Modelling that shaped the early COVID-19 pandemic response in the UK

Canada's provincial COVID-19 pandemic modelling efforts: A review of mathematical models and their impacts on the responses

SETTING

Mathematical modelling played an important role in the public health response to COVID-19 in Canada. Variability in epidemic trajectories, modelling approaches, and data infrastructure across provinces provides a unique opportunity to understand the factors that shaped modelling strategies.

INTERVENTION

Provinces implemented stringent pandemic interventions to mitigate SARS-CoV-2 transmission, considering evidence from epidemic models. This study aimed to summarize provincial COVID-19 modelling efforts. We identified modelling teams working with provincial decision-makers, through referrals and membership in Canadian modelling networks. Information on models, data sources, and knowledge translation were abstracted using standardized instruments.

OUTCOMES

We obtained information from six provinces. For provinces with sustained community transmission, initial modelling efforts focused on projecting epidemic trajectories and healthcare demands, and evaluating impacts of proposed interventions. In provinces with low community transmission, models emphasized quantifying importation risks. Most of the models were compartmental and deterministic, with projection horizons of a few weeks. Models were updated regularly or replaced by new ones, adapting to changing local epidemic dynamics, pathogen characteristics, vaccines, and requests from public health. Surveillance datasets for cases, hospitalizations and deaths, and serological studies were the main data sources for model calibration. Access to data for modelling and the structure for knowledge translation differed markedly between provinces.

IMPLICATION

Provincial modelling efforts during the COVID-19 pandemic were tailored to local contexts and modulated by available resources. Strengthening Canadian modelling capacity, developing and sustaining collaborations between modellers and governments, and ensuring earlier access to linked and timely surveillance data could help improve pandemic preparedness.

Fitting Epidemic Models to Data: A Tutorial in Memory of Fred Brauer

Fred Brauer was an eminent mathematician who studied dynamical systems, especially differential equations. He made many contributions to mathematical epidemiology, a field that is strongly connected to data, but he always chose to avoid data analysis. Nevertheless, he recognized that fitting models to data is usually necessary when attempting to apply infectious disease transmission models to real public health problems. He was curious to know how one goes about fitting dynamical models to data, and why it can be hard. Initially in response to Fred's questions, we developed a user-friendly R package, fitode, that facilitates fitting ordinary differential equations to observed time series. Here, we use this package to provide a brief tutorial introduction to fitting compartmental epidemic models to a single observed time series. We assume that, like Fred, the reader is familiar with dynamical systems from a mathematical perspective, but has limited experience with statistical methodology or optimization techniques.

When should lockdown be implemented? Devising cost-effective strategies for managing epidemics amid vaccine uncertainty

During an infectious disease outbreak, public health policy makers are tasked with strategically implementing interventions whilst balancing competing objectives. To provide a quantitative framework that can be used to guide these decisions, it is helpful to devise a clear and specific objective function that can be evaluated to determine the optimal outbreak response. In this study, we have developed a mathematical modelling framework representing outbreaks of a novel emerging pathogen for which non-pharmaceutical interventions (NPIs) are imposed or removed based on thresholds for hospital occupancy. These thresholds are set at different levels to define four unique strategies for disease control. We illustrate that the optimal intervention strategy is contingent on the choice of objective function. Specifically, the optimal strategy depends on the extent to which policy makers prioritise reducing health costs due to infection over the costs associated with maintaining interventions. Motivated by the scenario early in the COVID-19 pandemic, we incorporate the development of a vaccine into our modelling framework and demonstrate that a policy maker's belief about when a vaccine will become available in future, and its eventual coverage (and/or effectiveness), affects the optimal strategy to adopt early in the outbreak. Furthermore, we show how uncertainty in these quantities can be accounted for when deciding which interventions to introduce. This research highlights the benefits of policy makers being explicit about the precise objectives of introducing interventions.

A multiscale modeling framework for Scenario Modeling: Characterizing the heterogeneity of the COVID-19 epidemic in the US

The Scenario Modeling Hub (SMH) initiative provides projections of potential epidemic scenarios in the United States (US) by using a multi-model approach. Our contribution to the SMH is generated by a multiscale model that combines the global epidemic metapopulation modeling approach (GLEAM) with a local epidemic and mobility model of the US (LEAM-US), first introduced here. The LEAM-US model consists of 3142 subpopulations each representing a single county across the 50 US states and the District of Columbia, enabling us to project state and national trajectories of COVID-19 cases, hospitalizations, and deaths under different epidemic scenarios. The model is age-structured, and multi-strain. It integrates data on vaccine administration, human mobility, and non-pharmaceutical interventions. The model contributed to all 17 rounds of the SMH, and allows for the mechanistic characterization of the spatio-temporal heterogeneities observed during the COVID-19 pandemic. Here we describe the mathematical and computational structure of our model, and present the results concerning the emergence of the SARS-CoV-2 Alpha variant (lineage designation B.1.1.7) as a case study. Our findings show considerable spatial and temporal heterogeneity in the introduction and diffusion of the Alpha variant, both at the level of individual states and combined statistical areas, as it competes against the ancestral lineage. We discuss the key factors driving the time required for the Alpha variant to rise to dominance within a population, and quantify the impact that the emergence of the Alpha variant had on the effective reproduction number at the state level. Overall, we show that our multiscale modeling approach is able to capture the complexity and heterogeneity of the COVID-19 pandemic response in the US.

Real-time forecasting of COVID-19-related hospital strain in France using a non-Markovian mechanistic model

Projects such as the European Covid-19 Forecast Hub publish forecasts on the national level for new deaths, new cases, and hospital admissions, but not direct measurements of hospital strain like critical care bed occupancy at the sub-national level, which is of particular interest to health professionals for planning purposes. We present a sub-national French framework for forecasting hospital strain based on a non-Markovian compartmental model, its associated online visualisation tool and a retrospective evaluation of the real-time forecasts it provided from January to December 2021 by comparing to three baselines derived from standard statistical forecasting methods (a naive model, auto-regression, and an ensemble of exponential smoothing and ARIMA). In terms of median absolute error for forecasting critical care unit occupancy at the two-week horizon, our model only outperformed the naive baseline for 4 out of 14 geographical units and underperformed compared to the ensemble baseline for 5 of them at the 90% confidence level (n = 38). However, for the same level at the 4 week horizon, our model was never statistically outperformed for any unit despite outperforming the baselines 10 times spanning 7 out of 14 geographical units. This implies modest forecasting utility for longer horizons which may justify the application of non-Markovian compartmental models in the context of hospital-strain surveillance for future pandemics.

Informing Public Health Policies with Models for Disease Burden, Impact Evaluation, and Economic Evaluation

Conducting real-world public health experiments is often costly, time-consuming, and ethically challenging, so mathematical models have a long-standing history of being used to inform policy. Applications include estimating disease burden, performing economic evaluation of interventions, and responding to health emergencies such as pandemics. Models played a pivotal role during the COVID-19 pandemic, providing early detection of SARS-CoV-2's pandemic potential and informing subsequent public health measures. While models offer valuable policy insights, they often carry limitations, especially when they depend on assumptions and incomplete data. Striking a balance between accuracy and timely decision-making in rapidly evolving situations such as disease outbreaks is challenging. Modelers need to explore the extent to which their models deviate from representing the real world. The uncertainties inherent in models must be effectively communicated to policy makers and the public. As the field becomes increasingly influential, it needs to develop reporting standards that enable rigorous external scrutiny.

Marburg virus disease outbreaks, mathematical models, and disease parameters: a systematic review

The 2023 Marburg virus disease outbreaks in Equatorial Guinea and Tanzania highlighted the importance of better understanding this lethal pathogen. We did a systematic review (PROSPERO CRD42023393345) of peer-reviewed articles reporting historical outbreaks, modelling studies, and epidemiological parameters focused on Marburg virus disease. We searched PubMed and Web of Science from database inception to March 31, 2023. Two reviewers evaluated all titles and abstracts with consensus-based decision making. To ensure agreement, 13 (31%) of 42 studies were double-extracted and a custom-designed quality assessment questionnaire was used for risk of bias assessment. We present detailed information on 478 reported cases and 385 deaths from Marburg virus disease. Analysis of historical outbreaks and seroprevalence estimates suggests the possibility of undetected Marburg virus disease outbreaks, asymptomatic transmission, or cross-reactivity with other pathogens, or a combination of these. Only one study presented a mathematical model of Marburg virus transmission. We estimate an unadjusted, pooled total random effect case fatality ratio of 61·9% (95% CI 38·8-80·6; I2=93%). We identify epidemiological parameters relating to transmission and natural history, for which there are few estimates. This systematic review and the accompanying database provide a comprehensive overview of Marburg virus disease epidemiology and identify key knowledge gaps, contributing crucial information for mathematical models to support future Marburg virus disease epidemic responses.

A case for ongoing structural support to maximise infectious disease modelling efficiency for future public health emergencies: A modelling perspective

This short communication reflects upon the challenges and recommendations of multiple COVID-19 modelling and data analytic groups that provided quantitative evidence to support health policy discussions in Switzerland and Germany during the SARS-CoV-2 pandemic. Capacity strengthening outside infectious disease emergencies will be required to enable an environment for a timely, efficient, and data-driven response to support decisions during any future infectious disease emergency. This will require 1) a critical mass of trained experts who continuously advance state-of-the-art methodological tools, 2) the establishment of structural liaisons amongst scientists and decision-makers, and 3) the foundation and management of data-sharing frameworks.

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

Background

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.

Methods

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.

Results

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.

Conclusions

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 is crucial, in our view, for ensuring the effectiveness of epidemic response work in the future.

Understanding and Bridging Gaps in the Use of Evidence from Modeling for Evidence-Based Policy Making in Nigeria's Health System

Background. Modeled evidence is a proven useful tool for decision makers in making evidence-based policies and plans that will ensure the best possible health system outcomes. Thus, we sought to understand constraints to the use of models in making decisions in Nigeria's health system and how such constraints can be addressed. Method. We adopted a mixed-methods study for the research and relied on the evidence to policy and Knowledge-to-Action (KTA) frameworks to guide the conceptualization of the study. An online survey was administered to 34 key individuals in health organizations that recognize modeling, which was followed by in-depth interviews with 24 of the 34 key informants. Analysis was done using descriptive analytic methods and thematic arrangements of narratives. Results. Overall, the data revealed poor use of modeled evidence in decision making within the health sector, despite reporting that modeled evidence and modelers are available in Nigeria. However, the disease control agency in Nigeria was reported to be an exception. The complexity of models was a top concern. Thus, suggestions were made to improve communication of models in ways that are easily comprehensible and to improve overall research culture within Nigeria's health sector. Conclusion. Modeled evidence plays a crucial role in evidence-based health decisions. Therefore, it is imperative to strengthen and sustain in-country capacity to value, produce, interpret, and use modeled evidence for decision making in health. To overcome limitations in the usage of modeled evidence, decision makers, modelers/researchers, and knowledge brokers should forge viable relationships that regard and promote evidence translation.

Highlights

Despite the use of modeling by Nigeria's disease control agency in containing the COVID-19 pandemic, modeling remains poorly used in the country's overall health sector.Although policy makers recognize the importance of evidence in making decisions, there are still pertinent concerns about the poor research culture of policy-making institutions and communication gaps that exist between researchers/modelers and policy makers.Nigeria's health system can be strengthened by improving the value and usage of scientific evidence generation through conscious efforts to institutionalize research culture in the health sector and bridge gaps between researchers/modelers and decision makers.

Public awareness of and opinions on the use of mathematical transmission modelling to inform public health policy in the United Kingdom

Mathematical modelling is used to inform public health policy, particularly so during the COVID-19 pandemic. As the public are key stakeholders, understanding the public perceptions of these tools is vital. To complement our previous study on the science-policy interface, novel survey data were collected via an online panel ('representative' sample) and social media ('non-probability' sample). Many questions were asked twice, in reference to the period 'prior to' (retrospectively) and 'during' the COVID-19 pandemic. Respondents reported being increasingly aware of modelling in informing policy during the pandemic, with higher levels of awareness among social media respondents. Modelling informing policy was perceived as more reliable during the pandemic than in reference to the pre-pandemic period in both samples. Trust in government public health advice remained high within both samples but was lower during the pandemic in comparison with the (retrospective) pre-pandemic period. The decay in trust was greater among social media respondents. Many respondents explicitly made the distinction that their trust was reserved for 'scientists' and not 'politicians'. Almost all respondents believed governments have responsibility for communicating modelling to the public. These results provide a reminder of the skewed conclusions that could be drawn from non-representative samples.

Comparing intervention measures in a model of a disease outbreak on a university campus

A number of theoretical models have been developed in recent years modelling epidemic spread in educational settings such as universities, often as part of efforts to inform re-opening strategies during the COVID-19 pandemic. However, these studies have had differing conclusions as to the most effective non-pharmaceutical interventions. They also largely assumed permanent acquired immunity, meaning we have less understanding of how disease dynamics will play out when immunity wanes. Here, we complement these studies by developing and analysing a general stochastic simulation model of disease spread on a university campus where we allow immunity to wane, exploring the effectiveness of different interventions. We find that the two most effective interventions to limit the severity of a disease outbreak are reducing extra-household mixing and surveillance testing backed-up by a moderate isolation period. We find that contact tracing only has a limited effect, while reducing class sizes only has much effect if extra-household mixing is already low. We identify a range of measures that can not only limit an outbreak but prevent it entirely, and also comment on the variation in measures of severity that emerge from our stochastic simulations. We hope that our model may help in designing effective strategies for universities in future disease outbreaks.

Model based on COVID-19 evidence to predict and improve pandemic control

Based on the extensive data accumulated during the COVID-19 pandemic, we put forward simple to implement indicators, that should alert authorities and provide early warnings of an impending sanitary crisis. In fact, Testing, Tracing, and Isolation (TTI) in conjunction with disciplined social distancing and vaccination were expected to achieve negligible COVID-19 contagion levels; however, they proved to be insufficient, and their implementation has led to controversial social, economic and ethical challenges. This paper focuses on the development of simple indicators, based on the experience gained by COVID-19 data, which provide a sort of yellow light as to when an epidemic might expand, despite some short term decrements. We show that if case growth is not stopped during the 7 to 14 days after onset, the growth risk increases considerably, and warrants immediate attention. Our model examines not only the COVID contagion propagation speed, but also how it accelerates as a function of time. We identify trends that emerge under the various policies that were applied, as well as their differences among countries. The data for all countries was obtained from ourworldindata.org. Our main conclusion is that if the reduction spread is lost during one, or at most two weeks, urgent measures should be implemented to avoid scenarios in which the epidemic gains strong impetus.

Heterogeneity is a key factor describing the initial outbreak of COVID-19

Assessing the transmission potential of emerging infectious diseases, such as COVID-19, is crucial for implementing prompt and effective intervention policies. The basic reproduction number is widely used to measure the severity of the early stages of disease outbreaks. The basic reproduction number of standard ordinary differential equation models is computed for homogeneous contact patterns; however, realistic contact patterns are far from homogeneous, specifically during the early stages of disease transmission. Heterogeneity of contact patterns can lead to superspreading events that show a significantly high level of heterogeneity in generating secondary infections. This is primarily due to the large variance in the contact patterns of complex human behaviours. Hence, in this work, we investigate the impacts of heterogeneity in contact patterns on the basic reproduction number by developing two distinct model frameworks: 1) an SEIR-Erlang ordinary differential equation model and 2) an SEIR stochastic agent-based model. Furthermore, we estimated the transmission probability of both models in the context of COVID-19 in South Korea. Our results highlighted the importance of heterogeneity in contact patterns and indicated that there should be more information than one quantity (the basic reproduction number as the mean quantity), such as a degree-specific basic reproduction number in the distributional sense when the contact pattern is highly heterogeneous.

Effectiveness assessment of non-pharmaceutical interventions: lessons learned from the COVID-19 pandemic

Effectiveness of non-pharmaceutical interventions (NPIs), such as school closures and stay-at-home orders, during the COVID-19 pandemic has been assessed in many studies. Such assessments can inform public health policies and contribute to evidence-based choices of NPIs during subsequent waves or future epidemics. However, methodological issues and no standardised assessment practices have restricted the practical value of the existing evidence. Here, we present and discuss lessons learned from the COVID-19 pandemic and make recommendations for standardising and improving assessment, data collection, and modelling. These recommendations could contribute to reliable and policy-relevant assessments of the effectiveness of NPIs during future epidemics.

Inferring ASF transmission in domestic pigs and wild boars using a paired model iterative approach

The rapid spread of African swine fever (ASF) in recent years has once again raised awareness of the need to improve our preparedness in preventing and managing outbreaks, for which modelling-based forecasts can play an important role. This is even more important in the case of a disease such as ASF, involving several types of hosts, characterised by a high case-fatality rate and for which there is currently no treatment or vaccine. Within the framework of the ASF challenge, we proposed a modelling approach based on a stochastic mechanistic model and an inference procedure to estimate key transmission parameters from provided data (incomplete and noisy) and generate forecasts for unobserved time horizons. The model is partly data driven and composed of two modules, corresponding to epidemic and demographic dynamics in domestic pig and wild boar (WB) populations, interconnected through the networks of animal trade and/or spatial proximity. The inference consists in an iterative procedure, alternating between the two models and based on a criterion optimisation. Estimates of transmission and detection parameters appeared to be of similar magnitude for each of the three periods of the challenge, except for the transmission rates in WB population through contact with infectious individuals and carcasses, higher during the first period. The predicted number of infected domestic pig farms was in overall agreement with the data. The proportion of positive tested WB was overestimated, but with a trend close to that observed in the data. Comparison of the spatial simulated and observed distributions of detected cases also showed an overestimation of the spread of the pathogen within WB metapopulation. Beyond the quantitative results and the inherent difficulties of real-time forecasting, we built a modelling framework that is flexible enough to accommodate changes in transmission processes and control measures that may occur during an epidemic emergency.

Supporting COVID-19 policy-making with a predictive epidemiological multi-model warning system

BACKGROUND

In response to the SARS-CoV-2 pandemic, the Austrian governmental crisis unit commissioned a forecast consortium with regularly projections of case numbers and demand for hospital beds. The goal was to assess how likely Austrian ICUs would become overburdened with COVID-19 patients in the upcoming weeks.

METHODS

We consolidated the output of three epidemiological models (ranging from agent-based micro simulation to parsimonious compartmental models) and published weekly short-term forecasts for the number of confirmed cases as well as estimates and upper bounds for the required hospital beds.

RESULTS

We report on three key contributions by which our forecasting and reporting system has helped shaping Austria's policy to navigate the crisis, namely (i) when and where case numbers and bed occupancy are expected to peak during multiple waves, (ii) whether to ease or strengthen non-pharmaceutical intervention in response to changing incidences, and (iii) how to provide hospital managers guidance to plan health-care capacities.

CONCLUSIONS

Complex mathematical epidemiological models play an important role in guiding governmental responses during pandemic crises, in particular when they are used as a monitoring system to detect epidemiological change points.

Uncomfortable science: How mathematical models, and consensus, come to be in public policy

We explore messy translations of evidence in policy as a site of 'uncomfortable science'. Drawing on the work of John Law, we follow evidence as a 'fluid object' of its situation, also enacted in relation to a hinterland of practices. Working with the qualitative interview accounts of mathematical modellers and other scientists engaged in the UK COVID-19 response, we trace how models perform as evidence. Our point of departure is a moment of controversy in the public announcement of second national lockdown in the UK, and specifically, the projected daily deaths from COVID-19 presented in support of this policy decision. We reflect on this event to trace the messy translations of "scientific consensus" in the face of uncertainty. Efforts among scientists to realise evidence-based expectation and to manage the troubled translations of models in policy, including via "scientific consensus", can extend the dis-ease of uncomfortable science rather than clean it up or close it down. We argue that the project of evidence-based policy is not so much in need of technical management or repair, but that we need to be thinking altogether differently.

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'.

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'.

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'.

Public perceptions and interactions with UK COVID-19 Test, Trace and Isolate policies, and implications for pandemic infectious disease modelling

Background The efforts to contain SARS-CoV-2 and reduce the impact of the COVID-19 pandemic have been supported by Test, Trace and Isolate (TTI) systems in many settings, including the United Kingdom. Mathematical models of transmission and TTI interventions, used to inform design and policy choices, make assumptions about the public’s behaviour in the context of a rapidly unfolding and changeable emergency. This study investigates public perceptions and interactions with UK TTI policy in July 2021, assesses them against how TTI processes are conceptualised and represented in models, and then interprets the findings with modellers who have been contributing evidence to TTI policy. Methods 20 members of the public recruited via social media were interviewed for one hour about their perceptions and interactions with the UK TTI system. Thematic analysis identified key themes, which were then presented back to a workshop of pandemic infectious disease modellers who assessed these findings against assumptions made in TTI intervention modelling. Workshop members co-drafted this report. Results Themes included education about SARS-CoV-2, perceived risks, trust, mental health and practical concerns. Findings covered testing practices, including the uses of and trust in different types of testing, and the challenges of testing and isolating faced by different demographic groups. This information was judged as consequential to the modelling process, from guiding the selection of research questions, influencing choice of model structure, informing parameter ranges and validating or challenging assumptions, to highlighting where model assumptions are reasonable or where their poor reflection of practice might lead to uninformative results. Conclusions We conclude that deeper engagement with members of the public should be integrated at regular stages of public health intervention modelling.

Minimising the use of costly control measures in an epidemic elimination strategy: A simple mathematical model

Countries such as New Zealand, Australia and Taiwan responded to the Covid-19 pandemic with an elimination strategy. This involves a combination of strict border controls with a rapid and effective response to eliminate border-related re-introductions. An important question for decision makers is, when there is a new re-introduction, what is the right threshold at which to implement strict control measures designed to reduce the effective reproduction number below 1. Since it is likely that there will be multiple re-introductions, responding at too low a threshold may mean repeatedly implementing controls unnecessarily for outbreaks that would self-eliminate even without control measures. On the other hand, waiting for too high a threshold to be reached creates a risk that controls will be needed for a longer period of time, or may completely fail to contain the outbreak. Here, we use a highly idealised branching process model of small border-related outbreaks to address this question. We identify important factors that affect the choice of threshold in order to minimise the expect time period for which control measures are in force. We find that the optimal threshold for introducing controls decreases with the effective reproduction number, and increases with overdispersion of the offspring distribution and with the effectiveness of control measures. Our results are not intended as a quantitative decision-making algorithm. However, they may help decision makers understand when a wait-and-see approach is likely to be preferable over an immediate response.

Critical policies disparity of the first and second waves of COVID-19 in the United Kingdom

Objective

This study aims to compare the differences in COVID-19 prevention and control policies adopted by the United Kingdom (UK) during the first wave (31 January 2020 to 6 September 2020) and the second wave (7 September 2020 to 12 April 2021), and analyze the effectiveness of the policies, so as to provide empirical experience for the prevention and control of COVID-19.

Methods We systematically summarized the pandemic prevention and control policies of the UK from official websites and government documents, collated the epidemiological data from 31 January 2020 to 12 April 2021, and analyzed the effectiveness of the two waves of pandemic prevention and control policies.

Results

The main pandemic prevention and control policies adopted by the UK include surveillance and testing measures, border control measures, community and social measures, blockade measures, health care measures, COVID-19 vaccination measure, and relaxed pandemic prevention measures. The new cases per day curve showed only one peak in the first wave and two peaks in the second wave. The number of new cases per million in the second wave was much higher than that in the first wave, and the curve fluctuated less. The difference between mortality per million was small, and the curve fluctuated widely.

Conclusion

During the first and second waves of COVID-19, the UK implemented three lockdowns and managed to slow the spread of the pandemic. The UK’s experience in mitigating the second wave proves that advancing COVID-19 vaccination needs to be accompanied by ongoing implementation of non-pharmacological interventions to reduce the transmission rate of infection. And a stricter lockdown ensures that the containment effect is maximized during the lockdown period. In addition, these three lockdowns featured distinct mitigation strategies and the UK’s response to COVID-19 is mitigation strategy that reduce new cases in the short term, but with the risk of the pandemic rebound.

Modelling: Understanding pandemics and how to control them

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.

Making pandemics big: On the situational performance of Covid-19 mathematical models

In this paper, we trace how mathematical models are made 'evidence enough' and 'useful for policy'. Working with the interview accounts of mathematical modellers and other scientists engaged in the UK Covid-19 response, we focus on two weeks in March 2020 prior to the announcement of an unprecedented national lockdown. A key thread in our analysis is how pandemics are made 'big'. We follow the work of one particular device, that of modelled 'doubling-time'. By following how modelled doubling-time entangles in its assemblage of evidence-making, we draw attention to multiple actors, including beyond models and metrics, which affect how evidence is performed in relation to the scale of epidemic and its policy response. We draw attention to: policy; Government scientific advice infrastructure; time; uncertainty; and leaps of faith. The 'bigness' of the pandemic, and its evidencing, is situated in social and affective practices, in which uncertainty and dis-ease are inseparable from calculus. This materialises modelling in policy as an 'uncomfortable science'. We argue that situational fit in-the-moment is at least as important as empirical fit when attending to what models perform in policy.

Disease transmission and control modelling at the science-policy interface

The coronavirus disease 2019 (COVID-19) pandemic has disrupted the lives of billions across the world. Mathematical modelling has been a key tool deployed throughout the pandemic to explore the potential public health impact of an unmitigated epidemic. The results of such studies have informed governments' decisions to implement non-pharmaceutical interventions to control the spread of the virus. In this article, we explore the complex relationships between models, decision-making, the media and the public during the COVID-19 pandemic in the United Kingdom of Great Britain and Northern Ireland (UK). Doing so not only provides an important historical context of COVID-19 modelling and how it has shaped the UK response, but as the pandemic continues and looking towards future pandemic preparedness, understanding these relationships and how they might be improved is critical. As such, we have synthesized information gathered via three methods: a survey to publicly list attendees of the Scientific Advisory Group for Emergencies, the Scientific Pandemic Influenza Group on Modelling and other comparable advisory bodies, interviews with science communication experts and former scientific advisors, and reviewing some of the key COVID-19 modelling literature from 2020. Our research highlights the desire for increased bidirectional communication between modellers, decision-makers and the public, as well as the need to convey uncertainty inherent in transmission models in a clear manner. These aspects should be considered carefully ahead of the next emergency response.

Communicating uncertainty in epidemic models

While mathematical models of disease transmission are widely used to inform public health decision-makers globally, the uncertainty inherent in results are often poorly communicated. We outline some potential sources of uncertainty in epidemic models, present traditional methods used to illustrate uncertainty and discuss alternative presentation formats used by modelling groups throughout the COVID-19 pandemic. Then, by drawing on the experience of our own recent modelling, we seek to contribute to the ongoing discussion of how to improve upon traditional methods used to visualise uncertainty by providing a suggestion of how this can be presented in a clear and simple manner.

Rigorous Policy-Making Amid COVID-19 and Beyond: Literature Review and Critical Insights

Policies shape society. Public health policies are of particular importance, as they often dictate matters in life and death. Accumulating evidence indicates that good-intentioned COVID-19 policies, such as shelter-in-place measures, can often result in unintended consequences among vulnerable populations such as nursing home residents and domestic violence victims. Thus, to shed light on the issue, this study aimed to identify policy-making processes that have the potential of developing policies that could induce optimal desirable outcomes with limited to no unintended consequences amid the pandemic and beyond. Methods: A literature review was conducted in PubMed, PsycINFO, and Scopus to answer the research question. To better structure the review and the subsequent analysis, theoretical frameworks such as the social ecological model were adopted to guide the process. Results: The findings suggested that: (1) people-centered; (2) artificial intelligence (AI)-powered; (3) data-driven, and (4) supervision-enhanced policy-making processes could help society develop policies that have the potential to yield desirable outcomes with limited unintended consequences. To leverage these strategies' interconnectedness, the people-centered, AI-powered, data-driven, and supervision-enhanced (PADS) model of policy making was subsequently developed. Conclusions: The PADS model can develop policies that have the potential to induce optimal outcomes and limit or eliminate unintended consequences amid COVID-19 and beyond. Rather than serving as a definitive answer to problematic COVID-19 policy-making practices, the PADS model could be best understood as one of many promising frameworks that could bring the pandemic policy-making process more in line with the interests of societies at large; in other words, more cost-effectively, and consistently anti-COVID and pro-human.

An operationally implementable model for predicting the effects of an infectious disease on a comprehensive regional healthcare system

An operationally implementable predictive model has been developed to forecast the number of COVID-19 infections in the patient population, hospital floor and ICU censuses, ventilator and related supply chain demand. The model is intended for clinical, operational, financial and supply chain leaders and executives of a comprehensive healthcare system responsible for making decisions that depend on epidemiological contingencies. This paper describes the model that was implemented at NorthShore University HealthSystem and is applicable to any communicable disease whose risk of reinfection for the duration of the pandemic is negligible.

Modelling that shaped the early COVID-19 pandemic response in the UK

Infectious disease modelling has played an integral part of the scientific evidence used to guide the response to the COVID-19 pandemic. In the UK, modelling evidence used for policy is reported to the Scientific Advisory Group for Emergencies (SAGE) modelling subgroup, SPI-M-O (Scientific Pandemic Influenza Group on Modelling-Operational). This Special Issue contains 20 articles detailing evidence that underpinned advice to the UK government during the SARS-CoV-2 pandemic in the UK between January 2020 and July 2020. Here, we introduce the UK scientific advisory system and how it operates in practice, and discuss how infectious disease modelling can be useful in policy making. We examine the drawbacks of current publishing practices and academic credit and highlight the importance of transparency and reproducibility during an epidemic emergency. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.