Generative Bayesian modeling to nowcast the effective reproduction number from line list data with missing symptom onset dates (preprint)

The time-varying effective reproduction number $R_t$ is a widely used indicator of transmission dynamics during infectious disease outbreaks. Timely estimates of $R_t$ can be obtained from observations close to the original date of infection, such as the date of symptom onset. However, these data often have missing information and are subject to right truncation. Previous methods have addressed these problems independently by first imputing missing onset dates, then adjusting truncated case counts, and finally estimating the effective reproduction number. This stepwise approach makes it difficult to propagate uncertainty and can introduce subtle biases during real-time estimation due to the continued impact of assumptions made in previous steps. In this work, we integrate imputation, truncation adjustment, and $R_t$ estimation into a single generative Bayesian model, allowing direct joint inference of case counts and $R_t$ from line list data with missing symptom onset dates. We then use this framework to compare the performance of nowcasting approaches with different stepwise and generative components on synthetic line list data for multiple outbreak scenarios and across different epidemic phases. We find that under long reporting delays, intermediate smoothing, as is common practice in stepwise approaches, can bias nowcasts of case counts and $R_t$, which is avoided in a joint generative approach due to shared regularization of all model components. On incomplete line list data, a fully generative approach enables the quantification of uncertainty due to missing onset dates without the need for an initial multiple imputation step. In a real-world comparison using hospitalization line list data from the COVID-19 pandemic in Switzerland, we observe the same qualitative differences between approaches. Our generative modeling components have been integrated into the R package epinowcast.

Improving modelling for epidemic responses: reflections from members of the UK infectious disease modelling community on their experiences during the COVID-19 pandemic (preprint)

The COVID-19 pandemic both relied and placed significant burdens on the experts involved from research and public health sectors. The sustained high pressure of a pandemic on responders, such as healthcare workers, can lead to lasting psychological impacts including acute stress disorder, post-traumatic stress disorder, burnout, and moral injury, which can impact individual wellbeing and productivity. As members of the infectious disease modelling community, we convened a reflective workshop to understand the professional and personal impacts of response work on our community and to propose recommendations for future epidemic responses. The attendees represented a range of career stages, institutions, and disciplines. This piece was collectively produced by those present at the session based on our collective experiences. Key issues we identified at the workshop were lack of institutional support, insecure contracts, unequal credit and recognition, and mental health impacts. Our recommendations include rewarding impactful work, fostering academia-public health collaboration, decreasing dependence on key individuals by developing teams, increasing transparency in decision-making, and implementing sustainable work practices. Despite limitations in representation, this workshop provided valuable insights into the UK COVID-19 modelling experience and guidance for future public health crises. Recognising and addressing the issues highlighted here is crucial, in our view, for ensuring the effectiveness of epidemic response work in the future.

Within-host SARS-CoV-2 viral kinetics informed by complex life course exposures reveals different intrinsic properties of Omicron and Delta variants (preprint)

The emergence of successive SARS-CoV-2 variants of concern (VOC) during 2020-22, each exhibiting increased epidemic growth relative to earlier circulating variants, has created a need to understand the drivers of such growth. However, both pathogen biology and changing host characteristics - such as varying levels of immunity - can combine to influence replication and transmission of SARS-CoV-2 within and between hosts. Disentangling the role of variant and host in individual-level viral shedding of VOCs is essential to inform COVID-19 planning and response, and interpret past epidemic trends. Using data from a prospective observational cohort study of healthy adult volunteers undergoing weekly occupational health PCR screening, we developed a Bayesian hierarchical model to reconstruct individual-level viral kinetics and estimate how different factors shaped viral dynamics, measured by PCR cycle threshold (Ct) values over time. Jointly accounting for both inter-individual variation in Ct values and complex host characteristics - such as vaccination status, exposure history and age - we found that age and number of prior exposures had a strong influence on peak viral replication. Older individuals and those who had at least five prior antigen exposures to vaccination and/or infection typically had much lower levels of shedding. Moreover, we found evidence of a correlation between the speed of early shedding and duration of incubation period when comparing different VOCs and age groups. Our findings illustrate the value of linking information on participant characteristics, symptom profile and infecting variant with prospective PCR sampling, and the importance of accounting for increasingly complex population exposure landscapes when analysing the viral kinetics of VOCs.

Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany (preprint)

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.

Collaborative nowcasting of COVID-19 hospitalization incidences in Germany (preprint)

Real-time surveillance is a crucial element in the response to infectious disease outbreaks. However, the interpretation of incidence data is often hampered by delays occurring at various stages of data gathering and reporting. As a result, recent values are biased downward, which obscures current trends. Statistical nowcasting techniques can be employed to correct these biases, allowing for accurate characterization of recent developments and thus enhancing situational awareness. In this paper, we present a preregistered real-time assessment of eight nowcasting approaches, applied by independent research teams to German 7-day hospitalization incidences. This indicator played an important role in the management of the pandemic in Germany and was linked to levels of non-pharmaceutical interventions via certain thresholds. Due to its definition, in which hospitalization counts are aggregated by the date of case report rather than admission, German hospitalization incidences are particularly affected by delays and can take several weeks or months to fully stabilize. For this study, all methods were applied from 22 November 2021 to 29 April 2022, with probabilistic nowcasts produced each day for the current and 28 preceding days. Nowcasts at the national, state, and age-group levels were collected in the form of quantiles in a public repository and displayed in a dashboard. Moreover, a mean and a median ensemble nowcast were generated. We find that overall, the compared methods were able to remove a large part of the biases introduced by delays. Most participating teams underestimated the importance of very long delays, though, resulting in nowcasts with a slight downward bias. The accompanying uncertainty intervals were also too narrow for almost all methods. Averaged over all nowcast horizons, the best performance was achieved by a model using case incidences as a covariate and taking into account longer delays than the other approaches. For the most recent days, which are often considered the most relevant in practice, a mean ensemble of the submitted nowcasts performed best. We conclude by providing some lessons learned on the definition of nowcasting targets and practical challenges.

Nowcasting the 2022 mpox outbreak in England (preprint)

In May 2022, a cluster of mpox cases were detected in the UK that could not be traced to recent travel history from an endemic region. Over the coming months, the outbreak grew, with over 3000 total cases reported in the UK, and similar outbreaks occurring worldwide. These outbreaks appeared linked to sexual contact networks between gay, bisexual and other men who have sex with men. Following the COVID-19 pandemic, local health systems were strained, and therefore effective surveillance for mpox was essential for managing public health policy. However, the mpox outbreak in the UK was characterised by substantial delays in the reporting of the symptom onset date and specimen collection date for confirmed positive cases. These delays led to substantial backfilling in the epidemic curve, making it challenging to interpret the epidemic trajectory in real-time. Many nowcasting models exist to tackle this challenge in epidemiological data, but these lacked sufficient flexibility. We have developed a novel nowcasting model using generalised additive models to correct the mpox epidemic curve in England, and provide real-time characteristics of the state of the epidemic, including the real-time growth rate. This model benefited from close collaboration with individuals involved in collecting and processing the data, enabling temporal changes in the reporting structure to be built into the model, which improved the robustness of the nowcasts generated.

Evaluating the use of social contact data to produce age-specific forecasts of SARS-CoV-2 incidence (preprint)

Short-term forecasts can provide predictions of how an epidemic will change in the near future and form a central part of outbreak mitigation and control. Renewal-equation based models are increasingly popular. They infer key epidemiological parameters from historical epidemiological data and forecast future epidemic dynamics without requiring complex mechanistic assumptions. However, these models typically ignore interaction between age-groups, partly due to challenges in parameterising a time varying interaction matrix. Social contact data collected regularly by the CoMix survey during the COVID-19 epidemic in England, provide a means to inform interaction between age-groups in real-time. We developed an age-specific forecasting framework and applied it to two age-stratified time-series: incidence of SARS-CoV-2 infection, estimated from a national infection and antibody prevalence survey; and, reported cases according to the UK national COVID-19 dashboard. Jointly fitting our model to social contact data from the CoMix study, we inferred a time-varying next generation matrix which we used to project infections and cases in the four weeks following each of 29 forecast dates between October 2021 and November 2022. We evaluated the forecasts using proper scoring rules and compared performance with three other models with alternative data and specifications alongside two naive baseline models. Overall, incorporating age-interaction improved forecasts of infections and the CoMix-data-informed model was the best performing model at time horizons between two and four weeks. However, this was not true when forecasting cases. We found that age-group-interaction was most important for predicting cases in children and older adults. The contact-data-informed models performed best during the winter months of 2020 - 2021, but performed comparatively poorly in other periods. We highlight challenges regarding the incorporation of contact data in forecasting and offer proposals as to how to extend and adapt our approach, which may lead to more successful forecasts in future.

Accumulation of immunity in heavy-tailed sexual contact networks shapes monkeypox outbreak sizes (preprint)

Many countries affected by the global outbreak of monkeypox in 2022 have observed a decline in cases. Our mathematical model incorporating empirical estimates of the heavy-tailed sexual partnership distribution among men who have sex with men (MSM) suggests that monkeypox epidemics can hit the infection-derived herd immunity threshold and begin to decline with less than 1% of sexually active MSM population infected regardless of interventions or behavioural changes. Consistently, we found that many countries and US states experienced an epidemic peak with cumulative cases of around 0.1–0.7% of MSM population. The observed decline in cases may not necessarily be attributable to interventions or behavioural changes primarily, although continuing these approaches in the most effective manner is still warranted to minimise total epidemic size.

Evaluating an epidemiologically motivated surrogate model of a multi-model ensemble (preprint)

Multi-model and multi-team ensemble forecasts have become widely used to generate reliable short-term predictions of infectious disease spread. Notably, various public health agencies have used them to leverage academic disease modelling during the COVID-19 pandemic. However, ensemble forecasts are difficult to interpret and require extensive effort from numerous participating groups as well as a coordination team. In other fields, resource usage has been reduced by training simplified models that reproduce some of the observed behaviour of more complex models. Here we used observations of the behaviour of the European COVID-19 Forecast Hub ensemble combined with our own forecasting experience to identify a set of properties present in current ensemble forecasts. We then developed a parsimonious forecast model intending to mirror these properties. We assess forecasts generated from this model in real time over six months (the 15th of January 2022 to the 19th o July 2022) and for multiple European countries. We focused on forecasts of cases one to four weeks ahead and compared them to those by the European forecast hub ensemble. We find that the surrogate model behaves qualitatively similarly to the ensemble in many instances, though with increased uncertainty and poorer performance around periods of peak incidence (as measured by the Weighted Interval Score). The performance differences, however, seem to be partially due to a subset of time points, and the proposed model appears better probabilistically calibrated than the ensemble. We conclude that our simplified forecast model may have captured some of the dynamics of the hub ensemble, but more work is needed to understand the implicit epidemiological model that it represents.

Inferring the differences in incubation-period and generation-interval distributions of the Delta and Omicron variants of SARS-CoV-2 (preprint)

Estimating the differences in the incubation-period, serial-interval, and generation-interval distributions of SARS-CoV-2 variants is critical to understanding their transmission and control. However, the impact of epidemic dynamics is often neglected in estimating the timing of infection and transmission---for example, when an epidemic is growing exponentially, a cohort of infected individuals who developed symptoms at the same time are more likely to have been infected recently. Here, we re-analyze incubation-period and serial-interval data describing transmissions of the Delta and Omicron variants from the Netherlands at the end of December 2021. Previous analysis of the same data set reported shorter mean observed incubation period (3.2 days vs 4.4 days) and serial interval (3.5 days vs 4.1 days) for the Omicron variant, but the number of infections caused by the Delta variant decreased during this period as the number of Omicron infections increased. When we account for growth-rate differences of two variants during the study period, we estimate similar mean incubation periods (3.8--4.5 days) for both variants but a shorter mean generation interval for the Omicron variant (3.0 days; 95\% CI: 2.7--3.2 days) than for the Delta variant (3.8 days; 95\% CI: 3.7--4.0 days). We further note that the differences in estimated generation intervals may be driven by the "network effect"---higher effective transmissibility of the Omicron variant can cause faster susceptible depletion among contact networks, which in turn prevents late transmission (therefore shortening realized generation intervals). Using up-to-date generation-interval distributions is critical to accurately estimating the reproduction advantage of the Omicron variant.

Predictive performance of multi-model ensemble forecasts of COVID-19 across European nations (preprint)

Background: Short-term forecasts of infectious disease burden can contribute to situational awareness and aid capacity planning. Based on best practice in other fields and recent insights in infectious disease epidemiology, one can maximise the predictive performance of such forecasts if multiple models are combined into an ensemble. Here we report on the performance of ensembles in predicting COVID-19 cases and deaths across Europe between 08 March 2021 and 07 March 2022. Methods: We used open-source tools to develop a public European COVID-19 Forecast Hub. We invited groups globally to contribute weekly forecasts for COVID-19 cases and deaths reported from a standardised source over the next one to four weeks. Teams submitted forecasts from March 2021 using standardised quantiles of the predictive distribution. Each week we created an ensemble forecast, where each predictive quantile was calculated as the equally-weighted average (initially the mean and then from 26th July the median) of all individual models predictive quantiles. We measured the performance of each model using the relative Weighted Interval Score (WIS), comparing models forecast accuracy relative to all other models. We retrospectively explored alternative methods for ensemble forecasts, including weighted averages based on models past predictive performance. Results: Over 52 weeks we collected and combined up to 28 forecast models for 32 countries. We found a weekly ensemble had a consistently strong performance across countries over time. Across all horizons and locations, the ensemble performed better on relative WIS than 84% of participating models forecasts of incident cases (with a total N=862), and 92% of participating models forecasts of deaths (N=746). Across a one to four week time horizon, ensemble performance declined with longer forecast periods when forecasting cases, but remained stable over four weeks for incident death forecasts. In every forecast across 32 countries, the ensemble outperformed most contributing models when forecasting either cases or deaths, frequently outperforming all of its individual component models. Among several choices of ensemble methods we found that the most influential and best choice was to use a median average of models instead of using the mean, regardless of methods of weighting component forecast models. Conclusions: Our results support the use of combining forecasts from individual models into an ensemble in order to improve predictive performance across epidemiological targets and populations during infectious disease epidemics. Our findings further suggest that median ensemble methods yield better predictive performance more than ones based on means. Our findings also highlight that forecast consumers should place more weight on incident death forecasts than incident case forecasts at forecast horizons greater than two weeks.

Cycle threshold values in symptomatic COVID-19 cases in England (preprint)

IntroductionSince the start of the pandemic SARS-CoV-2 infection has most commonly been confirmed using reverse transcriptase polymerase chain reaction (RT-PCR), with results translated into a binary positive/negative outcomes. Previous studies have found that there is additional useful information in the level of the Cycle threshold (Ct value) of positive cases. Here we characterise variation in Ct values as a proxy for viral loads in more than 3 million test-positive COVID-19 cases in England with the aim of better quantifying the utility of such data. MethodsWe used individual N gene Ct values from symptomatic PCR positive (with Ct value less than 30) Pillar 2 cases in England who self-reported the date of symptom onset, and for whom age, reinfection status, variant status, and the number of vaccines received was available. Those with a positive test result more than 6 days after their reported symptom onset were excluded to mitigate the potential impact of recall bias. We used a generalised additive model, to estimate Ct values empirical mean Ct values for each strata of interest independently as well as to predict Ct values using a model that adjusted for a range of demographic and epidemiological covariates jointly. We present empirical Ct values and compare them to predicted mean Ct values. ResultsWe found that mean Ct values varied by vaccine status, and reinfection status with the number of vaccine doses having little apparent effect. Modelling Ct values as a smooth function of time since onset and other variables struggled to reproduce the individual variation in the data but did match the population-level variation over time relatively well with this being apparently dominated by large differences between variants. Other variation over time was also captured to some degree though their remained several periods where the model could not capture the empirical means with a potential explanation being epidemic phase bias. ConclusionsAnalysing a large dataset of routine Ct values from symptomatic COVID-19 cases in England we found variation based on time since symptom onset, vaccine status, age, and variant. Ct values were highest 1-3 days after symptom onset and differed most due to variant status. We found no clear correlation between previously estimated differences in intrinsic transmissibility and Ct values indicating that this is potentially mediated at least partly by factors other than viral load as estimated using Ct values. We found evidence that a model adjusting for a range of covariates could explain some of the population-level variation over time but systematically underestimated Ct values when incidence was increasing, and overestimated them when incidence was decreasing. This indicates the utility of Ct values from this data source as a tool for surveillance, potentially avoiding some of the biases of aggregated positive counts.

Evaluating Forecasts with scoringutils in R (preprint)

Evaluating forecasts is essential in order to understand and improve forecasting and make forecasts useful to decision-makers. Much theoretical work has been done on the development of proper scoring rules and other scoring metrics that can help evaluate forecasts. In practice, however, conducting a forecast evaluation and comparison of different forecasters remains challenging. In this paper we introduce scoringutils, an R package that aims to greatly facilitate this process. It is especially geared towards comparing multiple forecasters, regardless of how forecasts were created, and visualising results. The package is able to handle missing forecasts and is the first R package to offer extensive support for forecasts represented through predictive quantiles, a format used by several collaborative ensemble forecasting efforts. The paper gives a short introduction to forecast evaluation, discusses the metrics implemented in scoringutils and gives guidance on when they are appropriate to use, and illustrates the application of the package using example data of forecasts for COVID-19 cases and deaths submitted to the European Forecast Hub between May and September 2021

Estimating epidemiological quantities from repeated cross-sectional prevalence measurements (preprint)

Background Repeated measurements of cross-sectional prevalence of Polymerase Chain Reaction (PCR) positivity or seropositivity provide rich insight into the dynamics of an infection. The UK Office for National Statistics (ONS) Community Infection Survey publishes such measurements for SARS-CoV-2 on a weekly basis based on testing enrolled households, contributing to situational awareness in the country. Here we present estimates of time-varying and static epidemiological quantities that were derived from the estimates published by ONS. Methods We used a gaussian process to model the incidence of infections and then estimated observed PCR prevalence by convolving our modelled incidence estimates with a previously published PCR detection curve describing the probability of a positive test as a function of the time since infection. We refined our incidence estimates using time-varying estimates of antibody prevalence combined with a model of antibody positivity and waning that moved individuals between compartments with or without antibodies based on estimates of new infections, vaccination, probability of seroconversion and waning. Results We produced incidence curves of infection describing the UK epidemic from late April 2020 until early 2022. We used these estimates of incidence to estimate the time-varying growth rate of infections and combined them with estimates of the generation interval to estimate time-varying reproduction numbers. Biological parameters describing seroconversion and waning, while based on a simple model, were broadly in line with plausible ranges from individual-level studies. Conclusions Beyond informing situational awareness and allowing for estimates using individual-level data, repeated cross-sectional studies make it possible to estimate epidemiological parameters from population-level models. Studies or public health surveillance methods based on similar designs offer opportunities for further improving our understanding of the dynamics of SARS-CoV-2 or other pathogens and their interaction with population-level immunity.

Estimation of the test to test distribution as a proxy for generation interval distribution for the Omicron variant in England (preprint)

Background Early estimates from South Africa indicated that the Omicron COVID-19 variant may be both more transmissible and have greater immune escape than the previously dominant Delta variant. The rapid turnover of the latest epidemic wave in South Africa as well as initial evidence from contact tracing and household infection studies has prompted speculation that the generation time of the Omicron variant may be shorter in comparable settings than the generation time of the Delta variant. Methods We estimated daily growth rates for the Omicron and Delta variants in each UKHSA region from the 23rd of November to the 23rd of December 2021 using surveillance case counts by date of specimen and S-gene target failure status with an autoregressive model that allowed for time-varying differences in the transmission advantage of the Delta variant where the evidence supported this. By assuming a gamma distributed generation distribution we then estimated the generation time distribution and transmission advantage of the Omicron variant that would be required to explain this time varying advantage. We repeated this estimation process using two different prior estimates for the generation time of the Delta variant first based on household transmission and then based on its intrinsic generation time. Results Visualising our growth rate estimates provided initial evidence for a difference in generation time distributions. Assuming a generation time distribution for Delta with a mean of 2.5-4 days (90% credible interval) and a standard deviation of 1.9-3 days we estimated a shorter generation time distribution for Omicron with a mean of 1.5-3.2 days and a standard deviation of 1.3-4.6 days. This implied a transmission advantage for Omicron in this setting of 160%-210% compared to Delta. We found similar relative results using an estimate of the intrinsic generation time for Delta though all estimates increased in magnitude due to the longer assumed generation time. Conclusions We found that a reduction in the generation time of Omicron compared to Delta was able to explain the observed variation over time in the transmission advantage of the Omicron variant. However, this analysis cannot rule out the role of other factors such as differences in the populations the variants were mixing in, differences in immune escape between variants or bias due to using the test to test distribution as a proxy for the generation time distribution.

Bounding the levels of transmissibility & immune evasion of the Omicron variant in South Africa (preprint)

A new SARS-CoV-2 variant of concern, Omicron (B.1.1.529), has been identified based on genomic sequencing and epidemiological data in South Africa. Presumptive Omicron cases in South Africa have grown extremely rapidly, despite high prior exposure and moderate vaccination coverage. The available evidence suggests that Omicron spread is at least in part due to evasion of this immune protection, though Omicron may also exhibit higher intrinsic transmissibility. Using detailed laboratory and epidemiological data from South Africa, we estimate the constraints on these two characteristics of the new variant and their relationship. Our estimates and associated uncertainties provide essential information to inform projection and scenario modeling analyses, which are crucial planning tools for governments around the world. One Sentence Summary We report a region of plausibility for the relative transmissibility and immune escape characteristics of the SARS-CoV-2 Omicron variant estimated by integrating laboratory and epidemiological data from South Africa.

Estimating the Local Burden of Disease During the First Wave of the COVID-19 Epidemic in England, Using Different Data Sources from Changing Surveillance Practices (preprint)

Background: The COVID-19 epidemic has differentially impacted communities across England, with regional variation in rates of confirmed cases, hospitalisations and deaths. Measurement of this burden changed substantially over the first months, as surveillance was expanded to accommodate the escalating epidemic. Laboratory confirmation was initially restricted to clinical need (“pillar 1”) before expanding to community-wide symptomatics (“pillar 2”). This study aimed to ascertain whether inconsistent measurement of case data resulting from varying testing coverage could be reconciled by drawing inference from COVID-19-related deaths. MethodsWe fit a Bayesian spatio-temporal model to weekly COVID-19-related deaths per local authority (LTLA) throughout the first wave (1 January - 30 June 2020), adjusting for the local epidemic timing and the age, deprivation and ethnic composition of its population. We combined predictions from this model with case data under community-wide, symptomatic testing and infection prevalence estimates from the ONS infection survey, to infer the likely trajectory of infections implied by the deaths in each LTLA.ResultsA model including temporally- and spatially-correlated random effects was found to best accommodate the observed variation in COVID-19-related deaths, after accounting for local population characteristics. Predicted case counts under community-wide symptomatic testing suggest a total of 275,000-420,000 cases over the first wave - a median of over 100,000 additional to the total confirmed in practice under varying testing coverage. This translates to a peak incidence of around 200,000 total infections per week across England. The extent to which estimated total infections are reflected in confirmed case counts was found to vary substantially across LTLAs, ranging from 7% in Leicester to 96% in Gloucester with a median of 23%. ConclusionsLimitations in testing capacity biased the observed trajectory of COVID-19 infections throughout the first wave. Basing inference on COVID-19-related mortality and higher-coverage testing later in the time period, we could explore the extent of this bias more explicitly. Evidence points towards substantial under-representation of initial growth and peak magnitude of infections nationally, to which different parts of the country contribute unequally.

Comparing human and model-based forecasts of COVID-19 in Germany and Poland (preprint)

Forecasts based on epidemiological modelling have played an important role in shaping public policy throughout the COVID-19 pandemic. This modelling combines knowledge about infectious disease dynamics with the subjective opinion of the researcher who develops and refines the model and often also adjusts model outputs. Developing a forecast model is difficult, resource- and time-consuming. It is therefore worth asking what modelling is able to add beyond the subjective opinion of the researcher alone. To investigate this, we analysed different real-time forecasts of cases of and deaths from COVID-19 in Germany and Poland over a 1-4 week horizon submitted to the German and Polish Forecast Hub. We compared crowd forecasts elicited from researchers and volunteers, against a) forecasts from two semi-mechanistic models based on common epidemiological assumptions and b) the ensemble of all other models submitted to the Forecast Hub. We found crowd forecasts, despite being overconfident, to outperform all other methods across all forecast horizons when forecasting cases (weighted interval score relative to the Hub ensemble 2 weeks ahead: 0.89). Forecasts based on computational models performed comparably better when predicting deaths (rel. WIS 1.26), suggesting that epidemiological modelling and human judgement can complement each other in important ways.

Estimating the increase in reproduction number associated with the Delta variant using local area dynamics in England (preprint)

Background: Local estimates of the time-varying effective reproduction number (Rt) of COVID-19 in England became increasingly heterogeneous during April and May 2021. This may have been attributable to the spread of the Delta SARS-CoV-2 variant. This paper documents real-time analysis that aimed to investigate the association between changes in the proportion of positive cases that were S-gene positive, an indicator of the Delta variant against a background of the previously predominant Alpha variant, and the estimated time-varying Rt at the level of upper-tier local authorities (UTLA). Method: We explored the relationship between the proportion of samples that were S-gene positive and the Rt of test-positive cases over time from the 23 February 2021 to the 25 May 2021. Effective reproduction numbers were estimated using the EpiNow2 R package independently for each local authority using two different estimates of the generation time. We then fit a range of regression models to estimate a multiplicative relationship between S-gene positivity and weekly mean Rt estimate. Results: We found evidence of an association between increased mean Rt estimates and the proportion of S-gene positives across all models evaluated with the magnitude of the effect increasing as model flexibility was decreased. Models that adjusted for either national level or NHS region level time-varying residuals were found to fit the data better, suggesting potential unexplained confounding. Conclusions: Our results indicated that even after adjusting for time-varying residuals between NHS regions, S-gene positivity was associated with an increase in the effective reproduction number of COVID-19. These findings were robust across a range of models and generation time assumptions, though the specific effect size was variable depending on the assumptions used. The lower bound of the estimated effect indicated that the reproduction number of Delta was above 1 in almost all local authorities throughout the period of investigation.

Unexposed populations and potential COVID-19 burden in European countries as of 21st November 2021 (preprint)

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