An exact method for quantifying the reliability of end-of-epidemic declarations in real time.

Funder: Christ Church University of Oxford Junior Research FellowshipWe 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

On the derivation of the renewal equation from an age-dependent branching process: an epidemic modelling perspective

Renewal processes are a popular approach used in modelling infectious disease outbreaks. In a renewal process, previous infections give rise to future infections. However, while this formulation seems sensible, its application to infectious disease can be difficult to justify from first principles. It has been shown from the seminal work of Bellman and Harris that the renewal equation arises as the expectation of an age-dependent branching process. In this paper we provide a detailed derivation of the original Bellman Harris process. We introduce generalisations, that allow for time-varying reproduction numbers and the accounting of exogenous events, such as importations. We show how inference on the renewal equation is easy to accomplish within a Bayesian hierarchical framework. Using off the shelf MCMC packages, we fit to South Korea COVID-19 case data to estimate reproduction numbers and importations. Our derivation provides the mathematical fundamentals and assumptions underpinning the use of the renewal equation for modelling outbreaks

Seasonal dynamics of the wild rodent faecal virome

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. Utilizing noninvasive faecal samples from a long-term wild rodent study, we characterized viral communities of three common European rodent species (Apodemus sylvaticus, A. flavicollis and Myodes 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 common virus families, Picornaviridae, show pronounced temporal changes in viral richness and evenness, 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

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 S\~o 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) -S{\~{a}}o Paulo Research Foundation (FAPESP) CADDE partnership award (MR/S0195/1 and FAPESP 18/14389-0

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)

Key questions for modelling COVID-19 exit strategies

Combinations of intense non-pharmaceutical interventions ('lockdowns') were introduced in countries worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement lockdown exit strategies that allow restrictions to be relaxed while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, will allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. The roadmap requires a global collaborative effort from the scientific community and policy-makers, and is made up of three parts: i) improve estimation of key epidemiological parameters; ii) understand sources of heterogeneity in populations; iii) focus on requirements for data collection, particularly in Low-to-Middle-Income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health

Database of epidemic trends and control measures during the first wave of COVID-19 in mainland China.

OBJECTIVES: In this data collation study, we aimed to provide a comprehensive database describing the epidemic trends and responses during the first wave of coronavirus disease 2019 (COVID-19) throughout the main provinces in China. METHODS: From mid-January to March 2020, we extracted publicly available data regarding 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 descriptive analyses of the epidemic 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 differed among provinces. Compared with 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 the local transmission of COVID-19 declined, switching the focus of measures to the testing and quarantine of inbound travellers may have helped 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 containing these indicators and information regarding control measures is a useful resource for further research and policy planning in response to the COVID-19 epidemic

Data from: Robust design for coalescent model inference

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

Robust coalescent design

Code for examining Fisher experimental design for coalescent processes

Using information theory to optimise epidemic models for real-time prediction and estimation.

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