection-age structured model described by a renewal equation. The model predicts the evolution of the reproduction number up to a week ahead of well-established estimates used in the literature. We show how lockdown policies, via reduction of proximity and mobility, reduce the impact of CoViD-19 and mitigate the risk of disease resurgence. We validate our theoretical framework using data from Google, Voxel51, Unacast, The CoViD-19 Mobility Data Network, and Analisi Distribuzione Aiuti.

Predicting the effective reproduction number of COVID-19: inference using human mobility, temperature, and risk awareness

OBJECTIVES

The effective reproduction number (R_t) has been critical for assessing the effectiveness of countermeasures during the coronavirus disease 2019 (COVID-19) pandemic. Conventional methods using reported incidences are unable to provide timely R_t data due to the delay from infection to reporting. Our study aimed to develop a framework for predicting R_t in real time, using timely accessible data - i.e. human mobility, temperature, and risk awareness.

METHODS

A linear regression model to predict R_t was designed and embedded in the renewal process. Four prefectures of Japan with high incidences in the first wave were selected for model fitting and validation. Predictive performance was assessed by comparing the observed and predicted incidences using cross-validation, and by testing on a separate dataset in two other prefectures with distinct geographical settings from the four studied prefectures.

RESULTS

The predicted mean values of R_t and 95% uncertainty intervals followed the overall trends for incidence, while predictive performance was diminished when R_t changed abruptly, potentially due to superspreading events or when stringent countermeasures were implemented.

CONCLUSIONS

The described model can potentially be used for monitoring the transmission dynamics of COVID-19 ahead of the formal estimates, subject to delay, providing essential information for timely planning and assessment of countermeasures.

The Epidemiology of COVID-19 in Malaysia

BACKGROUND

COVID-19 has rapidly spread across the globe. Critical to the control of COVID-19 is the characterisation of its epidemiology. Despite this, there has been a paucity of evidence from many parts of the world, including Malaysia. We aim to describe the epidemiology of COVID-19 in Malaysia to inform prevention and control policies better.

METHODS

Malaysian COVID-19 data was extracted from 16 March 2020 up to 31 May 2021. We estimated the following epidemiological indicators: 7-day incidence rates, 7-day mortality rates, case fatality rates, test positive ratios, testing rates and the time-varying reproduction number (Rt).

FINDINGS

Between 16 March 2020 and 31 May 2021, Malaysia has reported 571,901 cases and 2,796 deaths. Malaysia's average 7-day incidence rate was 26•6 reported infections per 100,000 population (95% CI: 17•8, 38•1). The average test positive ratio and testing rate were 4•3% (95% CI: 1•6, 10•2) and 0•8 tests per 1,000 population (95% CI: <0•1, 3•7), respectively. The case fatality rates (CFR) was 0•6% (95% CI: <0•1, 3•7). Among the 2,796 cases who died, 87•3% were ≥ 50 years.

INTERPRETATION

The public health response was successful in the suppression of COVID-19 transmission or the first half of 2020. However, a state election and outbreaks in institutionalised populations have been the catalyst for more significant community propagation. This rising community transmission has continued in 2021, leading to increased incidence and strained healthcare systems. Calibrating NPI based on epidemiological indicators remain critical for us to live with the virus. (243 words).

FUNDING

This study is part of the COVID-19 Epidemiological Analysis and Strategies (CEASe) Project with funding from the Ministry of Science, Technology and Innovation (UM.0000245/HGA.GV).

Cross-sectional cycle threshold values reflect epidemic dynamics of COVID-19 in Madagascar

As the national reference laboratory for febrile illness in Madagascar, we processed samples from the first epidemic wave of COVID-19, between March and September 2020. We fit generalized additive models to cycle threshold (C_t) value data from our RT-qPCR platform, demonstrating a peak in high viral load, low-C_t value infections temporally coincident with peak epidemic growth rates estimated in real time from publicly-reported incidence data and retrospectively from our own laboratory testing data across three administrative regions. We additionally demonstrate a statistically significant effect of duration of time since infection onset on C_t value, suggesting that C_t value can be used as a biomarker of the stage at which an individual is sampled in the course of an infection trajectory. As an extension, the population-level C_t distribution at a given timepoint can be used to estimate population-level epidemiological dynamics. We illustrate this concept by adopting a recently-developed, nested modeling approach, embedding a within-host viral kinetics model within a population-level Susceptible-Exposed-Infectious-Recovered (SEIR) framework, to mechanistically estimate epidemic growth rates from cross-sectional C_t distributions across three regions in Madagascar. We find that C_t-derived epidemic growth estimates slightly precede those derived from incidence data across the first epidemic wave, suggesting delays in surveillance and case reporting. Our findings indicate that public reporting of C_t values could offer an important resource for epidemiological inference in low surveillance settings, enabling forecasts of impending incidence peaks in regions with limited case reporting.

Joint Estimation of Generation Time and Incubation Period for Coronavirus Disease 2019

BACKGROUND

Coronavirus disease 2019 (COVID-19) has caused a heavy disease burden globally. The impact of process and timing of data collection on the accuracy of estimation of key epidemiological distributions are unclear. Because infection times are typically unobserved, there are relatively few estimates of generation time distribution.

METHODS

We developed a statistical framework to jointly estimate generation time and incubation period from human-to-human transmission pairs, accounting for sampling biases. We applied the framework on 80 laboratory-confirmed human-to-human transmission pairs in China. We further inferred the infectiousness profile, serial interval distribution, proportions of presymptomatic transmission, and basic reproduction number (R0) for COVID-19.

RESULTS

The estimated mean incubation period was 4.8 days (95% confidence interval [CI], 4.1-5.6), and mean generation time was 5.7 days (95% CI, 4.8-6.5). The estimated R0 based on the estimated generation time was 2.2 (95% CI, 1.9-2.4). A simulation study suggested that our approach could provide unbiased estimates, insensitive to the width of exposure windows.

CONCLUSIONS

Properly accounting for the timing and process of data collection is critical to have correct estimates of generation time and incubation period. R0 can be biased when it is derived based on serial interval as the proxy of generation time.

Empirical Analysis of the Impact of COVID-19 Social Distancing on Residential Electricity Consumption Based on Demographic Characteristics and Load Shape

Since January 2020, the COVID-19 pandemic has been impacting various aspects of people’s daily lives and the economy. The first case of COVID-19 in South Korea was identified on 20 January 2020. The Korean government implemented the first social distancing measures in the first week of March 2020. As a result, energy consumption in the industrial, commercial and educational sectors decreased. On the other hand, residential energy consumption increased as telecommuting work and remote online classes were encouraged. However, the impact of social distancing on residential energy consumption in Korea has not been systematically analyzed. This study attempts to analyze the impact of social distancing implemented as a result of COVID-19 on residential energy consumption with time-varying reproduction numbers of COVID-19. A two-way fixed effect model and demographic characteristics are used to account for the heterogeneity. The changes in household energy consumption by load shape group are also analyzed with the household energy consumption model. There some are key results of COVID-19 impact on household energy consumption. Based on the hourly smart meter data, an average increase of 0.3% in the hourly average energy consumption is caused by a unit increase in the time-varying reproduction number of COVID-19. For each income, mid-income groups show less impact on energy consumption compared to both low-income and high-income groups. In each family member, as the number of family members increases, the change in electricity consumption affected by social distancing tends to decrease. For area groups, large area consumers increase household energy consumption more than other area groups. Lastly, The COVID-19 impact on each load shape is influenced by their energy consumption patterns.

Impact of Governmental interventions on epidemic progression and workplace activity during the COVID-19 outbreak

In the first quarter of 2020, the COVID-19 pandemic brought the world to a state of paralysis. During this period, humanity saw by far the largest organized travel restrictions and unprecedented efforts and global coordination to contain the spread of the SARS-CoV-2 virus. Using large scale human mobility and fine grained epidemic incidence data, we develop a framework to understand and quantify the effectiveness of the interventions implemented by various countries to control epidemic growth. Our analysis reveals the importance of timing and implementation of strategic policy in controlling the epidemic. We also unearth significant spatial diffusion of the epidemic before and during the lockdown measures in several countries, casting doubt on the effectiveness or on the implementation quality of the proposed Governmental policies.

Predicting increases in COVID-19 incidence to identify locations for targeted testing in West Virginia: A machine learning enhanced approach

During the COVID-19 pandemic, West Virginia developed an aggressive SARS-CoV-2 testing strategy which included utilizing pop-up mobile testing in locations anticipated to have near-term increases in SARS-CoV-2 infections. This study describes and compares two methods for predicting near-term SARS-CoV-2 incidence in West Virginia counties. The first method, Rt Only, is solely based on producing forecasts for each county using the daily instantaneous reproductive numbers, Rt. The second method, ML+Rt, is a machine learning approach that uses a Long Short-Term Memory network to predict the near-term number of cases for each county using epidemiological statistics such as Rt, county population information, and time series trends including information on major holidays, as well as leveraging statewide COVID-19 trends across counties and county population size. Both approaches used daily county-level SARS-CoV-2 incidence data provided by the West Virginia Department Health and Human Resources beginning April 2020. The methods are compared on the accuracy of near-term SARS-CoV-2 increases predictions by county over 17 weeks from January 1, 2021- April 30, 2021. Both methods performed well (correlation between forecasted number of cases and the actual number of cases week over week is 0.872 for the ML+Rt method and 0.867 for the Rt Only method) but differ in performance at various time points. Over the 17-week assessment period, the ML+Rt method outperforms the Rt Only method in identifying larger spikes. Results show that both methods perform adequately in both rural and non-rural predictions. Finally, a detailed discussion on practical issues regarding implementing forecasting models for public health action based on Rt is provided, and the potential for further development of machine learning methods that are enhanced by Rt.

Assessing COVID-19 Prevention Strategies to Permit the Safe Opening of Residential Colleges in Fall 2021

BACKGROUND

Effective vaccines, improved testing technologies, and decreases in COVID-19 incidence prompt an examination of the choices available to residential college administrators seeking to safely resume in-person campus activities in fall 2021.

OBJECTIVE

To help college administrators design and evaluate customized COVID-19 safety plans.

DESIGN

Decision analysis using a compartmental epidemic model to optimize vaccination, testing, and other nonpharmaceutical interventions depending on decision makers' preferences, choices, and assumptions about epidemic severity and vaccine effectiveness against infection, transmission, and disease progression.

SETTING

U.S. residential colleges.

PARTICIPANTS

Hypothetical cohort of 5000 persons (students, faculty, and staff) living and working in close proximity on campus.

MEASUREMENTS

Cumulative infections over a 120-day semester.

RESULTS

Under base-case assumptions, if 90% coverage can be attained with a vaccine that is 85% protective against infection and 25% protective against asymptomatic transmission, the model finds that campus activities can be resumed while holding cumulative cases below 5% of the population without the need for routine, asymptomatic testing. With 50% population coverage using such a vaccine, a similar cap on cumulative cases would require either daily asymptomatic testing of unvaccinated persons or a combination of less frequent testing and resumption of aggressive distancing and other nonpharmaceutical prevention policies. Colleges returning to pre-COVID-19 campus activities without either broad vaccination coverage or high-frequency testing put their campus population at risk for widespread viral transmission.

LIMITATION

Uncertainty in data, particularly vaccine effectiveness (preventive and transmission); no distinguishing between students and employees; and assumes limited community intermixing.

CONCLUSION

Vaccination coverage is the most powerful tool available to residential college administrators seeking to achieve a safe return to prepandemic operations this fall. Given the breadth of potential outcomes in the face of uncontrollable and uncertain factors, even colleges with high vaccination rates should be prepared to reinstitute or expand testing and distancing policies on short notice.

PRIMARY FUNDING SOURCE

National Institute on Drug Abuse.

Impact of data accuracy on the evaluation of COVID-19 mitigation policies

Evaluating the effectiveness of nonpharmaceutical interventions (NPIs) to mitigate the COVID-19 pandemic is crucial to maximize the epidemic containment while minimizing the social and economic impact of these measures. However, this endeavor crucially relies on surveillance data publicly released by health authorities that can hide several limitations. In this article, we quantify the impact of inaccurate data on the estimation of the time-varying reproduction number $ R(t) $ , a pivotal quantity to gauge the variation of the transmissibility originated by the implementation of different NPIs. We focus on Italy and Spain, two European countries among the most severely hit by the COVID-19 pandemic. For these two countries, we highlight several biases of case-based surveillance data and temporal and spatial limitations in the data regarding the implementation of NPIs. We also demonstrate that a nonbiased estimation of $ R(t) $ could have had direct consequences on the decisions taken by the Spanish and Italian governments during the first wave of the pandemic. Our study shows that extreme care should be taken when evaluating intervention policies through publicly available epidemiological data and call for an improvement in the process of COVID-19 data collection, management, storage, and release. Better data policies will allow a more precise evaluation of the effects of containment measures, empowering public health authorities to take more informed decisions.

The risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions

Background

Countries around the world have introduced travel restrictions to reduce SARS-CoV-2 transmission. As vaccines are gradually rolled out, attention has turned to when travel restrictions and other non-pharmaceutical interventions (NPIs) can be relaxed.

Methods

Using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases arriving in low prevalence settings initiate a local outbreak. Our model accounts for changes in background population immunity due to vaccination. We consider two locations with low prevalence in which the vaccine rollout has progressed quickly – specifically, the Isle of Man (a British crown dependency in the Irish Sea) and the country of Israel.

Results

We show that the outbreak risk is unlikely to be eliminated completely when travel restrictions and other NPIs are removed. This general result is the most important finding of this study, rather than exact quantitative outbreak risk estimates in different locations. It holds even once vaccine programmes are completed. Key factors underlying this result are the potential for transmission even following vaccination, incomplete vaccine uptake, and the recent emergence of SARS-CoV-2 variants with increased transmissibility.

Conclusions

Combined, the factors described above suggest that, when travel restrictions are relaxed, it may still be necessary to implement surveillance of incoming passengers to identify infected individuals quickly. This measure, as well as tracing and testing (and/or isolating) contacts of detected infected passengers, remains useful to suppress potential outbreaks while global case numbers are high.

The effectiveness of public health measures against COVID-19 has varied between countries, with some experiencing many infections and others containing transmission successfully. As vaccines are deployed, an important challenge is deciding when to relax measures. Here, we consider locations with few cases, and investigate whether vaccination can ever eliminate the risk of COVID-19 outbreaks completely, allowing measures to be removed risk-free. Using a mathematical model, we demonstrate that there is still a risk that imported cases initiate outbreaks when measures are removed, even if most of the population is fully vaccinated. This highlights the need for continued vigilance in low prevalence settings to prevent imported cases leading to local transmission. Until case numbers are reduced globally, so that SARS-CoV-2 spread between countries is less likely, the risk of outbreaks in low prevalence settings will remain.

Sachak-Patwa et al. estimate the risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions and other non-pharmaceutical interventions, with the Isle of Man and Israel as case studies. Using a branching process mathematical model, the authors show that even after a large proportion of the population is vaccinated, there remains a risk of local outbreaks from imported cases.

Predicting increases in COVID-19 incidence to identify locations for targeted testing in West Virginia: A machine learning enhanced approach

During the COVID-19 pandemic, West Virginia developed an aggressive SARS-CoV-2 testing strategy which included utilizing pop-up mobile testing in locations anticipated to have near-term increases in SARS-CXoV-2 infections. In this study, we describe and compare two methods for predicting near-term SARS-CoV-2 incidence in West Virginia counties. The first method, R t Only, is solely based on producing forecasts for each county using the daily instantaneous reproductive numbers, R t. The second method, ML+ R t , is a machine learning approach that uses a Long Short-Term Memory network to predict the near-term number of cases for each county using epidemiological statistics such as Rt, county population information, and time series trends including information on major holidays, as well as leveraging statewide COVID-19 trends across counties and county population size. Both approaches used daily county-level SARS-CoV-2 incidence data provided by the West Virginia Department Health and Human Resources beginning April 2020. The methods are compared on the accuracy of near-term SARS-CoV-2 increases predictions by county over 17 weeks from January 1, 2021-April 30, 2021. Both methods performed well (correlation between forecasted number of cases and the actual number of cases week over week is 0.872 for the ML+R t method and 0.867 for the R t Only method) but differ in performance at various time points. Over the 17-week assessment period, the ML+R t method outperforms the R t Only method in identifying larger spikes. We also find that both methods perform adequately in both rural and non-rural predictions. Finally, we provide a detailed discussion on practical issues regarding implementing forecasting models for public health action based on R t , and the potential for further development of machine learning methods that are enhanced by R t.

Weather, air pollution, and SARS-CoV-2 transmission: a global analysis

BACKGROUND

Understanding how environmental factors affect SARS-CoV-2 transmission could inform global containment efforts. Despite high scientific and public interest and multiple research reports, there is currently no consensus on the association of environmental factors and SARS-CoV-2 transmission. To address this research gap, we aimed to assess the relative risk of transmission associated with weather conditions and ambient air pollution.

METHODS

In this global analysis, we adjusted for the delay between infection and detection, estimated the daily reproduction number at 3739 global locations during the COVID-19 pandemic up until late April, 2020, and investigated its associations with daily local weather conditions (ie, temperature, humidity, precipitation, snowfall, moon illumination, sunlight hours, ultraviolet index, cloud cover, wind speed and direction, and pressure data) and ambient air pollution (ie, PM2·5, nitrogen dioxide, ozone, and sulphur dioxide). To account for other confounding factors, we included both location-specific fixed effects and trends, controlling for between-location differences and heterogeneities in locations' responses over time. We built confidence in our estimations through synthetic data, robustness, and sensitivity analyses, and provided year-round global projections for weather-related risk of global SARS-CoV-2 transmission.

FINDINGS

Our dataset included data collected between Dec 12, 2019, and April 22, 2020. Several weather variables and ambient air pollution were associated with the spread of SARS-CoV-2 across 3739 global locations. We found a moderate, negative relationship between the estimated reproduction number and temperatures warmer than 25°C (a decrease of 3·7% [95% CI 1·9-5·4] per additional degree), a U-shaped relationship with outdoor ultraviolet exposure, and weaker positive associations with air pressure, wind speed, precipitation, diurnal temperature, sulphur dioxide, and ozone. Results were robust to multiple assumptions. Independent research building on our estimates provides strong support for the resulting projections across nations.

INTERPRETATION

Warmer temperature and moderate outdoor ultraviolet exposure result in a slight reduction in the transmission of SARS-CoV-2; however, changes in weather or air pollution alone are not enough to contain the spread of SARS-CoV-2 with other factors having greater effects.

FUNDING

None.

Synergistic interventions to control COVID-19: Mass testing and isolation mitigates reliance on distancing

Stay-at-home orders and shutdowns of non-essential businesses are powerful, but socially costly, tools to control the pandemic spread of SARS-CoV-2. Mass testing strategies, which rely on widely administered frequent and rapid diagnostics to identify and isolate infected individuals, could be a potentially less disruptive management strategy, particularly where vaccine access is limited. In this paper, we assess the extent to which mass testing and isolation strategies can reduce reliance on socially costly non-pharmaceutical interventions, such as distancing and shutdowns. We develop a multi-compartmental model of SARS-CoV-2 transmission incorporating both preventative non-pharmaceutical interventions (NPIs) and testing and isolation to evaluate their combined effect on public health outcomes. Our model is designed to be a policy-guiding tool that captures important realities of the testing system, including constraints on test administration and non-random testing allocation. We show how strategic changes in the characteristics of the testing system, including test administration, test delays, and test sensitivity, can reduce reliance on preventative NPIs without compromising public health outcomes in the future. The lowest NPI levels are possible only when many tests are administered and test delays are short, given limited immunity in the population. Reducing reliance on NPIs is highly dependent on the ability of a testing program to identify and isolate unreported, asymptomatic infections. Changes in NPIs, including the intensity of lockdowns and stay at home orders, should be coordinated with increases in testing to ensure epidemic control; otherwise small additional lifting of these NPIs can lead to dramatic increases in infections, hospitalizations and deaths. Importantly, our results can be used to guide ramp-up of testing capacity in outbreak settings, allow for the flexible design of combined interventions based on social context, and inform future cost-benefit analyses to identify efficient pandemic management strategies.

SARS-CoV-2 serology across scales: a framework for unbiased seroprevalence estimation incorporating antibody kinetics and epidemic recency

Serosurveys are a key resource for measuring SARS-CoV-2 cumulative incidence. A growing body of evidence suggests that asymptomatic and mild infections (together making up over 95% of all infections) are associated with lower antibody titers than severe infections. Antibody levels also peak a few weeks after infection and decay gradually. We developed a statistical approach to produce adjusted estimates of seroprevalence from raw serosurvey results that account for these sources of spectrum bias. We incorporate data on antibody responses on multiple assays from a post-infection longitudinal cohort, along with epidemic time series to account for the timing of a serosurvey relative to how recently individuals may have been infected. We applied this method to produce adjusted seroprevalence estimates from five large-scale SARS-CoV-2 serosurveys across different settings and study designs. We identify substantial differences between reported and adjusted estimates of over two-fold in the results of some surveys, and provide a tool for practitioners to generate adjusted estimates with pre-set or custom parameter values. While unprecedented efforts have been launched to generate SARS-CoV-2 seroprevalence estimates over this past year, interpretation of results from these studies requires properly accounting for both population-level epidemiologic context and individual-level immune dynamics.

Estimating the impact of reopening schools on the reproduction number of SARS-CoV-2 in England, using weekly contact survey data

BACKGROUND

Schools were closed in England on 4 January 2021 as part of increased national restrictions to curb transmission of SARS-CoV-2. The UK government reopened schools on 8 March. Although there was evidence of lower individual-level transmission risk amongst children compared to adults, the combined effects of this with increased contact rates in school settings and the resulting impact on the overall transmission rate in the population were not clear.

METHODS

We measured social contacts of > 5000 participants weekly from March 2020, including periods when schools were both open and closed, amongst other restrictions. We combined these data with estimates of the susceptibility and infectiousness of children compared with adults to estimate the impact of reopening schools on the reproduction number.

RESULTS

Our analysis indicates that reopening all schools under the same measures as previous periods that combined lockdown with face-to-face schooling would be likely to increase the reproduction number substantially. Assuming a baseline of 0.8, we estimated a likely increase to between 1.0 and 1.5 with the reopening of all schools or to between 0.9 and 1.2 reopening primary or secondary schools alone.

CONCLUSION

Our results suggest that reopening schools would likely halt the fall in cases observed between January and March 2021 and would risk a return to rising infections, but these estimates relied heavily on the latest estimates or reproduction number and the validity of the susceptibility and infectiousness profiles we used at the time of reopening.

Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves

We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. We find that this combination of maximising information and minimising assumptions significantly reduces the bias and variance of R estimates. Moreover, these properties make EpiFilter more statistically robust in periods of low incidence, where several existing methods can become destabilised. As a result, EpiFilter offers improved inference of time-varying transmission patterns that are advantageous for assessing the risk of upcoming waves of infection or the influence of interventions, in real time and at various spatial scales.

The Impact of Changes in Diagnostic Testing Practices on Estimates of COVID-19 Transmission in the United States

Estimates of the reproductive number for novel pathogens such as severe acute respiratory syndrome coronavirus 2 are essential for understanding the potential trajectory of the epidemic and the level of intervention that is needed to bring the epidemic under control. However, most methods for estimating the basic reproductive number (R₀) and time-varying effective reproductive number (R_t) assume that the fraction of cases detected and reported is constant through time. We explore the impact of secular changes in diagnostic testing and reporting on estimates of R₀ and R_t using simulated data. We then compare these patterns to data on reported cases of coronavirus disease and testing practices from different states in the United States from March 4 to August 30, 2020. We find that changes in testing practices and delays in reporting can result in biased estimates of R₀ and R_t. Examination of changes in the daily number of tests conducted and the percent of patients testing positive may be helpful for identifying the potential direction of bias. Changes in diagnostic testing and reporting processes should be monitored and taken into consideration when interpreting estimates of the reproductive number of coronavirus disease.

Improved estimation of time-varying reproduction numbers at low case incidence and between epidemic waves

We construct a recursive Bayesian smoother, termed EpiFilter, for estimating the effective reproduction number, R, from the incidence of an infectious disease in real time and retrospectively. Our approach borrows from Kalman filtering theory, is quick and easy to compute, generalisable, deterministic and unlike many current methods, requires no change-point or window size assumptions. We model R as a flexible, hidden Markov state process and exactly solve forward-backward algorithms, to derive R estimates that incorporate all available incidence information. This unifies and extends two popular methods, EpiEstim, which considers past incidence, and the Wallinga-Teunis method, which looks forward in time. We find that this combination of maximising information and minimising assumptions significantly reduces the bias and variance of R estimates. Moreover, these properties make EpiFilter more statistically robust in periods of low incidence, where several existing methods can become destabilised. As a result, EpiFilter offers improved inference of time-varying transmission patterns that are advantageous for assessing the risk of upcoming waves of infection or the influence of interventions, in real time and at various spatial scales.

A farewell to R: time-series models for tracking and forecasting epidemics

The time-dependent reproduction number, Rt, is a key metric used by epidemiologists to assess the current state of an outbreak of an infectious disease. This quantity is usually estimated using time-series observations on new infections combined with assumptions about the distribution of the serial interval of transmissions. Bayesian methods are often used with the new cases data smoothed using a simple, but to some extent arbitrary, moving average. This paper describes a new class of time-series models, estimated by classical statistical methods, for tracking and forecasting the growth rate of new cases and deaths. Very few assumptions are needed and those that are made can be tested. Estimates of Rt, together with their standard deviations, are obtained as a by-product.