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The ongoing COVID-19 pandemic continues to affect communities around the world. To date, almost 6 million people have died as a consequence of COVID-19, and more than one-quarter of a billion people are estimated to have been infected worldwide. The design of appropriate and timely mitigation strategies to curb the effects of this and future disease outbreaks requires close monitoring of their spatio-temporal trajectories. We present machine learning methods to anticipate sharp increases in COVID-19 activity in US counties in real-time. Our methods leverage Internet-based digital traces -- e.g., disease-related Internet search activity from the general population and clinicians, disease-relevant Twitter micro-blogs, and outbreak trajectories from neighboring locations -- to monitor potential changes in population-level health trends. Motivated by the need for finer spatial-resolution epidemiological insights to improve local decision-making, we build upon previous retrospective research efforts originally conceived at the state level and in the early months of the pandemic. Our methods -- tested in real-time and in an out-of-sample manner on a subset of 97 counties distributed across the US -- frequently anticipated sharp increases in COVID-19 activity 1-6 weeks before the onset of local outbreaks (defined as the time when the effective reproduction number $R_t$ becomes larger than 1 consistently). Given the continued emergence of COVID-19 variants of concern -- such as the most recent one, Omicron -- and the fact that multiple countries have not had full access to vaccines, the framework we present, while conceived for the county-level in the US, could be helpful in countries where similar data sources are available.

Viral discovery studies in wild animals often rely on cross-sectional surveys at a single time point. As a result, our understanding of the temporal stability of wild animal viromes remains poorly resolved. While studies of single host-virus systems indicate that host and environmental factors influence seasonal virus transmission dynamics, comparable insights for whole viral communities in multiple hosts are lacking. Leveraging non-invasive faecal samples from a long-term wild rodent study, we characterised viral communities of three common European rodent species (Apodemus sylvaticus, A. flavicollis, and M. glareolus) living in temperate woodland over a single year. Our findings indicate that a substantial fraction of the rodent virome is seasonally transient and associated with vertebrate or bacteria hosts. Further analyses of one of the most abundant virus families, Picornaviruses, show pronounced temporal changes in viral richness and diversity, which were associated with concurrent and up to ∼3-month lags in host density, ambient temperature, rainfall and humidity, suggesting complex feedbacks from the host and environmental factors on virus transmission and shedding in seasonal habitats. Overall, this study emphasizes the importance of understanding the seasonal dynamics of wild animal viromes in order to better predict and mitigate zoonotic risks.

Summary statistics, often derived from simplified models of epidemic spread, inform public health policy in real time. The instantaneous reproduction number, Rt, is predominant among these statistics, measuring the average ability of an infection to multiply. However, Rt encodes no temporal information and is sensitive to modelling assumptions. Consequently, some have proposed the epidemic growth rate, rt, i.e., the rate of change of the log-transformed case incidence, as a more temporally meaningful and model-agnostic policy guide. We examine this assertion, identifying if and when estimates of rt are more informative than those of Rt. We assess their relative strengths both for learning about pathogen transmission mechanisms and for guiding public health interventions in real time.

Limited genomic sampling in many high-incidence countries has impeded studies of severe respiratory syndrome coronavirus 2 (SARS-CoV-2) genomic epidemiology. Consequently, critical questions remain about the generation and global distribution of virus genetic diversity. We investigated SARS-CoV-2 transmission dynamics in Gujarat, India, during the state’s first epidemic wave to shed light on spread of the virus in one of the regions hardest hit by the pandemic. By integrating case data and 434 whole-genome sequences sampled across 20 districts, we reconstructed the epidemic dynamics and spatial spread of SARS-CoV-2 in Gujarat. Our findings indicate global and regional connectivity and population density were major drivers of the Gujarat outbreak. We detected >100 virus lineage introductions, most of which appear to be associated with international travel. Within Gujarat, virus dissemination occurred predominantly from densely populated regions to geographically proximate locations that had low population density, suggesting that urban centers contributed disproportionately to virus spread.

Summary Background COVID-19 has the potential to cause substantial disruptions to health services, due to cases overburdening the health system or response measures limiting usual programmatic activities. We aimed to quantify the extent to which disruptions to services for HIV, tuberculosis, and malaria in low-income and middle-income countries with high burdens of these diseases could lead to additional loss of life over the next 5 years. Methods Assuming a basic reproduction number of 3·0, we constructed four scenarios for possible responses to the COVID-19 pandemic: no action, mitigation for 6 months, suppression for 2 months, or suppression for 1 year. We used established transmission models of HIV, tuberculosis, and malaria to estimate the additional impact on health that could be caused in selected settings, either due to COVID-19 interventions limiting activities, or due to the high demand on the health system due to the COVID-19 pandemic. Findings In high-burden settings, deaths due to HIV, tuberculosis, and malaria over 5 years could increase by up to 10%, 20%, and 36%, respectively, compared with if there was no COVID-19 pandemic. The greatest impact on HIV was estimated to be from interruption to antiretroviral therapy, which could occur during a period of high health system demand. For tuberculosis, the greatest impact would be from reductions in timely diagnosis and treatment of new cases, which could result from any prolonged period of COVID-19 suppression interventions. The greatest impact on malaria burden could be as a result of interruption of planned net campaigns. These disruptions could lead to a loss of life-years over 5 years that is of the same order of magnitude as the direct impact from COVID-19 in places with a high burden of malaria and large HIV and tuberculosis epidemics. Interpretation Maintaining the most critical prevention activities and health-care services for HIV, tuberculosis, and malaria could substantially reduce the overall impact of the COVID-19 pandemic. Funding Bill & Melinda Gates Foundation, Wellcome Trust, UK Department for International Development, and Medical Research Council.

In Bayesian phylogenetics, the coalescent process provides an informative framework for inferring changes in the effective size of a population from a phylogeny (or tree) of sequences sampled from that population. Popular coalescent inference approaches such as the Bayesian Skyline Plot, Skyride, and Skygrid all model these population size changes with a discontinuous, piecewise-constant function but then apply a smoothing prior to ensure that their posterior population size estimates transition gradually with time. These prior distributions implicitly encode extra population size information that is not available from the observed coalescent data or tree. Here, we present a novel statistic, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\Omega$\end{document}, to quantify and disaggregate the relative contributions of the coalescent data and prior assumptions to the resulting posterior estimate precision. Our statistic also measures the additional mutual information introduced by such priors. Using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\Omega$\end{document} we show that, because it is surprisingly easy to overparametrize piecewise-constant population models, common smoothing priors can lead to overconfident and potentially misleading inference, even under robust experimental designs. We propose \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\Omega$\end{document} as a useful tool for detecting when effective population size estimates are overly reliant on prior assumptions and for improving quantification of the uncertainty in those estimates.[Coalescent processes; effective population size; information theory; phylodynamics; prior assumptions; skyline plots.]

Whether an outbreak of infectious disease is likely to grow or dissipate is determined through the time-varying reproduction number,Rt. Real-time or retrospective identification of changes inRtfollowing the imposition or relaxation of interventions can thus contribute important evidence about disease transmission dynamics which can inform policymaking. Here, we present a method for estimating shifts inRtwithin a renewal model framework. Our method, which we call EpiCluster, is a Bayesian nonparametric model based on the Pitman-Yor process. We assume thatRtis piecewise-constant, and the incidence data and priors determine when or whetherRtshould change and how many times it should do so throughout the series. We also introduce a prior which induces sparsity over the number of changepoints. Being Bayesian, our approach yields a measure of uncertainty inRtand its changepoints. EpiCluster is fast, straightforward to use, and we demonstrate that it provides automated detection of rapid changes in transmission, either in real-time or retrospectively, for synthetic data series where theRtprofile is known. We illustrate the practical utility of our method by fitting it to case data of outbreaks of COVID-19 in Australia and Hong Kong, where it finds changepoints coinciding with the imposition of non-pharmaceutical interventions. Bayesian nonparametric methods, such as ours, allow the volume and complexity of the data to dictate the number of parameters required to approximate the process and should find wide application in epidemiology.HighlightsIdentifying periods of rapid change in transmission is important for devising strategies to control epidemics.We assume that the time-varying reproduction number,Rt, is piecewise-constant and transmission is determined by a Poisson renewal model.We develop a Bayesian nonparametric method, called EpiCluster, which uses a Pitman Yor process to infer changepoints inRt.Using simulated incidence series, we demonstrate that our method is adept at inferring changepoints.Using real COVID-19 incidence series, we infer abrupt changes in transmission at times coinciding with the imposition of non-pharmaceutical interventions.

Inferring the transmission potential of an infectious disease during the low-incidence period following an epidemic wave is crucial for preparedness. In this period, necessarily scarce data hamper existing inference methods, blurring early-warning signals essential for discriminating between the likelihoods of resurgence versus elimination. Advanced insight into whether a region of interest will face elevating caseloads (requiring swift community-wide interventions) or achieve local elimination (allowing interventions to be relaxed or refocussed on controlling the importation of infections), can be the difference between decisive and ineffective policy. We propose a novel early-warning framework that formally maximises information extracted from low-incidence data to robustly infer the chances of sustained local transmission or elimination in real time, at any desired scale of investigation. Applying this framework, we decipher previously hidden disease-transmission signals from the prolonged low-incidence COVID-19 data of New Zealand, Hong Kong and Victoria state, Australia. We uncover how timely interventions averted dangerous, resurgent waves of COVID-19 and support official declarations of elimination. Across these locations, we obtain strong evidence for the effectiveness of rapid and adaptive COVID-19 responses.

Mathematical models can provide insights into the control of pandemic COVID-19, which remains a global priority. The dynamics of directly-transmitted infectious diseases, such as COVID-19, are usually described by compartmental models where individuals are classified as susceptible, infected and removed. These SIR models typically assume homogenous transmission of infection, even in large populations, a simplification that is convenient but inconsistent with observations. Here we use original data on the dynamics of COVID-19 spread in a Brazilian city to investigate the structure of the transmission network. We find that transmission can be described by a network in which each infectious individual has a small number of susceptible contacts, of the order of 2-5, which is independent of total population size. Compared with standard models of homogenous mixing, this scale-free, fractal infection process gives a better description of COVID-19 dynamics through time. In addition, the contact process explains the geographically localized clusters of disease seen in this Brazilian city. Our scale-free model can help refine criteria for physical and social distancing in order to more effectively mitigate the spread of COVID-19. We propose that scale-free COVID-19 dynamics could be a widespread phenomenon, a topic for further investigation.

We find that epidemic resurgence, defined as an upswing in the effective reproduction number (R) of the contagion from subcritical to supercritical values, is fundamentally difficult to detect in real time. Inherent latencies in pathogen transmission, coupled with smaller and intrinsically noisier case incidence across periods of subcritical spread, mean that resurgence cannot be reliably detected without significant delays of the order of the generation time of the disease, even when case reporting is perfect. In contrast, epidemic suppression (where R falls from supercritical to subcritical values) may be ascertained 5–10 times faster due to the naturally larger incidence at which control actions are generally applied. We prove that these innate limits on detecting resurgence only worsen when spatial or demographic heterogeneities are incorporated. Consequently, we argue that resurgence is more effectively handled proactively, potentially at the expense of false alarms. Timely responses to recrudescent infections or emerging variants of concern are more likely to be possible when policy is informed by a greater quality and diversity of surveillance data than by further optimisation of the statistical models used to process routine outbreak data.Author summaryThe timely detection of epidemic resurgence (i.e., upcoming waves of infected cases) is crucial for informing public health policy, providing valuable signals for implementing interventions and identifying emerging pathogenic variants or important population-level behavioural shifts. Increases in epidemic transmissibility, parametrised by the time-varying reproduction number, R, commonly signify resurgence. While many studies have improved computational methods for inferring R from case data, to enhance real-time resurgence detection, few have examined what limits, if any, fundamentally restrict our ability to perform this inference. We apply optimal Bayesian detection algorithms and sensitivity tests and discover that resurgent (upward) R-changes are intrinsically more difficult to detect than equivalent downward changes indicating control. This asymmetry derives from the often lower and stochastically noisier case numbers that associate with resurgence, and induces detection delays on the order of the disease generation time. We prove these delays only worsen if spatial or demographic differences in transmissibility are modelled. As these fundamental limits exist even if case data are perfect, we conclude that designing integrated surveillance systems that fuse potentially timelier data sources (e.g., wastewater) may be more important than improving R-estimation methodology and deduce that there may be merit (subject to false alarm costs) in conservative resurgence response initiatives.

Genomic surveillance of SARS-CoV-2 has played a decisive role in understanding the transmission and evolution of the virus during its emergence and continued circulation. However, limited genomic sampling in many high-incidence countries has impeded detailed studies of SARS-CoV-2 genomic epidemiology. Consequently, critical questions remain about the generation and global distribution of virus genetic diversity. To address this gap, we investigated SARS-CoV-2 transmission dynamics in Gujarat, India, during its first epidemic wave and shed light on virus’ spread in one of the pandemic’s hardest-hit regions. By integrating regional case data and 434 whole virus genome sequences sampled across 20 districts from March to July 2020, we reconstructed the epidemic dynamics and spatial spread of SARS-CoV-2 in Gujarat, India. Our findings revealed that global and regional connectivity, along with population density, were significant drivers of the Gujarat SARS-CoV-2 outbreak. The three most populous districts in Gujarat accounted ∼84% of total cases during the first wave. Moreover, we detected over 100 virus lineage introductions, which were primarily associated with international travel. Within Gujarat, virus dissemination occurred predominantly from densely populated regions to geographically proximate locations with low-population density. Our findings suggest SARS-CoV-2 transmission follows a gravity model in India, with urban centres contributing disproportionately to onward virus spread.

Background: As of July 2021, more than 180,000,000 cases of COVID-19 have been reported across the world, with more than 4 million deaths. Mathematical modelling and forecasting efforts have been widely used to inform policy-making and to create situational awareness. Methods and Findings: From 8th March to 29th November 2020, we produced weekly estimates of SARS-CoV-2 transmissibility and forecasts of deaths due to COVID-19 for countries with evidence of sustained transmission. The estimates and forecasts were based on an ensemble model comprising of three models that were calibrated using only the reported number of COVID-19 cases and deaths in each country. We also developed a novel heuristic to combine weekly estimates of transmissibility and potential changes in population immunity due to infection to produce forecasts over a 4-week horizon. We evaluated the robustness of the forecasts using relative error, coverage probability, and comparisons with null models. Conclusions: During the 39-week period covered by this study, we produced short- and medium-term forecasts for 81 countries. Both the short- and medium-term forecasts captured well the epidemic trajectory across different waves of COVID-19 infections with small relative errors over the forecast horizon. The model was well calibrated with 56.3% and 45.6% of the observations lying in the 50% Credible Interval in 1-week and 4-week ahead forecasts respectively. We could accurately characterise the overall phase of the epidemic up to 4-weeks ahead in 84.9% of country-days. The medium-term forecasts can be used in conjunction with the short-term forecasts of COVID-19 mortality as a useful planning tool as countries continue to relax stringent public health measures that were implemented to contain the pandemic.

BackgroundAs of July 2021, more than 180,000,000 cases of COVID-19 have been reported across the world, with more than 4 million deaths. Mathematical modelling and forecasting efforts have been widely used to inform policy-making and to create situational awareness.Methods and FindingsFrom 8th March to 29th November 2020, we produced weekly estimates of SARS-CoV-2 transmissibility and forecasts of deaths due to COVID-19 for countries with evidence of sustained transmission. The estimates and forecasts were based on an ensemble model comprising of three models that were calibrated using only the reported number of COVID-19 cases and deaths in each country. We also developed a novel heuristic to combine weekly estimates of transmissibility and potential changes in population immunity due to infection to produce forecasts over a 4-week horizon. We evaluated the robustness of the forecasts using relative error, coverage probability, and comparisons with null models.ConclusionsDuring the 39-week period covered by this study, we produced short- and medium-term forecasts for 81 countries. Both the short- and medium-term forecasts captured well the epidemic trajectory across different waves of COVID-19 infections with small relative errors over the forecast horizon. The model was well calibrated with 56.3% and 45.6% of the observations lying in the 50% Credible Interval in 1-week and 4-week ahead forecasts respectively. We could accurately characterise the overall phase of the epidemic up to 4-weeks ahead in 84.9% of country-days. The medium-term forecasts can be used in conjunction with the short-term forecasts of COVID-19 mortality as a useful planning tool as countries continue to relax stringent public health measures that were implemented to contain the pandemic.

Understanding and uncovering the mechanisms or motifs that molecular networks employ to regulate noise is a key problem in cell biology. As it is often difficult to obtain direct and detailed insight into these mechanisms, many studies instead focus on assessing the best precision attainable on the signalling pathways that compose these networks. Molecules signal one another over such pathways to solve noise regulating estimation and control problems. Quantifying the maximum precision of these solutions delimits what is achievable and allows hypotheses about underlying motifs to be tested without requiring detailed biological knowledge. The pathway capacity, which defines the maximum rate of transmitting information along it, is a widely used proxy for precision. Here it is shown, for estimation problems involving elementary yet biologically relevant birth-process networks, that capacity can be surprisingly misleading. A time-optimal signalling motif, called birth-following, is derived and proven to better the precision expected from the capacity, provided the maximum signalling rate constraint is large and the mean one above a certain threshold. When the maximum constraint is relaxed, perfect estimation is predicted by the capacity. However, the true achievable precision is found highly variable and sensitive to the mean constraint. Since the same capacity can map to different combinations of rate constraints, it can only equivocally measure precision. Deciphering the rate constraints on a signalling pathway may therefore be more important than computing its capacity.

BackgroundBrazil is one of the countries worst affected by the COVID-19 pandemic with over 20 million cases and 557,000 deaths reported. 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.MethodsWe 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 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.FindingsAfter 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:13·2,8·9] 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.InterpretationThis 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.FundingThis 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)

In response to the COVID-19 pandemic, countries have sought to control SARS-CoV-2 transmission by restricting population movement through social distancing interventions, thus reducing the number of contacts. Mobility data represent an important proxy measure of social distancing, and here, we characterise the relationship between transmission and mobility for 52 countries around the world. Transmission significantly decreased with the initial reduction in mobility in 73% of the countries analysed, but we found evidence of decoupling of transmission and mobility following the relaxation of strict control measures for 80% of countries. For the majority of countries, mobility explained a substantial proportion of the variation in transmissibility (median adjusted R-squared: 48%, interquartile range - IQR - across countries [27–77%]). Where a change in the relationship occurred, predictive ability decreased after the relaxation; from a median adjusted R-squared of 74% (IQR across countries [49–91%]) pre-relaxation, to a median adjusted R-squared of 30% (IQR across countries [12–48%]) post-relaxation. In countries with a clear relationship between mobility and transmission both before and after strict control measures were relaxed, mobility was associated with lower transmission rates after control measures were relaxed indicating that the beneficial effects of ongoing social distancing behaviours were substantial., Social distancing policies aiming to reduce COVID-19 transmission have been reflected in reductions in human mobility. Here, the authors show that reduced mobility is correlated with decreased transmission, but that this relationship weakened over time as social distancing measures were relaxed.

Understanding the causes and consequences of the emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants of concern is crucial to pandemic control yet difficult to achieve because they arise in the context of variable human behavior and immunity. We investigated the spatial invasion dynamics of lineage B.1.1.7 by jointly analyzing UK human mobility, virus genomes, and community-based polymerase chain reaction data. We identified a multistage spatial invasion process in which early B.1.1.7 growth rates were associated with mobility and asymmetric lineage export from a dominant source location, enhancing the effects of B.1.1.7's increased intrinsic transmissibility. We further explored how B.1.1.7 spread was shaped by nonpharmaceutical interventions and spatial variation in previous attack rates. Our findings show that careful accounting of the behavioral and epidemiological context within which variants of concern emerge is necessary to interpret correctly their observed relative growth rates. ispartof: SCIENCE vol:373 issue:6557 pages:889-+ ispartof: location:United States status: published

As of 1st June 2020, the US Centres for Disease Control and Prevention reported 104,232 confirmed or probable COVID-19-related deaths in the US. This was more than twice the number of deaths reported in the next most severely impacted country. We jointly model the US epidemic at the state-level, using publicly available death data within a Bayesian hierarchical semi-mechanistic framework. For each state, we estimate the number of individuals that have been infected, the number of individuals that are currently infectious and the time-varying reproduction number (the average number of secondary infections caused by an infected person). We use changes in mobility to capture the impact that non-pharmaceutical interventions and other behaviour changes have on the rate of transmission of SARS-CoV-2. We estimate that Rt was only below one in 23 states on 1st June. We also estimate that 3.7% [3.4%–4.0%] of the total population of the US had been infected, with wide variation between states, and approximately 0.01% of the population was infectious. We demonstrate good 3 week model forecasts of deaths with low error and good coverage of our credible intervals., High numbers of COVID-19-related deaths have been reported in the United States, but estimation of the true numbers of infections is challenging. Here, the authors estimate that on 1 June 2020, 3.7% of the US population was infected with SARS-CoV-2, and 0.01% was infectious, with wide variation by state.

The UK’s COVID-19 epidemic during early 2020 was one of world’s largest and unusually well represented by virus genomic sampling. Here we reveal the fine-scale genetic lineage structure of this epidemic through analysis of 50,887 SARS-CoV-2 genomes, including 26,181 from the UK sampled throughout the country’s first wave of infection. Using large-scale phylogenetic analyses, combined with epidemiological and travel data, we quantify the size, spatio-temporal origins and persistence of genetically-distinct UK transmission lineages. Rapid fluctuations in virus importation rates resulted in >1000 lineages; those introduced prior to national lockdown were larger and more dispersed. Lineage importation and regional lineage diversity declined after lockdown, whilst lineage elimination was size-dependent. We discuss the implications of our genetic perspective on transmission dynamics for COVID-19 epidemiology and control.

Inferring the dynamics of pathogen transmission during an outbreak is an important problem in both infectious disease epidemiology. In mathematical epidemiology, estimates are often informed by time series of confirmed cases, while in phylodynamics genetic sequences of the pathogen, sampled through time, are the primary data source. Each data type provides different, and potentially complementary, insight; recent studies have recognised that combining data sources can improve estimates of the transmission rate and number of infected individuals. However, inference methods are typically highly specialised and field-specific and are either computationally prohibitive or require intensive simulation, limiting their real-time utility.We present a novel birth-death phylogenetic model and derive a tractable analytic approximation of its likelihood, the computational complexity of which is linear in the size of the dataset. This approach combines epidemiological and phylodynamic data to produce estimates of key parameters of transmission dynamics and the number of unreported infections. Using simulated data we show (a) that the approximation agrees well with existing methods, (b) validate the claim of linear complexity and (c) explore robustness to model misspecification. This approximation facilitates inference on large datasets, which is increasingly important as large genomic sequence datasets become commonplace.Author summaryMathematical epidemiologists typically studies time series of cases, ie the epidemic curve, to understand the spread of pathogens. Genetic epidemiologists study similar problems but do so using measurements of the genetic sequence of the pathogen which also contain information about the transmission process. There have been many attempts to unite these approaches so that both data sources can be utilised. However, striking a suitable balance between model flexibility and fidelity, in a way that is computationally tractable, has proven challenging; there are several competing methods but for large datasets they are intractable. As sequencing of pathogen genomes becomes more common, and an increasing amount of epidemiological data is collected, this situation will only be exacerbated. To bridge the gap between the time series and genomic methods we developed an approximation scheme, called TimTam, which can accurately and efficiently estimate key features of an epidemic such as the prevalence of the infection and the effective reproduction number, ie how many people are currently infected and the degree to which the infection is spreading.

Highlights • COVID-19 measures were applied at similar dates across provinces in China • Hubei showed much greater disease severity compared to other provinces • Provincial data on epidemics and interventions are available for further research, Objectives This data collation effort aims to provide a comprehensive database to describe the epidemic trends and responses during the first wave of coronavirus disease 2019 (COVID-19) across main provinces in China. Methods From mid-January to March 2020, we extracted publicly available data on the spread and control of COVID-19 from 31 provincial health authorities and major media outlets in mainland China. Based on these data, we conducted a descriptive analysis of the epidemics in the six most-affected provinces. Results School closures, travel restrictions, community-level lockdown, and contact tracing were introduced concurrently around late January but subsequent epidemic trends were different across provinces. Compared to Hubei, the other five most-affected provinces reported a lower crude case fatality ratio and proportion of critical and severe hospitalised cases. From March 2020, as local transmission of COVID-19 declined, switching the focus of measures to testing and quarantine of inbound travellers could help to sustain the control of the epidemic. Conclusions Aggregated indicators of case notifications and severity distributions are essential for monitoring an epidemic. A publicly available database with these indicators and information on control measures provides a useful source for exploring further research and policy planning for response to the COVID-19 epidemic.

Attack rate in Manaus Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) incidence peaked in Manaus, Brazil, in May 2020 with a devastating toll on the city's inhabitants, leaving its health services shattered and cemeteries overwhelmed. Buss et al. collected data from blood donors from Manaus and São Paulo, noted when transmission began to fall, and estimated the final attack rates in October 2020 (see the Perspective by Sridhar and Gurdasani). Heterogeneities in immune protection, population structure, poverty, modes of public transport, and uneven adoption of nonpharmaceutical interventions mean that despite a high attack rate, herd immunity may not have been achieved. This unfortunate city has become a sentinel for how natural population immunity could influence future transmission. Events in Manaus reveal what tragedy and harm to society can unfold if this virus is left to run its course. Science , this issue p. 288 ; see also p. 230

Highlight We estimated SARS-CoV-2 infection prevalence in cohorts of repatriated citizens from Wuhan to be 0.44% (95% CI: 0.19%–1.03%). Although not representative of the wider population we believe these estimates are helpful in providing a conservative estimate of infection prevalence in Wuhan City, China, in the absence of large-scale population testing early in the epidemic.

The first case of COVID-19 was detected in Brazil on 25 February 2020. We report and contextualize epidemiological, demographic and clinical findings for COVID-19 cases during the first 3 months of the epidemic. By 31 May 2020, 514,200 COVID-19 cases, including 29,314 deaths, had been reported in 75.3% (4,196 of 5,570) of municipalities across all five administrative regions of Brazil. The R0 value for Brazil was estimated at 3.1 (95% Bayesian credible interval = 2.4–5.5), with a higher median but overlapping credible intervals compared with some other seriously affected countries. A positive association between higher per-capita income and COVID-19 diagnosis was identified. Furthermore, the severe acute respiratory infection cases with unknown aetiology were associated with lower per-capita income. Co-circulation of six respiratory viruses was detected but at very low levels. These findings provide a comprehensive description of the ongoing COVID-19 epidemic in Brazil and may help to guide subsequent measures to control virus transmission.

As of 1st June 2020, the US Centers for Disease Control and Prevention reported 104,232 confirmed or probable COVID-19-related deaths in the US. This was more than twice the number of deaths reported in the next most severely impacted country. We jointly modelled the US epidemic at the state-level, using publicly available death data within a Bayesian hierarchical semi-mechanistic framework. For each state, we estimate the number of individuals that have been infected, the number of individuals that are currently infectious and the time-varying reproduction number (the average number of secondary infections caused by an infected person). We used changes in mobility to capture the impact that non-pharmaceutical interventions and other behaviour changes have on the rate of transmission of SARS-CoV-2. Nationally, we estimated 3.7% [3.4%-4.0%] of the population had been infected by 1st June 2020, with wide variation between states, and approximately 0.01% of the population was infectious. We also demonstrated that good model forecasts of deaths for the next 3 weeks with low error and good coverage of our credible intervals.

We derive and validate a novel and analytic method for estimating the probability that an epidemic has been eliminated (i.e. that no future local cases will emerge) in real time. When this probability crosses 0.95 an outbreak can be declared over with 95% confidence. Our method is easy to compute, only requires knowledge of the incidence curve and the serial interval distribution, and evaluates the statistical lifetime of the outbreak of interest. Using this approach, we show how the time-varying under-reporting of infected cases will artificially inflate the inferred probability of elimination, leading to premature (false-positive) end-of-epidemic declarations. Contrastingly, we prove that incorrectly identifying imported cases as local will deceptively decrease this probability, resulting in delayed (false-negative) declarations. Failing to sustain intensive surveillance during the later phases of an epidemic can therefore substantially mislead policymakers on when it is safe to remove travel bans or relax quarantine and social distancing advisories. World Health Organisation guidelines recommend fixed (though disease-specific) waiting times for end-of-epidemic declarations that cannot accommodate these variations. Consequently, there is an unequivocal need for more active and specialised metrics for reliably identifying the conclusion of an epidemic., Author summary Deciding on when to declare an infectious disease epidemic over is an important and non-trivial problem. Early declarations can mean that interventions such as lockdowns, social distancing advisories and travel bans are relaxed prematurely, elevating the risk of additional waves of the disease. Late declarations can unnecessarily delay the re-opening of key economic sectors, for example trade, tourism and agriculture, potentially resulting in significant financial and livelihood losses. Here we develop and test a novel and exact data-driven method for optimising the timing of end-of-epidemic declarations. Our approach converts observations of infected cases up to any given time into a prediction of the likelihood that the epidemic is over at that time. Using this method, we quantify the reliability of end-of-epidemic declarations in real time, under ideal case surveillance, showing that it can depend strongly on past infection numbers. We then prove that failing to compensate for practical issues such as the time-varying under-reporting and importing of cases necessarily results in premature and delayed declarations, respectively. These variations and biases cannot be accommodated by current worldwide declaration guidelines. Sustained and intensive surveillance coupled with more adaptive declaration metrics are vital if informed end-of-epidemic declarations are to be made.

The effective reproduction number, Rt, is a key time-varying prognostic for the growth rate of any infectious disease epidemic. Significant changes in Rt can forewarn about new transmissions within a population or predict the efficacy of interventions. Inferring Rt reliably and in real-time from observed time-series of infected (demographic) data is an important problem in population dynamics. The renewal or branching process model is a popular solution that has been applied to Ebola and Zika virus disease outbreaks, among others, and is currently being used to investigate the ongoing COVID-19 pandemic. This model estimates Rt using a heuristically chosen piecewise function. While this facilitates real-time detection of statistically significant Rt changes, inference is highly sensitive to the function choice. Improperly chosen piecewise models might ignore meaningful changes or over-interpret noise-induced ones, yet produce visually reasonable estimates. No principled piecewise selection scheme exists. We develop a practical yet rigorous scheme using the accumulated prediction error (APE) metric from information theory, which deems the model capable of describing the observed data using the fewest bits as most justified. We derive exact posterior prediction distributions for infected population size and integrate these within an APE framework to obtain an exact and reliable method for identifying the piecewise function best supported by available epidemic data. We find that this choice optimises short-term prediction accuracy and can rapidly detect salient fluctuations in Rt, and hence the infected population growth rate, in real-time over the course of an unfolding epidemic. Moreover, we emphasise the need for formal selection by exposing how common heuristic choices, which seem sensible, can be misleading. Our APE-based method is easily computed and broadly applicable to statistically similar models found in phylogenetics and macroevolution, for example. Our results explore the relationships among estimate precision, forecast reliability and model complexity., Author summary Understanding how the population of infected individuals (which may be humans, animals or plants) fluctuates in size over the course of an epidemic is an important problem in epidemiology and ecology. The effective reproduction number, R, provides an intuitive and useful way of describing these fluctuations by characterising the growth rate of the infected population. An R > 1 signifies a burgeoning epidemic whereas R < 1 indicates a declining one. Public health agencies often use R to inform or corroborate vaccination and quarantine policies. However, popular approaches to inferring R from epidemic data make heuristic choices, which may lead to visually reasonable estimates that are deceptive or unreliable. By adapting mathematical tools from information theory, we develop a general and principled scheme for estimating R in a data-justified way. Our method exposes the pitfalls of heuristic estimates and provides an easily computable correction that also maximises our ability to predict upcoming population fluctuations. Our work is widely applicable to similar inference problems found in evolution and genetics, demonstrably useful for reliably analysing emerging epidemics in real time and highlights how abstract mathematical concepts can inspire novel and practical biological solutions, showcasing the importance of multidisciplinary research.

1AbstractBrazil is currently reporting the second highest number of COVID-19 deaths in the world. Here we characterise the initial dynamics of COVID-19 across the country and assess the impact of non-pharmaceutical interventions (NPIs) that were implemented using a semi-mechanistic Bayesian hierarchical modelling approach. Our results highlight the significant impact these NPIs had across states, reducing an average Rt > 3 to an average of 1.5 by 9-May-2020, but that these interventions failed to reduce Rt < 1, congruent with the worsening epidemic Brazil has experienced since. We identify extensive heterogeneity in the epidemic trajectory across Brazil, with the estimated number of days to reach 0.1% of the state population infected since the first nationally recorded case ranging from 20 days in São Paulo compared to 60 days in Goiás, underscoring the importance of sub-national analyses in understanding asynchronous state-level epidemics underlying the national spread and burden of COVID-19.

Summary Italy was the first European country to experience sustained local transmission of COVID-19. As of 1st May 2020, the Italian health authorities reported 28,238 deaths nationally. To control the epidemic, the Italian government implemented a suite of non-pharmaceutical interventions (NPIs), including school and university closures, social distancing and full lockdown involving banning of public gatherings and non essential movement. In this report, we model the effect of NPIs on transmission using data on average mobility. We estimate that the average reproduction number (a measure of transmission intensity) is currently below one for all Italian regions, and significantly so for the majority of the regions. Despite the large number of deaths, the proportion of population that has been infected by SARS-CoV-2 (the attack rate) is far from the herd immunity threshold in all Italian regions, with the highest attack rate observed in Lombardy (13.18% [10.66%-16.70%]). Italy is set to relax the currently implemented NPIs from 4th May 2020. Given the control achieved by NPIs, we consider three scenarios for the next 8 weeks: a scenario in which mobility remains the same as during the lockdown, a scenario in which mobility returns to pre-lockdown levels by 20%, and a scenario in which mobility returns to pre-lockdown levels by 40%. The scenarios explored assume that mobility is scaled evenly across all dimensions, that behaviour stays the same as before NPIs were implemented, that no pharmaceutical interventions are introduced, and it does not include transmission reduction from contact tracing, testing and the isolation of confirmed or suspected cases. New interventions, such as enhanced testing and contact tracing are going to be introduced and will likely contribute to reductions in transmission; therefore our estimates should be viewed as pessimistic projections. We find that, in the absence of additional interventions, even a 20% return to pre-lockdown mobility could lead to a resurgence in the number of deaths far greater than experienced in the current wave in several regions. Future increases in the number of deaths will lag behind the increase in transmission intensity and so a second wave will not be immediately apparent from just monitoring of the daily number of deaths. Our results suggest that SARS-CoV-2 transmission as well as mobility should be closely monitored in the next weeks and months. To compensate for the increase in mobility that will occur due to the relaxation of the currently implemented NPIs, adherence to the recommended social distancing measures alongside enhanced community surveillance including swab testing, contact tracing and the early isolation of infections are of paramount importance to reduce the risk of resurgence in transmission. SUGGESTED CITATION Michaela A. C. Vollmer, Swapnil Mishra, H Juliette T Unwin, Axel Gandy et al. Using mobility to estimate the transmission intensity of COVID-19 in Italy: a subnational analysis with future scenarios. Imperial College London (2020) doi:https://doi.org/10.25561/78677 This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Estimating past population dynamics from molecular sequences that have been sampled longitudinally through time is an important problem in infectious disease epidemiology, molecular ecology, and macroevolution. Popular solutions, such as the skyline and skygrid methods, infer past effective population sizes from the coalescent event times of phylogenies reconstructed from sampled sequences but assume that sequence sampling times are uninformative about population size changes. Recent work has started to question this assumption by exploring how sampling time information can aid coalescent inference. Here, we develop, investigate, and implement a new skyline method, termed the epoch sampling skyline plot (ESP), to jointly estimate the dynamics of population size and sampling rate through time. The ESP is inspired by real-world data collection practices and comprises a flexible model in which the sequence sampling rate is proportional to the population size within an epoch but can change discontinuously between epochs. We show that the ESP is accurate under several realistic sampling protocols and we prove analytically that it can at least double the best precision achievable by standard approaches. We generalize the ESP to incorporate phylogenetic uncertainty in a new Bayesian package (BESP) in BEAST2. We re-examine two well-studied empirical data sets from virus epidemiology and molecular evolution and find that the BESP improves upon previous coalescent estimators and generates new, biologically useful insights into the sampling protocols underpinning these data sets. Sequence sampling times provide a rich source of information for coalescent inference that will become increasingly important as sequence collection intensifies and becomes more formalized., Molecular Biology and Evolution, 37 (8), ISSN:0737-4038, ISSN:1537-1719

The effective reproduction number, Rt, is an important prognostic for infectious disease epidemics. Significant changes in Rt can forewarn about new transmissions or predict the efficacy of interventions. The renewal model infers Rt from incidence data and has been applied to Ebola virus disease and pandemic influenza outbreaks, among others. This model estimates Rt using a sliding window of length k. While this facilitates real-time detection of statistically significant Rt fluctuations, inference is highly k -sensitive. Models with too large or small k might ignore meaningful changes or over-interpret noise-induced ones. No principled k -selection scheme exists. We develop a practical yet rigorous scheme using the accumulated prediction error (APE) metric from information theory. We derive exact incidence prediction distributions and integrate these within an APE framework to identify the k best supported by available data. We find that this k optimises short-term prediction accuracy and expose how common, heuristic k -choices, which seem sensible, could be misleading.

Estimating temporal changes in a target population from phylogenetic or count data is an important problem in ecology and epidemiology. Reliable estimates can provide key insights into the climatic and biological drivers influencing the diversity or structure of that population and evidence hypotheses concerning its future growth or decline. In infectious disease applications, the individuals infected across an epidemic form the target population. The renewal model estimates the effective reproduction number,R, of the epidemic from counts of its observed cases. The skyline model infers the effective population size,N, underlying a phylogeny of sequences sampled from that epidemic. Practically,Rmeasures ongoing epidemic growth whileNinforms on historical caseload. While both models solve distinct problems, the reliability of their estimates depends onp-dimensional piecewise-constant functions. Ifpis misspecified, the model might underfit significant changes or overfit noise and promote a spurious understanding of the epidemic, which might misguide intervention policies or misinform forecasts. Surprisingly, no transparent yet principled approach for optimisingpexists. Usually,pis heuristically set, or obscurely controlled via complex algorithms. We present a computable and interpretablep-selection method based on the minimum description length (MDL) formalism of information theory. Unlike many standard model selection techniques, MDL accounts for the additional statistical complexity induced by how parameters interact. As a result, our method optimisespso thatRandNestimates properly adapt to the available data. It also outperforms comparable Akaike and Bayesian information criteria on several classification problems. Our approach requires some knowledge of the parameter space and exposes the similarities between renewal and skyline models.

Understanding the epidemiological dynamics of highly pathogenic avian influenza virus (HPAIV) in wild birds is crucial for guiding effective surveillance and control measures. The spread of H5 HPAIV has been well characterized over large geographical and temporal scales. However, information about the detailed dynamics and demographics of individual outbreaks in wild birds is rare and important epidemiological parameters remain unknown. We present data from a wild population of long-lived birds (mute swans; Cygnus olor ) that has experienced three outbreaks of related H5 HPAIVs in the past decade, specifically, H5N1 (2007), H5N8 (2016) and H5N6 (2017). Detailed demographic data were available and intense sampling was conducted before and after the outbreaks; hence the population is unusually suitable for exploring the natural epidemiology, evolution and ecology of HPAIV in wild birds. We show that key epidemiological features remain remarkably consistent across multiple outbreaks, including the timing of virus incursion and outbreak duration, and the presence of a strong age-structure in morbidity that likely arises from an equivalent age-structure in immunological responses. The predictability of these features across a series of outbreaks in a complex natural population is striking and contributes to our understanding of HPAIV in wild birds. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’. This issue is linked with the subsequent theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’.

Motivation Inferring the rates of change of a population from a reconstructed phylogeny of genetic sequences is a central problem in macro-evolutionary biology, epidemiology and many other disciplines. A popular solution involves estimating the parameters of a birth-death process (BDP), which links the shape of the phylogeny to its birth and death rates. Modern BDP estimators rely on random Markov chain Monte Carlo (MCMC) sampling to infer these rates. Such methods, while powerful and scalable, cannot be guaranteed to converge, leading to results that may be hard to replicate or difficult to validate. Results We present a conceptually and computationally different parametric BDP inference approach using flexible and easy to implement Snyder filter (SF) algorithms. This method is deterministic so its results are provable, guaranteed and reproducible. We validate the SF on constant rate BDPs and find that it solves BDP likelihoods known to produce robust estimates. We then examine more complex BDPs with time-varying rates. Our estimates compare well with a recently developed parametric MCMC inference method. Lastly, we perform model selection on an empirical Agamid species phylogeny, obtaining results consistent with the literature. The SF makes no approximations, beyond those required for parameter quantization and numerical integration and directly computes the posterior distribution of model parameters. It is a promising alternative inference algorithm that may serve either as a standalone Bayesian estimator or as a useful diagnostic reference for validating more involved MCMC strategies. Availability and implementation The Snyder filter is implemented in Matlab and the time-varying BDP models are simulated in R. The source code and data are freely available at https://github.com/kpzoo/snyder-birth-death-code. Supplementary information Supplementary data are available at Bioinformatics online.

The coalescent process describes how changes in the size or structure of a population influence the genealogical patterns of sequences sampled from that population. The estimation of (effective) population size changes from genealogies that are reconstructed from these sampled sequences is an important problem in many biological fields. Often, population size is characterized by a piecewise-constant function, with each piece serving as a population size parameter to be estimated. Estimation quality depends on both the statistical coalescent inference method employed, and on the experimental protocol, which controls variables such as the sampling of sequences through time and space, or the transformation of model parameters. While there is an extensive literature on coalescent inference methodology, there is comparatively little work on experimental design. The research that does exist is largely simulation-based, precluding the development of provable or general design theorems. We examine three key design problems: temporal sampling of sequences under the skyline demographic coalescent model, spatio-temporal sampling under the structured coalescent model, and time discretization for sequentially Markovian coalescent models. In all cases, we prove that 1) working in the logarithm of the parameters to be inferred (e.g., population size) and 2) distributing informative coalescent events uniformly among these log-parameters, is uniquely robust. “Robust” means that the total and maximum uncertainty of our parameter estimates are minimized, and made insensitive to their unknown (true) values. This robust design theorem provides rigorous justification for several existing coalescent experimental design decisions and leads to usable guidelines for future empirical or simulation-based investigations. Given its persistence among models, this theorem may form the basis of an experimental design paradigm for coalescent inference.