Fitting the reproduction number from UK coronavirus case data and why it is close to 1

Combining models to generate consensus medium-term projections of hospital admissions, occupancy and deaths relating to COVID-19 in England

Mathematical modelling has played an important role in offering informed advice during the COVID-19 pandemic. In England, a cross government and academia collaboration generated medium-term projections (MTPs) of possible epidemic trajectories over the future 4-6 weeks from a collection of epidemiological models. In this article, we outline this collaborative modelling approach and evaluate the accuracy of the combined and individual model projections against the data over the period November 2021-December 2022 when various Omicron subvariants were spreading across England. Using a number of statistical methods, we quantify the predictive performance of the model projections for both the combined and individual MTPs, by evaluating the point and probabilistic accuracy. Our results illustrate that the combined MTPs, produced from an ensemble of heterogeneous epidemiological models, were a closer fit to the data than the individual models during the periods of epidemic growth or decline, with the 90% confidence intervals widest around the epidemic peaks. We also show that the combined MTPs increase the robustness and reduce the biases associated with a single model projection. Learning from our experience of ensemble modelling during the COVID-19 epidemic, our findings highlight the importance of developing cross-institutional multi-model infectious disease hubs for future outbreak control.

Modelling herd immunity requirements in Queensland: impact of vaccination effectiveness, hesitancy and variants of SARS-CoV-2

Long-term control of SARS-CoV-2 outbreaks depends on the widespread coverage of effective vaccines. In Australia, two-dose vaccination coverage of above 90% of the adult population was achieved. However, between August 2020 and August 2021, hesitancy fluctuated dramatically. This raised the question of whether settings with low naturally derived immunity, such as Queensland where less than [Formula: see text] of the population is known to have been infected in 2020, could have achieved herd immunity against 2021's variants of concern. To address this question, we used the agent-based model Covasim. We simulated outbreak scenarios (with the Alpha, Delta and Omicron variants) and assumed ongoing interventions (testing, tracing, isolation and quarantine). We modelled vaccination using two approaches with different levels of realism. Hesitancy was modelled using Australian survey data. We found that with a vaccine effectiveness against infection of 80%, it was possible to control outbreaks of Alpha, but not Delta or Omicron. With 90% effectiveness, Delta outbreaks may have been preventable, but not Omicron outbreaks. We also estimated that a decrease in hesitancy from 20% to 14% reduced the number of infections, hospitalizations and deaths by over 30%. Overall, we demonstrate that while herd immunity may not be attainable, modest reductions in hesitancy and increases in vaccine uptake may greatly improve health outcomes. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Estimation of age-stratified contact rates during the COVID-19 pandemic using a novel inference algorithm

Well parameterized epidemiological models including accurate representation of contacts are fundamental to controlling epidemics. However, age-stratified contacts are typically estimated from pre-pandemic/peace-time surveys, even though interventions and public response likely alter contacts. Here, we fit age-stratified models, including re-estimation of relative contact rates between age classes, to public data describing the 2020-2021 COVID-19 outbreak in England. This data includes age-stratified population size, cases, deaths, hospital admissions and results from the Coronavirus Infection Survey (almost 9000 observations in all). Fitting stochastic compartmental models to such detailed data is extremely challenging, especially considering the large number of model parameters being estimated (over 150). An efficient new inference algorithm ABC-MBP combining existing approximate Bayesian computation (ABC) methodology with model-based proposals (MBPs) is applied. Modified contact rates are inferred alongside time-varying reproduction numbers that quantify changes in overall transmission due to pandemic response, and age-stratified proportions of asymptomatic cases, hospitalization rates and deaths. These inferences are robust to a range of assumptions including the values of parameters that cannot be estimated from available data. ABC-MBP is shown to enable reliable joint analysis of complex epidemiological data yielding consistent parametrization of dynamic transmission models that can inform data-driven public health policy and interventions. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Heterogeneity in the onwards transmission risk between local and imported cases affects practical estimates of the time-dependent reproduction number

During infectious disease outbreaks, inference of summary statistics characterizing transmission is essential for planning interventions. An important metric is the time-dependent reproduction number (Rt), which represents the expected number of secondary cases generated by each infected individual over the course of their infectious period. The value of Rt varies during an outbreak due to factors such as varying population immunity and changes to interventions, including those that affect individuals' contact networks. While it is possible to estimate a single population-wide Rt, this may belie differences in transmission between subgroups within the population. Here, we explore the effects of this heterogeneity on Rt estimates. Specifically, we consider two groups of infected hosts: those infected outside the local population (imported cases), and those infected locally (local cases). We use a Bayesian approach to estimate Rt, made available for others to use via an online tool, that accounts for differences in the onwards transmission risk from individuals in these groups. Using COVID-19 data from different regions worldwide, we show that different assumptions about the relative transmission risk between imported and local cases affect Rt estimates significantly, with implications for interventions. This highlights the need to collect data during outbreaks describing heterogeneities in transmission between different infected hosts, and to account for these heterogeneities in methods used to estimate Rt. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Technical challenges of modelling real-life epidemics and examples of overcoming these

The coronavirus disease 2019 (COVID-19) pandemic has highlighted the importance of mathematical modelling in informing and advising policy decision-making. Effective practice of mathematical modelling has challenges. These can be around the technical modelling framework and how different techniques are combined, the appropriate use of mathematical formalisms or computational languages to accurately capture the intended mechanism or process being studied, in transparency and robustness of models and numerical code, in simulating the appropriate scenarios via explicitly identifying underlying assumptions about the process in nature and simplifying approximations to facilitate modelling, in correctly quantifying the uncertainty of the model parameters and projections, in taking into account the variable quality of data sources, and applying established software engineering practices to avoid duplication of effort and ensure reproducibility of numerical results. Via a collection of 16 technical papers, this special issue aims to address some of these challenges alongside showcasing the usefulness of modelling as applied in this pandemic. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

The Royal Society RAMP modelling initiative

Normally, science proceeds following a well-established set of principles. Studies are done with an emphasis on correctness, are submitted to a journal editor who evaluates their relevance, and then undergo anonymous peer review by experts before publication in a journal and acceptance by the scientific community via the open literature. This process is slow, but its accuracy has served all fields of science well. In an emergency situation, different priorities come to the fore. Research and review need to be conducted quickly, and the target audience consists of policymakers. Scientists must jostle for the attention of non-specialists without sacrificing rigour, and must deal not only with peer assessment but also with media scrutiny by journalists who may have agendas other than ensuring scientific correctness. Here, we describe how the Royal Society coordinated efforts of diverse scientists to help model the coronavirus epidemic. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Tracking the national and regional COVID-19 epidemic status in the UK using weighted principal component analysis

One of the difficulties in monitoring an ongoing pandemic is deciding on the metric that best describes its status when multiple intercorrelated measurements are available. Having a single measure, such as the effective reproduction number [Formula: see text], has been a simple and useful metric for tracking the epidemic and for imposing policy interventions to curb the increase when [Formula: see text]. While [Formula: see text] is easy to interpret in a fully susceptible population, it is more difficult to interpret for a population with heterogeneous prior immunity, e.g. from vaccination and prior infection. We propose an additional metric for tracking the UK epidemic that can capture the different spatial scales. These are the principal scores from a weighted principal component analysis. In this paper, we have used the methodology across the four UK nations and across the first two epidemic waves (January 2020-March 2021) to show that first principal score across nations and epidemic waves is a representative indicator of the state of the pandemic and is correlated with the trend in R. Hospitalizations are shown to be consistently representative; however, the precise dominant indicator, i.e. the principal loading(s) of the analysis, can vary geographically and across epidemic waves. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.