SARS-CoV-2 lineage-specific disease symptoms and disease severity in Sao Caetano do Sul city, Brazil (preprint)

Background: The city of Sao Caetano do Sul, Brazil, established a web-based platform to provide primary care to suspected COVID-19 patients, integrating clinical and demographic data and sample metadata. Here we describe lineage-specific spatiotemporal dynamics of infections, clinical symptoms, and disease severity during the first year of the epidemic. Methods: We selected and sequenced 879 PCR+ swab samples (8% of all reported cases), obtaining a spatially and temporally representative set of sequences. Daily lineage-specific prevalence was estimating using a moving-window approach, allowing inference of cumulative cases and symptom probability stratified by lineage using integrated data from the platform. Results: Most infections were caused by B.1.1.28 (41.3%), followed by Gamma (31.7%), Zeta (9.6%) and B1.1.33 (9.0%). Gamma and Zeta were associated with larger prevalence of dyspnoea (respectively 81.3% and 78.5%) and persistent fever (84.7% and 61.1%) compared to B.1.1.28 and B.1.1.33. Ageusia, anosmia, and coryza were respectively 18.9%, 20.3% and 17.8% less commonly caused by Gamma, while altered mental status was 108.9% more common in Zeta. Case incidence was spatially heterogeneous and larger in poorer and younger districts. Discussion: Our study demonstrates that Gamma was associated with more severe disease, emphasising the role of its increased disease severity in the heightened mortality levels in Brazil.

Encoding generation time changes within reproduction numbers (preprint)

We derive and introduce the angular reproduction number, {Omega}, which measures time-varying changes in epidemic transmissibility resulting from variations in both the effective reproduction number, R, and the generation time distribution, w. Predominant approaches for tracking the dynamics of pathogen spread either infer R or the epidemic growth rate r. However, R is easily biased by mismatches between the assumed and true w, while r is difficult to interpret in terms of the individual-level branching process underpinning transmission. Moreover, R and r may disagree on the relative transmissibility of two epidemics or variants (i.e., rA > rB does not imply RA > RB for variants A and B). We find that {Omega} responds meaningfully to mismatches in w while maintaining most of the interpretability of R. Additionally, we prove that {Omega} > 1 if and only if R > 1 and that {Omega} agrees with r on the relative transmissibility of pathogens. Estimating {Omega} is no harder than inferring R, uses existing software, and requires no generation time measurement. These advantages come at the expense of selecting one free parameter. We propose {Omega} as a useful statistic for tracking and comparing the spread of infectious diseases that may better reflect the impact of interventions when those interventions concurrently change both R and w or alter the relative risk of co-circulating pathogens.

Risk averse reproduction numbers improve resurgence detection (preprint)

The effective reproduction number R is a prominent statistic for inferring the transmissibility of infectious diseases and the effectiveness of interventions. R purportedly provides an easy-to-interpret threshold for deducing if an epidemic will grow (R >1) or decline (R < 1). We posit that this interpretation can be misleading and overconfident when applied to infections aggregated from groups with heterogeneous dynamics. In these settings, R implicitly weights the dynamics of groups by their number of circulating infections. This induces losses in sensitivity to the dynamics of high-risk groups that may spur resurgences, promotes premature indications of epidemic control, and renders the R = 1 threshold uninformative. Applying E-optimal experimental design theory, we derive the risk averse reproduction number E to ameliorate these issues. Using analytic approaches, simulations, and a real-world case study, we find that E achieves more meaningful consensus of the dynamics across groups without being overconfident in its estimates. An E >1 generates timely resurgence signals (upweighting the impact of high-risk groups), while E < 1 ensures constituent sub-outbreaks are under control. We propose E as an alternative to R for informing policy and assessing transmissibility over large scales (e.g., state or nationwide), where well-mixed assumptions break down.

Fundamental limits on inferring epidemic resurgence in real time using effective reproduction numbers

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.

Quantifying the information in noisy epidemic curves (preprint)

Reliably estimating the dynamics of transmissible diseases from noisy surveillance data is an enduring problem in modern epidemiology. Key parameters, such as the time-varying reproduction number, Rt at time t, are often inferred from incident time series, with the aim of informing policymakers on the growth rate of outbreaks or testing hypotheses about the effectiveness of public health interventions. However, the reliability of these inferences depends critically on reporting errors and latencies innate to those time series. While studies have proposed corrections for these issues, methodology for formally assessing how these noise sources degrade Rt estimate quality is lacking. By adapting Fisher information and experimental design theory, we develop an analytical framework to quantify the uncertainty induced by under-reporting and delays in reporting infections. This yields a novel metric, defined by the geometric means of reporting and cumulative delay probabilities, for ranking surveillance data informativeness. We apply this metric to two primary data sources for inferring Rt: epidemic case and death curves. We show that the assumption of death curves as more reliable, commonly made for acute infectious diseases such as COVID-19 and influenza, is not obvious and possibly untrue in many settings. Our framework clarifies and quantifies how actionable information about pathogen transmissibility is lost due to surveillance limitations.

Impact of spatiotemporal heterogeneity in COVID-19 disease surveillance on epidemiological parameters and case growth rates (preprint)

SARS-CoV-2 case data are primary sources for estimating epidemiological parameters and for modelling the dynamics of outbreaks. Understanding biases within case based data sources used in epidemiological analyses are important as they can detract from the value of these rich datasets. This raises questions of how variations in surveillance can affect the estimation of epidemiological parameters such as the case growth rates. We use standardised line list data of COVID-19 from Argentina, Brazil, Mexico and Colombia to estimate delay distributions of symptom-onset-to-confirmation, -hospitalisation and -death as well as hospitalisation-to-death at high spatial resolutions and throughout time. Using these estimates, we model the biases introduced by the delay from symptom-onset-to-confirmation on national and state level case growth rates (rt) using an adaptation of the Richardson-Lucy deconvolution algorithm. We find significant heterogeneities in the estimation of delay distributions through time and space with delay difference of up to 19 days between epochs at the state level. Further, we find that by changing the spatial scale, estimates of case growth rate can vary by up to 0.13 d-1. Lastly, we find that states with a high variance and/or mean delay in symptom-onset-to-diagnosis also have the largest difference between the rt estimated from raw and deconvolved case counts at the state level. We highlight the importance of high-resolution case based data in understanding biases in disease reporting and how these biases can be avoided by adjusting case numbers based on empirical delay distributions. Code and openly accessible data to reproduce analyses presented here are available.

Using digital traces to build prospective and real-time county-level early warning systems to anticipate COVID-19 outbreaks in the United States (preprint)

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.

Using multiple sampling strategies to estimate SARS-CoV-2 epidemiological parameters from genomic sequencing data (preprint)

SARS-CoV-2 virus genomes are currently being sequenced at an unprecedented pace. The choice of sequences used in genetic and epidemiological analysis is important as it can induce biases that detract from the value of these rich datasets. This raises questions about how a set of sequences should be chosen for analysis, and which epidemiological parameters derived from genomic data are sensitive or robust to changes in sampling. We provide initial insights on these largely understudied problems using SARS-CoV-2 genomic sequences from Hong Kong and the Amazonas State, Brazil. We consider sampling schemes that select sequences uniformly, in proportion or reciprocally with case incidence and which simply use all available sequences (unsampled). We apply Birth-Death Skyline and Skygrowth methods to estimate the time-varying reproduction number (Rt) and growth rate (rt) under these strategies as well as related R0 and date of origin parameters. We compare these to estimates from case data derived from EpiFilter, which we use as a reference for assessing bias. We find that both Rt and rt are sensitive to changes in sampling whilst R0 and date of origin are relatively robust. Moreover, we find that the unsampled datasets (opportunistic sampling) provided, overall, the worst Rt and rt estimates for both Hong Kong and the Amazonas case studies. We highlight that sampling strategy may be an influential yet neglected component of sequencing analysis pipelines. More targeted attempts at genomic surveillance and epidemic analyses, particularly in resource-poor settings which have a limited genomic capability, are necessary to maximise the informativeness of virus genomic datasets.

Scale-free dynamics of Covid-19 in a Brazilian city (preprint)

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.

Genomic epidemiology of early SARS-CoV-2 transmission dynamics in Gujarat, India (preprint)

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 pandemics 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.

Global predictions of short- to medium-term COVID-19 transmission trends : a retrospective assessment (preprint)

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.

Tracking the emergence of disparities in the subnational spread of COVID-19 in Brazil using an online application for real-time data visualisation. (preprint)

Brazil is one of the countries worst affected by the COVID-19 pandemic. We have developed CLIC-Brazil an online application for the real-time visualisation of COVID-19 data in Brazil at the municipality level. In the app, case and death data are standardised to allow comparisons to be made between places and over time. Estimates of Rt , a measure of the rate of propagation of the epidemic, over time are also made. Using data from the app, regression analyses identified factors associated with; the rate of initial spread, early epidemic intensity and predictions of the likelihood of occurrence of new incidence maxima. Municipalities with higher metrics of social development experienced earlier onset and faster growing epidemics, although space and time were the predominant predictive factors. Differences in the initial epidemic intensity (mean Rt ) were largely driven by geographic location and the date of local onset. This study demonstrates that by monitoring, standardising and analysing the development of an epidemic at a local level, insights can be gained into spatial and temporal heterogeneities.

Novel early-warning system for evaluating control and elimination of SARS-CoV-2 reveals alignment of policy with local transmission in New Zealand (preprint)

Discriminating between second waves of community transmission, which necessitate broad-spectrum interventions, and multiple stuttering epidemic chains from repeated importations, which require targeted controls, is crucial for outbreak preparedness. However, necessarily scarce data available in the lull between potential epidemic waves cripples standard inference engines, blurring early-warning signals. We propose a novel framework for denoising inter-wave data, revealing how timely policy in New Zealand achieved local elimination and avoided dangerous resurgence.

Establishment & lineage dynamics of the SARS-CoV-2 epidemic in the UK (preprint)

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.

State-level tracking of COVID-19 in the United States (preprint)

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.

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

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.

Key Questions for Modelling COVID-19 Exit Strategies (preprint)

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.

Report 21: Estimating COVID-19 cases and reproduction number in Brazil (preprint)

Brazil is an epicentre for COVID-19 in Latin America. In this report we describe the Brazilian epidemic using three epidemiological measures: the number of infections, the number of deaths and the reproduction number. Our modelling framework requires sufficient death data to estimate trends, and we therefore limit our analysis to 16 states that have experienced a total of more than fifty deaths. The distribution of deaths among states is highly heterogeneous, with 5 states---Sao Paulo, Rio de Janeiro, Ceara, Pernambuco and Amazonas---accounting for 81% of deaths reported to date. In these states, we estimate that the percentage of people that have been infected with SARS-CoV-2 ranges from 3.3% (95% CI: 2.8%-3.7%) in Sao Paulo to 10.6% (95% CI: 8.8%-12.1%) in Amazonas. The reproduction number (a measure of transmission intensity) at the start of the epidemic meant that an infected individual would infect three or four others on average. Following non-pharmaceutical interventions such as school closures and decreases in population mobility, we show that the reproduction number has dropped substantially in each state. However, for all 16 states we study, we estimate with high confidence that the reproduction number remains above 1. A reproduction number above 1 means that the epidemic is not yet controlled and will continue to grow. These trends are in stark contrast to other major COVID-19 epidemics in Europe and Asia where enforced lockdowns have successfully driven the reproduction number below 1. While the Brazilian epidemic is still relatively nascent on a national scale, our results suggest that further action is needed to limit spread and prevent health system overload.

A sub-national analysis of the rate of transmission of COVID-19 in Italy (preprint)

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.