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Grøntved S, Jørgine Kirkeby M, Paaske Johnsen S, Mainz J, Brink Valentin J, Mohr Jensen C. Towards reliable forecasting of healthcare capacity needs: A scoping review and evidence mapping. Int J Med Inform 2024; 189:105527. [PMID: 38901268 DOI: 10.1016/j.ijmedinf.2024.105527] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2024] [Revised: 05/31/2024] [Accepted: 06/14/2024] [Indexed: 06/22/2024]
Abstract
BACKGROUND The COVID-19 pandemic has highlighted the critical importance of robust healthcare capacity planning and preparedness for emerging crises. However, healthcare systems must also adapt to more gradual temporal changes in disease prevalence and demographic composition over time. To support proactive healthcare planning, statistical capacity forecasting models can provide valuable information to healthcare planners. This systematic literature review and evidence mapping aims to identify and describe studies that have used statistical forecasting models to estimate healthcare capacity needs within hospital settings. METHOD Studies were identified in the databases MEDLINE and Embase and screened for relevance before items were defined and extracted within the following categories: forecast methodology, measure of capacity, forecast horizon, healthcare setting, target diagnosis, validation methods, and implementation. RESULTS 84 studies were selected, all focusing on various capacity outcomes, including number of hospital beds/ patients, staffing, and length of stay. The selected studies employed different analytical models grouped in six items; discrete event simulation (N = 13, 15 %), generalized linear models (N = 21, 25 %), rate multiplication (N = 15, 18 %), compartmental models (N = 14, 17 %), time series analysis (N = 22, 26 %), and machine learning not otherwise categorizable (N = 12, 14 %). The review further provides insights into disease areas with infectious diseases (N = 24, 29 %) and cancer (N = 12, 14 %) being predominant, though several studies forecasted healthcare capacity needs in general (N = 24, 29 %). Only about half of the models were validated using either temporal validation (N = 39, 46 %), cross-validation (N = 2, 2 %) or/and geographical validation (N = 4, 5 %). CONCLUSION The forecasting models' applicability can serve as a resource for healthcare stakeholders involved in designing future healthcare capacity estimation. The lack of routine performance validation of the used algorithms is concerning. There is very little information on implementation and follow-up validation of capacity planning models.
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Affiliation(s)
- Simon Grøntved
- Psychiatry, Aalborg University Hospital, Aalborg, Denmark; Danish Center for Health Services Research, Department of Clinical Medicine, Aalborg University, Aalborg, Denmark.
| | - Mette Jørgine Kirkeby
- Danish Center for Health Services Research, Department of Clinical Medicine, Aalborg University, Aalborg, Denmark; Aalborg University Hospital - Research, Education and Innovation, Aalborg, Denmark
| | - Søren Paaske Johnsen
- Danish Center for Health Services Research, Department of Clinical Medicine, Aalborg University, Aalborg, Denmark; Aalborg University Hospital - Research, Education and Innovation, Aalborg, Denmark
| | - Jan Mainz
- Psychiatry, Aalborg University Hospital, Aalborg, Denmark; Danish Center for Health Services Research, Department of Clinical Medicine, Aalborg University, Aalborg, Denmark
| | - Jan Brink Valentin
- Danish Center for Health Services Research, Department of Clinical Medicine, Aalborg University, Aalborg, Denmark
| | - Christina Mohr Jensen
- Psychiatry, Aalborg University Hospital, Aalborg, Denmark; Institute of Communication and Psychology, Psychology, Aalborg University, Aalborg, Denmark
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Liu Z, Guo W. Dynamic hierarchical state space forecasting. Stat Med 2024; 43:2655-2671. [PMID: 38693595 PMCID: PMC11168190 DOI: 10.1002/sim.10097] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2023] [Revised: 04/15/2024] [Accepted: 04/19/2024] [Indexed: 05/03/2024]
Abstract
In this paper, we aim to both borrow information from existing units and incorporate the target unit's history data in time series forecasting. We consider a situation when we have time series data from multiple units that share similar patterns when aligned in terms of an internal time. The internal time is defined as an index according to evolving features of interest. When mapped back to the calendar time, these time series can span different time intervals that can include the future calendar time of the targeted unit, over which we can borrow the information from other units in forecasting the targeted unit. We first build a hierarchical state space model for the multiple time series data in terms of the internal time, where the shared components capture the similarities among different units while allowing for unit-specific deviations. A conditional state space model is then constructed to incorporate the information of existing units as the prior information in forecasting the targeted unit. By running the Kalman filtering based on the conditional state space model on the targeted unit, we incorporate both the information from the other units and the history of the targeted unit. The forecasts are then transformed from internal time back into calendar time for ease of interpretation. A simulation study is conducted to evaluate the finite sample performance. Forecasting state-level new COVID-19 cases in United States is used for illustration.
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Affiliation(s)
- Ziyue Liu
- Department of Biostatistics and Health Data Science, Indiana University School of Medicine, Indianapolis, Indiana, USA
| | - Wensheng Guo
- Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, Philadelphia, Pennsylvania, USA
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Léger AE, Rizzi S. Month-to-month all-cause mortality forecasting: a method allowing for changes in seasonal patterns. Am J Epidemiol 2024; 193:898-907. [PMID: 38343158 PMCID: PMC11145908 DOI: 10.1093/aje/kwae004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Revised: 11/20/2023] [Accepted: 02/02/2024] [Indexed: 06/04/2024] Open
Abstract
Forecasting of seasonal mortality patterns can provide useful information for planning health-care demand and capacity. Timely mortality forecasts are needed during severe winter spikes and/or pandemic waves to guide policy-making and public health decisions. In this article, we propose a flexible method for forecasting all-cause mortality in real time considering short-term changes in seasonal patterns within an epidemiologic year. All-cause mortality data have the advantage of being available with less delay than cause-specific mortality data. In this study, we use all-cause monthly death counts obtained from the national statistical offices of Denmark, France, Spain, and Sweden from epidemic seasons 2012-2013 through 2021-2022 to demonstrate the performance of the proposed approach. The method forecasts deaths 1 month ahead, based on their expected ratio to the next month. Prediction intervals are obtained via bootstrapping. The forecasts accurately predict the winter mortality peaks before the COVID-19 pandemic. Although the method predicts mortality less accurately during the first wave of the COVID-19 pandemic, it captures the aspects of later waves better than other traditional methods. The method is attractive for health researchers and governmental offices for aiding public health responses because it uses minimal input data, makes simple and intuitive assumptions, and provides accurate forecasts both during seasonal influenza epidemics and during novel virus pandemics.
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Affiliation(s)
- Ainhoa-Elena Léger
- Corresponding author: Ainhoa-Elena Leger, Interdisciplinary Centre on Population Dynamics, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark ()
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Wang YY, Zhang WW, Lu ZX, Sun JL, Jing MX. Evaluating the Demand for Nucleic Acid Testing in Different Scenarios of COVID-19 Transmission: A Simulation Study. Infect Dis Ther 2024; 13:813-826. [PMID: 38498107 PMCID: PMC11058130 DOI: 10.1007/s40121-024-00954-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2024] [Accepted: 02/26/2024] [Indexed: 03/20/2024] Open
Abstract
INTRODUCTION The 2019 novel coronavirus (COVID-19) has been recognized as the most severe human infectious disease pandemic in the past century. To enhance our ability to control potential infectious diseases in the future, this study simulated the influence of nucleic acid testing on the transmission of COVID-19 across varied scenarios. Additionally, it assessed the demand for nucleic acid testing under different circumstances, aiming to furnish a decision-making foundation for the implementation of nucleic acid screening measures, the provision of emergency materials, and the allocation of human resources. METHODS Considering the transmission dynamics of COVID-19 and the preventive measures implemented by countries, we explored three distinct levels of epidemic intensity: community transmission, outbreak, and sporadic cases. Integrating the theory of scenario analysis, we formulated six hypothetical epidemic scenarios, each corresponding to possible occurrences during different phases of the pandemic. We developed an improved SEIR model, validated its accuracy using real-world data, and conducted a comprehensive analysis and prediction of COVID-19 infections under these six scenarios. Simultaneously, we assessed the testing resource requirements associated with each scenario. RESULTS We compared the predicted number of infections simulated by the modified SEIR model with the actual reported cases in Israel to validate the model. The root mean square error (RMSE) was 350.09, and the R-squared (R2) was 0.99, indicating a well-fitted model. Scenario 4 demonstrated the most effective prevention and control outcomes. Strengthening non-pharmaceutical interventions and increasing nucleic acid testing frequency, even under low testing capacity, resulted in a delayed epidemic peak by 78 days. The proportion of undetected cases decreased from 77.83% to 31.21%, and the overall testing demand significantly decreased, meeting maximum demand even with low testing capacity. The initiation of testing influenced case detection probability. Under high testing capacity, increasing testing frequency elevated the detection rate from 36.40% to 77.83%. Nucleic acid screening proved effective in reducing the demand for testing resources under diverse epidemic prevention and control strategies. While effective interventions and nucleic acid screening measures substantially diminished the demand for testing-related resources, varying degrees of insufficient testing capacity may still persist. CONCLUSIONS The nucleic acid detection strategy proves effective in promptly identifying and isolating infected individuals, thereby mitigating the infection peak and extending the time to peak. In situations with constrained testing capacity, implementing more stringent measures can notably decrease the number of infections and alleviate resource demands. The improved SEIR model demonstrates proficiency in predicting both reported and unreported cases, offering valuable insights for future infection risk assessments. Rapid evaluations of testing requirements across diverse scenarios can aptly address resource limitations in specific regions, offering substantial evidence for the formulation of future infectious disease testing strategies.
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Affiliation(s)
- Yu-Yuan Wang
- Department of Preventive Medicine, School of Medicine, Shihezi University, 221 Beisi Road, Shihezi, 832003, People's Republic of China
- Key Laboratory for Prevention and Control of Emerging Infectious Diseases and Public Health Security, The Xinjiang Production and Construction Corps, Xinjiang, People's Republic of China
| | - Wei-Wen Zhang
- Department of Preventive Medicine, School of Medicine, Shihezi University, 221 Beisi Road, Shihezi, 832003, People's Republic of China
- Key Laboratory for Prevention and Control of Emerging Infectious Diseases and Public Health Security, The Xinjiang Production and Construction Corps, Xinjiang, People's Republic of China
| | - Ze-Xi Lu
- Department of Preventive Medicine, School of Medicine, Shihezi University, 221 Beisi Road, Shihezi, 832003, People's Republic of China
- Key Laboratory for Prevention and Control of Emerging Infectious Diseases and Public Health Security, The Xinjiang Production and Construction Corps, Xinjiang, People's Republic of China
| | - Jia-Lin Sun
- Department of Preventive Medicine, School of Medicine, Shihezi University, 221 Beisi Road, Shihezi, 832003, People's Republic of China.
- Key Laboratory for Prevention and Control of Emerging Infectious Diseases and Public Health Security, The Xinjiang Production and Construction Corps, Xinjiang, People's Republic of China.
- Department of Nutrition and Food Hygiene, School of Public Health, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, China.
| | - Ming-Xia Jing
- Department of Preventive Medicine, School of Medicine, Shihezi University, 221 Beisi Road, Shihezi, 832003, People's Republic of China.
- Key Laboratory for Prevention and Control of Emerging Infectious Diseases and Public Health Security, The Xinjiang Production and Construction Corps, Xinjiang, People's Republic of China.
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Klinkenberg D, Backer J, de Keizer N, Wallinga J. Projecting COVID-19 intensive care admissions for policy advice, the Netherlands, February 2020 to January 2021. Euro Surveill 2024; 29:2300336. [PMID: 38456214 PMCID: PMC10986673 DOI: 10.2807/1560-7917.es.2024.29.10.2300336] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Accepted: 12/07/2023] [Indexed: 03/09/2024] Open
Abstract
BackgroundModel projections of coronavirus disease 2019 (COVID-19) incidence help policymakers about decisions to implement or lift control measures. During the pandemic, policymakers in the Netherlands were informed on a weekly basis with short-term projections of COVID-19 intensive care unit (ICU) admissions.AimWe aimed at developing a model on ICU admissions and updating a procedure for informing policymakers.MethodThe projections were produced using an age-structured transmission model. A consistent, incremental update procedure integrating all new surveillance and hospital data was conducted weekly. First, up-to-date estimates for most parameter values were obtained through re-analysis of all data sources. Then, estimates were made for changes in the age-specific contact rates in response to policy changes. Finally, a piecewise constant transmission rate was estimated by fitting the model to reported daily ICU admissions, with a changepoint analysis guided by Akaike's Information Criterion.ResultsThe model and update procedure allowed us to make weekly projections. Most 3-week prediction intervals were accurate in covering the later observed numbers of ICU admissions. When projections were too high in March and August 2020 or too low in November 2020, the estimated effectiveness of the policy changes was adequately adapted in the changepoint analysis based on the natural accumulation of incoming data.ConclusionThe model incorporates basic epidemiological principles and most model parameters were estimated per data source. Therefore, it had potential to be adapted to a more complex epidemiological situation with the rise of new variants and the start of vaccination.
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Affiliation(s)
- Don Klinkenberg
- National Institute for Public Health and the Environment, Bilthoven, The Netherlands
| | - Jantien Backer
- National Institute for Public Health and the Environment, Bilthoven, The Netherlands
| | - Nicolette de Keizer
- Department of Medical Informatics, Amsterdam UMC, Amsterdam Public Health Research Institute, Amsterdam, The Netherlands
- National Intensive Care Evaluation (NICE) Foundation, Amsterdam, The Netherlands
| | - Jacco Wallinga
- Leiden University Medical Centre, Leiden, The Netherlands
- National Institute for Public Health and the Environment, Bilthoven, The Netherlands
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Yin ZJ, Xiao H, McDonald S, Brusic V, Qiu TY. Dynamically adjustable SVEIR(MH) model of multiwave epidemics: Estimating the effects of public health measures against COVID-19. J Med Virol 2023; 95:e29301. [PMID: 38087460 DOI: 10.1002/jmv.29301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Revised: 10/16/2023] [Accepted: 11/24/2023] [Indexed: 12/18/2023]
Abstract
The COVID-19 pandemic was characterized by multiple subsequent, overlapping outbreaks, as well as extremely rapid changes in viral genomes. The information about local epidemics spread and the epidemic control measures was shared on a daily basis (number of cases and deaths) via centralized repositories. The vaccines were developed within the first year of the pandemic. New modes of monitoring and sharing of epidemic data were implemented using Internet resources. We modified the basic SEIR compartmental model to include public health measures, multiwave scenarios, and the variation of viral infectivity and transmissibility reflected by the basic reproduction number R0 of emerging viral variants. SVEIR(MH) model considers the capacity of the medical system, lockdowns, vaccination, and changes in viral reproduction rate on the epidemic spread. The developed model uses daily infection reports for assessing the epidemic dynamics, and daily changes of mobility data from mobile phone networks to assess the lockdown effectiveness. This model was deployed to six European regions Baden-Württemberg (Germany), Belgium, Czechia, Lombardy (Italy), Sweden, and Switzerland for the first 2 years of the pandemic. The correlation coefficients between observed and reported infection data showed good concordance for both years of the pandemic (ρ = 0.84-0.94 for the raw data and ρ = 0.91-0.98 for smoothed 7-day averages). The results show stability across the regions and the different epidemic waves. Optimal control of epidemic waves can be achieved by dynamically adjusting epidemic control measures in real-time. SVEIR(MH) model can simulate different scenarios and inform adjustments to the public health policies to achieve the target outcomes. Because this model is highly representative of actual epidemic situations, it can be used to assess both the public health and socioeconomic effects of the public health measures within the first 7 days of the outbreak.
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Affiliation(s)
- Zuo-Jing Yin
- Institute of Clinical Science, Zhongshan Hospital; Shanghai Institute of Infectious Disease and Biosecurity; Intelligent Medicine Institute, Fudan University, Shanghai, China
| | - Han Xiao
- Department of Computer Science, Aalto University, Espoo, Finland
| | - Stuart McDonald
- Smart Medicine Laboratory, School of Economics, University of Nottingham Ningbo China, Ningbo, China
| | - Vladimir Brusic
- Smart Medicine Laboratory, School of Economics, University of Nottingham Ningbo China, Ningbo, China
| | - Tian-Yi Qiu
- Institute of Clinical Science, Zhongshan Hospital; Shanghai Institute of Infectious Disease and Biosecurity; Intelligent Medicine Institute, Fudan University, Shanghai, China
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Ma Y, Xu S, Luo Y, Qin Y, Li J, Lei L, He L, Wang T, Yu H, Xie J. Epidemiological characteristics and transmission dynamics of the COVID-19 outbreak in Hohhot, China: a time-varying SQEIAHR model analysis. Front Public Health 2023; 11:1175869. [PMID: 37415698 PMCID: PMC10321150 DOI: 10.3389/fpubh.2023.1175869] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Accepted: 06/01/2023] [Indexed: 07/08/2023] Open
Abstract
Background On September 28, 2022, the first case of Omicron subvariant BF.7 was discovered among coronavirus disease 2019 (COVID-19) infections in Hohhot, China, and then the epidemic broke out on a large scale during the National Day holiday. It is imminently necessary to construct a mathematical model to investigate the transmission dynamics of COVID-19 in Hohhot. Methods In this study, we first investigated the epidemiological characteristics of COVID-19 cases in Hohhot, including the spatiotemporal distribution and sociodemographic distribution. Then, we proposed a time-varying Susceptible-Quarantined Susceptible-Exposed-Quarantined Exposed-Infected-Asymptomatic-Hospitalized-Removed (SQEIAHR) model to derive the epidemic curves. The next-generation matrix method was used to calculate the effective reproduction number (Re). Finally, we explored the effects of higher stringency measures on the development of the epidemic through scenario analysis. Results Of the 4,889 positive infected cases, the vast majority were asymptomatic and mild, mainly concentrated in central areas such as Xincheng District. People in the 30-59 age group primarily were affected by the current outbreak, accounting for 53.74%, but females and males were almost equally affected (1.03:1). Community screening (35.70%) and centralized isolation screening (26.28%) were the main ways to identify positive infected cases. Our model predicted the peak of the epidemic on October 6, 2022, the dynamic zero-COVID date on October 15, 2022, a number of peak cases of 629, and a cumulative number of infections of 4,963 (95% confidential interval (95%CI): 4,692 ~ 5,267), all four of which were highly consistent with the actual situation in Hohhot. Early in the outbreak, the basic reproduction number (R0) was approximately 7.01 (95%CI: 6.93 ~ 7.09), and then Re declined sharply to below 1.0 on October 6, 2022. Scenario analysis of higher stringency measures showed the importance of decreasing the transmission rate and increasing the quarantine rate to shorten the time to peak, dynamic zero-COVID and an Re below 1.0, as well as to reduce the number of peak cases and final affected population. Conclusion Our model was effective in predicting the epidemic trends of COVID-19, and the implementation of a more stringent combination of measures was indispensable in containing the spread of the virus.
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Affiliation(s)
- Yifei Ma
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Shujun Xu
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Yuxin Luo
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Yao Qin
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Jiantao Li
- School of Management, Shanxi Medical University, Taiyuan, China
| | - Lijian Lei
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Lu He
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Tong Wang
- School of Public Health, Shanxi Medical University, Taiyuan, China
| | - Hongmei Yu
- School of Public Health, Shanxi Medical University, Taiyuan, China
- Shanxi Provincial Key Laboratory of Major Diseases Risk Assessment, Taiyuan, China
| | - Jun Xie
- Center of Reverse Microbial Etiology, Shanxi Medical University, Taiyuan, China
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Toh KB, Runge M, Richardson RA, Hladish TJ, Gerardin J. Design of effective outpatient sentinel surveillance for COVID-19 decision-making: a modeling study. BMC Infect Dis 2023; 23:287. [PMID: 37142984 PMCID: PMC10158704 DOI: 10.1186/s12879-023-08261-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Accepted: 04/17/2023] [Indexed: 05/06/2023] Open
Abstract
BACKGROUND Decision-makers impose COVID-19 mitigations based on public health indicators such as reported cases, which are sensitive to fluctuations in supply and demand for diagnostic testing, and hospital admissions, which lag infections by up to two weeks. Imposing mitigations too early has unnecessary economic costs while imposing too late leads to uncontrolled epidemics with unnecessary cases and deaths. Sentinel surveillance of recently-symptomatic individuals in outpatient testing sites may overcome biases and lags in conventional indicators, but the minimal outpatient sentinel surveillance system needed for reliable trend estimation remains unknown. METHODS We used a stochastic, compartmental transmission model to evaluate the performance of various surveillance indicators at reliably triggering an alarm in response to, but not before, a step increase in transmission of SARS-CoV-2. The surveillance indicators included hospital admissions, hospital occupancy, and sentinel cases with varying levels of sampling effort capturing 5, 10, 20, 50, or 100% of incident mild cases. We tested 3 levels of transmission increase, 3 population sizes, and conditions of either simultaneous transmission increase or lagged increase in the older population. We compared the indicators' performance at triggering alarm soon after, but not prior, to the transmission increase. RESULTS Compared to surveillance based on hospital admissions, outpatient sentinel surveillance that captured at least 20% of incident mild cases could trigger an alarm 2 to 5 days earlier for a mild increase in transmission and 6 days earlier for a moderate or strong increase. Sentinel surveillance triggered fewer false alarms and averted more deaths per day spent in mitigation. When transmission increase in older populations lagged the increase in younger populations by 14 days, sentinel surveillance extended its lead time over hospital admissions by an additional 2 days. CONCLUSIONS Sentinel surveillance of mild symptomatic cases can provide more timely and reliable information on changes in transmission to inform decision-makers in an epidemic like COVID-19.
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Affiliation(s)
- Kok Ben Toh
- Department of Preventive Medicine, Institute for Global Health, Northwestern University Feinberg School of Medicine, Chicago, IL, USA.
| | - Manuela Runge
- Department of Preventive Medicine, Institute for Global Health, Northwestern University Feinberg School of Medicine, Chicago, IL, USA
| | - Reese Ak Richardson
- Department of Chemical and Biological Engineering, Northwestern University, Chicago, IL, USA
| | - Thomas J Hladish
- Department of Biology, University of Florida, Gainesville, FL, USA
- Emerging Pathogen Institute, University of Florida, Gainesville, FL, USA
| | - Jaline Gerardin
- Department of Preventive Medicine, Institute for Global Health, Northwestern University Feinberg School of Medicine, Chicago, IL, USA
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McClymont H, Si X, Hu W. Using weather factors and google data to predict COVID-19 transmission in Melbourne, Australia: A time-series predictive model. Heliyon 2023; 9:e13782. [PMID: 36845036 PMCID: PMC9941072 DOI: 10.1016/j.heliyon.2023.e13782] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2022] [Revised: 02/09/2023] [Accepted: 02/10/2023] [Indexed: 02/23/2023] Open
Abstract
Background Forecast models have been essential in understanding COVID-19 transmission and guiding public health responses throughout the pandemic. This study aims to assess the effect of weather variability and Google data on COVID-19 transmission and develop multivariable time series AutoRegressive Integrated Moving Average (ARIMA) models for improving traditional predictive modelling for informing public health policy. Methods COVID-19 case notifications, meteorological factors and Google data were collected over the B.1.617.2 (Delta) outbreak in Melbourne, Australia from August to November 2021. Timeseries cross-correlation (TSCC) was used to evaluate the temporal correlation between weather factors, Google search trends, Google Mobility data and COVID-19 transmission. Multivariable time series ARIMA models were fitted to forecast COVID-19 incidence and Effective Reproductive Number (R eff ) in the Greater Melbourne region. Five models were fitted to compare and validate predictive models using moving three-day ahead forecasts to test the predictive accuracy for both COVID-19 incidence and R eff over the Melbourne Delta outbreak. Results Case-only ARIMA model resulted in an R squared (R2) value of 0.942, Root Mean Square Error (RMSE) of 141.59, and Mean Absolute Percentage Error (MAPE) of 23.19. The model including transit station mobility (TSM) and maximum temperature (Tmax) had greater predictive accuracy with R2 0.948, RMSE 137.57, and MAPE 21.26. Conclusion Multivariable ARIMA modelling for COVID-19 cases and R eff was useful for predicting epidemic growth, with higher predictive accuracy for models including TSM and Tmax. These results suggest that TSM and Tmax would be useful for further exploration for developing weather-informed early warning models for future COVID-19 outbreaks with potential application for the inclusion of weather and Google data with disease surveillance in developing effective early warning systems for informing public health policy and epidemic response.
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Aleta A, Blas-Laína JL, Tirado Anglés G, Moreno Y. Unraveling the COVID-19 hospitalization dynamics in Spain using Bayesian inference. BMC Med Res Methodol 2023; 23:24. [PMID: 36698070 PMCID: PMC9875773 DOI: 10.1186/s12874-023-01842-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2021] [Accepted: 01/13/2023] [Indexed: 01/26/2023] Open
Abstract
BACKGROUND One of the main challenges of the COVID-19 pandemic is to make sense of available, but often heterogeneous and noisy data. This contribution presents a data-driven methodology that allows exploring the hospitalization dynamics of COVID-19, exemplified with a study of 17 autonomous regions in Spain from summer 2020 to summer 2021. METHODS We use data on new daily cases and hospitalizations reported by the Spanish Ministry of Health to implement a Bayesian inference method that allows making short-term predictions of bed occupancy of COVID-19 patients in each of the autonomous regions of the country. RESULTS We show how to use the temporal series for the number of daily admissions and discharges from hospital to reproduce the hospitalization dynamics of COVID-19 patients. For the case-study of the region of Aragon, we estimate that the probability of being admitted to hospital care upon infection is 0.090 [0.086-0.094], (95% C.I.), with the distribution governing hospital admission yielding a median interval of 3.5 days and an IQR of 7 days. Likewise, the distribution on the length of stay produces estimates of 12 days for the median and 10 days for the IQR. A comparison between model parameters for the regions analyzed allows to detect differences and changes in policies of the health authorities. CONCLUSIONS We observe important regional differences, signaling that to properly compare very different populations, it is paramount to acknowledge all the diversity in terms of culture, socio-economic status, and resource availability. To better understand the impact of this pandemic, much more data, disaggregated and properly annotated, should be made available.
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Affiliation(s)
- Alberto Aleta
- grid.418750.f0000 0004 1759 3658ISI Foundation, Via Chisola 5, 10126 Torino, Italy ,grid.11205.370000 0001 2152 8769Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain
| | - Juan Luis Blas-Laína
- grid.413293.e0000 0004 1764 9746Servicio de Cirugía General y Aparato Digestivo (Jefe de Servicio), Hospital Royo Villanova, Av San Gregorio s/n, 50015 Zaragoza, Spain
| | - Gabriel Tirado Anglés
- grid.413293.e0000 0004 1764 9746Unidad de Cuidados Intensivos (Jefe de Servicio), Hospital Royo Villanova, Av San Gregorio s/n, 50015 Zaragoza, Spain
| | - Yamir Moreno
- grid.11205.370000 0001 2152 8769Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain ,grid.11205.370000 0001 2152 8769Department of Theoretical Physics, University of Zaragoza, 50018 Zaragoza, Spain ,Centai Institute, 10138 Torino, Italy ,grid.484678.1Complexity Science Hub, 1080 Vienna, Austria
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Zheng HL, An SY, Qiao BJ, Guan P, Huang DS, Wu W. A data-driven interpretable ensemble framework based on tree models for forecasting the occurrence of COVID-19 in the USA. ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH INTERNATIONAL 2023; 30:13648-13659. [PMID: 36131178 PMCID: PMC9492466 DOI: 10.1007/s11356-022-23132-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 09/16/2022] [Indexed: 06/15/2023]
Abstract
This prevalence of coronavirus disease 2019 (COVID-19) has become one of the most serious public health crises. Tree-based machine learning methods, with the advantages of high efficiency, and strong interpretability, have been widely used in predicting diseases. A data-driven interpretable ensemble framework based on tree models was designed to forecast daily new cases of COVID-19 in the USA and to determine the important factors related to COVID-19. Based on a hyperparametric optimization technique, we developed three machine learning algorithms based on decision trees, including random forest (RF), eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), and three linear ensemble models were used to integrate these outcomes for better prediction accuracy. Finally, the SHapley Additive explanation (SHAP) value was used to obtain the feature importance ranking. Our outcomes demonstrated that, among the three basic machine learners, the prediction accuracy was the following in descending order: LightGBM, XGBoost, and RF. The optimized LAD ensemble was the most precise prediction model that reduced the prediction error of the best base learner (LightGBM) by approximately 3.111%, while vaccination, wearing masks, less mobility, and government interventions had positive effects on the control and prevention of COVID-19.
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Affiliation(s)
- Hu-Li Zheng
- Department of Epidemiology, School of Public Health, China Medical University, No. 77 Puhe Road, Shenyang, Liaoning Province China
| | - Shu-Yi An
- Liaoning Provincial Center for Disease Control and Prevention, Shenyang, Liaoning China
| | - Bao-Jun Qiao
- Liaoning Provincial Center for Disease Control and Prevention, Shenyang, Liaoning China
| | - Peng Guan
- Department of Epidemiology, School of Public Health, China Medical University, No. 77 Puhe Road, Shenyang, Liaoning Province China
| | - De-Sheng Huang
- Department of Mathematics, School of Intelligent Medicine, China Medical University, Shenyang, Liaoning China
| | - Wei Wu
- Department of Epidemiology, School of Public Health, China Medical University, No. 77 Puhe Road, Shenyang, Liaoning Province China
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Van Yperen J, Campillo-Funollet E, Inkpen R, Memon A, Madzvamuse A. A hospital demand and capacity intervention approach for COVID-19. PLoS One 2023; 18:e0283350. [PMID: 37134085 PMCID: PMC10156009 DOI: 10.1371/journal.pone.0283350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Accepted: 03/06/2023] [Indexed: 05/04/2023] Open
Abstract
The mathematical interpretation of interventions for the mitigation of epidemics in the literature often involves finding the optimal time to initiate an intervention and/or the use of the number of infections to manage impact. Whilst these methods may work in theory, in order to implement effectively they may require information which is not likely to be available in the midst of an epidemic, or they may require impeccable data about infection levels in the community. In reality, testing and cases data can only be as good as the policy of implementation and the compliance of the individuals, which implies that accurately estimating the levels of infections becomes difficult or complicated from the data that is provided. In this paper, we demonstrate a different approach to the mathematical modelling of interventions, not based on optimality or cases, but based on demand and capacity of hospitals who have to deal with the epidemic on a day to day basis. In particular, we use data-driven modelling to calibrate a susceptible-exposed-infectious-recovered-died type model to infer parameters that depict the dynamics of the epidemic in several regions of the UK. We use the calibrated parameters for forecasting scenarios and understand, given a maximum capacity of hospital healthcare services, how the timing of interventions, severity of interventions, and conditions for the releasing of interventions affect the overall epidemic-picture. We provide an optimisation method to capture when, in terms of healthcare demand, an intervention should be put into place given a maximum capacity on the service. By using an equivalent agent-based approach, we demonstrate uncertainty quantification on the likelihood that capacity is not breached, by how much if it does, and the limit on demand that almost guarantees capacity is not breached.
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Affiliation(s)
- James Van Yperen
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, United Kingdom
| | - Eduard Campillo-Funollet
- Department of Mathematics, School of Mathematical, Statistical and Actuarial Sciences, University of Kent, Canterbury, United Kingdom
- Department of Mathematics and Statistics, Lancaster University, Lancaster, United Kingdom
| | - Rebecca Inkpen
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, United Kingdom
| | - Anjum Memon
- Department of Primary Care and Public Health, Brighton and Sussex Medical School, Brighton, United Kingdom
| | - Anotida Madzvamuse
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, United Kingdom
- Department of Mathematics, University of Johannesburg, Johannesburg, South Africa
- Department of Mathematics, University of British Columbia, Vancouver, Canada
- Department of Mathematics, University of Pretoria, Pretoria, South Africa
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Campillo-Funollet E, Wragg H, Van Yperen J, Duong DL, Madzvamuse A. Reformulating the susceptible-infectious-removed model in terms of the number of detected cases: well-posedness of the observational model. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210306. [PMID: 35965462 PMCID: PMC9376718 DOI: 10.1098/rsta.2021.0306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/05/2021] [Accepted: 02/23/2022] [Indexed: 06/15/2023]
Abstract
Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the observed data are typically akin to a boundary value-type problem: we observe some of the dependent variables at given times, but we do not know the initial conditions. In this paper, we reformulate the classical susceptible-infectious-recovered system in terms of the number of detected positive infected cases at different times to yield what we term the observational model. We then prove the existence and uniqueness of a solution to the boundary value problem associated with the observational model and present a numerical algorithm to approximate the solution. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.
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Affiliation(s)
- Eduard Campillo-Funollet
- Department of Statistical Methodology and Applications, School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7PE, UK
| | - Hayley Wragg
- Department of Engineering Mathematics, School of Computer Science, Electrical and Electronic Engineering and Engineering Maths, University of Bristol, Bristol BS8 1TW, UK
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, East Sussex BN1 9QH, UK
| | - James Van Yperen
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, East Sussex BN1 9QH, UK
| | - Duc-Lam Duong
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, East Sussex BN1 9QH, UK
- School of Engineering Science, LUT University, Lappeenranta 53850, Finland
| | - Anotida Madzvamuse
- Department of Mathematics, School of Mathematical and Physical Sciences, University of Sussex, Brighton, East Sussex BN1 9QH, UK
- Department of Mathematics, University of Johannesburg, Johannesburg, South Africa
- University of British Columbia, Department of Mathematics, Vancouver, Canada
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Zhang W, Huggins T, Zheng W, Liu S, Du Z, Zhu H, Raza A, Tareq AH. Assessing the Dynamic Outcomes of Containment Strategies against COVID-19 under Different Public Health Governance Structures: A Comparison between Pakistan and Bangladesh. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2022; 19:ijerph19159239. [PMID: 35954595 PMCID: PMC9368361 DOI: 10.3390/ijerph19159239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Revised: 07/24/2022] [Accepted: 07/25/2022] [Indexed: 11/16/2022]
Abstract
COVID-19 scenarios were run using an epidemiological mathematical model (system dynamics model) and counterfactual analysis to simulate the impacts of different control and containment measures on cumulative infections and deaths in Bangladesh and Pakistan. The simulations were based on national-level data concerning vaccination level, hospital capacity, and other factors, from the World Health Organization, the World Bank, and the Our World in Data web portal. These data were added to cumulative infections and death data from government agencies covering the period from 18 March 2020 to 28 February 2022. Baseline curves for Pakistan and Bangladesh were obtained using piecewise fitting with a consideration of different events against the reported data and allowing for less than 5% random errors in cumulative infections and deaths. The results indicate that Bangladesh could have achieved more reductions in each key outcome measure by shifting its initial lockdown at least five days backward, while Pakistan would have needed to extend its lockdown to achieve comparable improvements. Bangladesh’s second lockdown appears to have been better timed than Pakistan’s. There were potential benefits from starting the third lockdown two weeks earlier for Bangladesh and from combining this with the fourth lockdown or canceling the fourth lockdown altogether. Adding a two-week lockdown at the beginning of the upward slope of the second wave could have led to a more than 40 percent reduction in cumulative infections and a 35 percent reduction in cumulative deaths for both countries. However, Bangladesh’s reductions were more sensitive to the duration of the lockdown. Pakistan’s response was more constrained by medical resources, while Bangladesh’s outcomes were more sensitive to both vaccination timing and capacities. More benefits were lost when combining multiple scenarios for Bangladesh compared to the same combinations in Pakistan. Clearly, cumulative infections and deaths could have been highly impacted by adjusting the control and containment measures in both national settings. However, COVID-19 outcomes were more sensitive to adjustment interventions for the Bangladesh context. Disaggregated analyses, using a wider range of factors, may reveal several sub-national dynamics. Nonetheless, the current research demonstrates the relevance of lockdown timing adjustments and discrete adjustments to several other control and containment measures.
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Affiliation(s)
- Weiwei Zhang
- Research Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu 610074, China; (W.Z.); (H.Z.); (A.R.)
| | - Thomas Huggins
- Division of Science & Technology, BNU-HKBU United International College, Zhuhai 519087, China;
| | - Wenwen Zheng
- Personal Finance Department, HQ of China Construction Bank, Beijing 100033, China;
| | - Shiyong Liu
- Institute of Advanced Studies in Humanities and Social Sciences, Beijing Normal University at Zhuhai, Zhuhai 519087, China
- Correspondence: or
| | - Zhanwei Du
- Division of Epidemiology and Biostatistics, School of Public Health, Hong Kong University, Hong Kong, China;
| | - Hongli Zhu
- Research Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu 610074, China; (W.Z.); (H.Z.); (A.R.)
| | - Ahmad Raza
- Research Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu 610074, China; (W.Z.); (H.Z.); (A.R.)
| | - Ahmad Hussen Tareq
- Ministry of National Health Services Regulations and Coordination, Islamabad 44010, Pakistan;
- Health Services Academy, Islamabad 44010, Pakistan
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Human judgement forecasting tournaments: A feasibility study based on the COVID-19 pandemic with public health practitioners in England. PUBLIC HEALTH IN PRACTICE 2022; 3:100260. [PMID: 35479262 PMCID: PMC9023363 DOI: 10.1016/j.puhip.2022.100260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Revised: 03/28/2022] [Accepted: 04/16/2022] [Indexed: 11/09/2022] Open
Abstract
Objectives To explore the viability of running human judgement forecasting tournaments with public health practitioners, and to gather initial data on forecasting accuracy and participant perceptions of forecasting. Study design Quality improvement study comprising two COVID-19 forecasting tournaments using Brier Skill Score scoring and a follow-up participant questionnaire. Methods Over two forecasting tournaments, public health registrars in the East Midlands, UK, assigned probabilities to future possible binary events relating to COVID-19. Participants also completed a questionnaire on their experiences of forecasting. Results There were 17 participants in the first tournament and nine in the second tournament, with no new participants. In both tournaments, the majority of participants scored a Brier Skill Score above the benchmark of 0. The median Brier Skill Score improved slightly between the two tournaments. Participants reported luck and changing political climates as impacting their performance. Participants reported forecasting in their day job but had received no formal training to do so. Conclusions Forecasting is an important public health skill, and human judgement forecasting tournaments can be run amongst public health practitioners with little time and resource requirements. Further research would help identify whether training, teamwork or other interventions can improve public health forecasting accuracy.
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Computational and Mathematical Methods in Medicine Prediction of COVID-19 in BRICS Countries: An Integrated Deep Learning Model of CEEMDAN-R-ILSTM-Elman. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2022; 2022:1566727. [PMID: 35419081 PMCID: PMC9001070 DOI: 10.1155/2022/1566727] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/12/2021] [Revised: 03/08/2022] [Accepted: 03/10/2022] [Indexed: 11/29/2022]
Abstract
Since the outbreak of COVID-19, BRICS countries have experienced different epidemic spread due to different health conditions, social isolation measures, vaccination rates, and other factors. A descriptive analysis is conducted for the spread of the epidemic in the BRICS countries. Considering the nonlinear and nonstationary characteristics of COVID-19 data, a principle of decomposition-reconstruction(R)-prediction-integration is proposed. Correspondingly, this paper constructs an integrated deep learning prediction model of CEEMDAN-R-ILSTM-Elman. Specifically, the prediction model is integrated by complete ensemble empirical mode decomposition (CEEMDAN), improved long-term and short-term memory network (ILSTM), and Elman neural network. First, the data is decomposed by adopting CEEMDAN. Then, by calculating the permutation entropy and average period, the decomposed eigenmode component IMFs are reconstructed into four sequences of high, medium, low level, and trend term. Thus, ILSTM and Elman algorithms are used for component sequence prediction, whose results are integrated as the final results. The ILSTM is established based on the LSTM model and the improved beetle antennae search algorithm (IBAS). The ILSTM mainly considers that the prediction accuracy of LSTM model is vulnerable to the influence of parameter selection. The IBAS with adaptive step size is used to automatically optimize the super parameters of LSTM model and to improve the modeling efficiency and prediction accuracy. Experimental results indicate that compared with other benchmark models, CEEMDAN-R-ILSTM-Elman integrated model predicts the number of newly confirmed cases of COVID-19 in BRICS countries with higher accuracy and lower error. Strict social policies have a greater impact on the infection rate and mortality rate of the epidemic. During July-August 2021, epidemic spread in BRICS countries will slow down, and the overall situation is still quite severe.
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Wood RM, Pratt AC, Murch BJ, Powell AL, Booton RD, Thomas DG, Twigger J, Diakou E, Coleborn S, Manning T, Davies C, Turner KM. Establishing an SEIR-based framework for local modelling of COVID-19 infections, hospitalisations and deaths. Health Syst (Basingstoke) 2021; 10:337-347. [PMID: 34745593 PMCID: PMC8567954 DOI: 10.1080/20476965.2021.1973348] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Accepted: 08/19/2021] [Indexed: 12/13/2022] Open
Abstract
Without timely assessments of the number of COVID-19 cases requiring hospitalisation, healthcare providers will struggle to ensure an appropriate number of beds are made available. Too few could cause excess deaths while too many could result in additional waits for elective treatment. As well as supporting capacity considerations, reliably projecting future "waves" is important to inform the nature, timing and magnitude of any localised restrictions to reduce transmission. In making the case for locally owned and locally configurable models, this paper details the approach taken by one major healthcare system in founding a multi-disciplinary "Scenario Review Working Group", comprising commissioners, public health officials and academic epidemiologists. The role of this group, which met weekly during the pandemic, was to define and maintain an evolving library of plausible scenarios to underpin projections obtained through an SEIR-based compartmental model. Outputs have informed decision-making at the system's major incident Bronze, Silver and Gold Commands. This paper presents illustrated examples of use and offers practical considerations for other healthcare systems that may benefit from such a framework.
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Affiliation(s)
- R. M. Wood
- Bristol, North Somerset and South Gloucestershire CCG, National Health Service, Bristol, UK
- School of Management, University of Bath, Bath, UK
| | - A. C. Pratt
- Bristol, North Somerset and South Gloucestershire CCG, National Health Service, Bristol, UK
| | - B. J. Murch
- Bristol, North Somerset and South Gloucestershire CCG, National Health Service, Bristol, UK
| | - A. L. Powell
- Bristol, North Somerset and South Gloucestershire CCG, National Health Service, Bristol, UK
| | - R. D. Booton
- Bristol Medical School, University of Bristol, Bristol, UK
| | - D. G. Thomas
- Public Health, Bristol City Council, Bristol, UK
| | - J. Twigger
- Public Health, Bristol City Council, Bristol, UK
| | - E. Diakou
- Business Intelligence, North Somerset Council, Weston-Super-Mare, UK
| | - S. Coleborn
- Public Health, South Gloucestershire Council, Yate, UK
| | - T. Manning
- Bristol, North Somerset and South Gloucestershire CCG, National Health Service, Bristol, UK
| | - C. Davies
- Bristol, North Somerset and South Gloucestershire CCG, National Health Service, Bristol, UK
| | - K. M. Turner
- Bristol Medical School, University of Bristol, Bristol, UK
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