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Klimek P, Ledebur K, Thurner S. Epidemic modelling suggests that in specific circumstances masks may become more effective when fewer contacts wear them. COMMUNICATIONS MEDICINE 2024; 4:134. [PMID: 38971886 PMCID: PMC11227579 DOI: 10.1038/s43856-024-00561-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 06/25/2024] [Indexed: 07/08/2024] Open
Abstract
BACKGROUND The effectiveness of non-pharmaceutical interventions to control the spread of SARS-CoV-2 depends on many contextual factors, including adherence. Conventional wisdom holds that the effectiveness of protective behaviours, such as wearing masks, increases with the number of people who adopt them. Here we show in a simulation study that this is not always true. METHODS We use a parsimonious network model based on the well-established empirical facts that adherence to such interventions wanes over time and that individuals tend to align their adoption strategies with their close social ties (homophily). RESULTS When these assumptions are combined, a broad dynamic regime emerges in which the individual-level reduction in infection risk for those adopting protective behaviour increases as adherence to protective behaviour decreases. For instance, at 10 % coverage, we find that adopters face nearly a 30 % lower infection risk than at 60 % coverage. Based on surgical mask effectiveness estimates, the relative risk reduction for masked individuals ranges from 5 % to 15 %, or a factor of three. This small coverage effect occurs when the outbreak is over before the pathogen is able to invade small but closely knit groups of individuals who protect themselves. CONCLUSIONS Our results confirm that lower coverage reduces protection at the population level while contradicting the common belief that masking becomes ineffective at the individual level as more people drop their masks.
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Affiliation(s)
- Peter Klimek
- Section for Science of Complex Systems, Medical University of Vienna, Vienna, Austria.
- Complexity Science Hub Vienna, Vienna, Austria.
- Supply Chain Intelligence Institute Austria, Vienna, Austria.
- Division of Insurance Medicine, Karolinska Institutet, Stockholm, Sweden.
| | - Katharina Ledebur
- Section for Science of Complex Systems, Medical University of Vienna, Vienna, Austria
- Complexity Science Hub Vienna, Vienna, Austria
| | - Stefan Thurner
- Section for Science of Complex Systems, Medical University of Vienna, Vienna, Austria
- Complexity Science Hub Vienna, Vienna, Austria
- Santa Fe Institute, Santa Fe, NM, USA
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Paltra S, Bostanci I, Nagel K. The effect of mobility reductions on infection growth is quadratic in many cases. Sci Rep 2024; 14:14475. [PMID: 38914583 PMCID: PMC11196635 DOI: 10.1038/s41598-024-64230-1] [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: 02/16/2024] [Accepted: 06/06/2024] [Indexed: 06/26/2024] Open
Abstract
Stay-at-home orders were introduced in many countries during the COVID-19 pandemic, limiting the time people spent outside their home and the attendance of gatherings. In this study, we argue from a theoretical model that in many cases the effect of such stay-at-home orders on incidence growth should be quadratic, and that this statement should also hold beyond COVID-19. That is, a reduction of the out-of-home duration to, say, 70% of its original value should reduce incidence growth and thus the effective R-value to 70 % · 70 % = 49 % of its original value. We then show that this hypothesis can be substantiated from data acquired during the COVID-19 pandemic by using a multiple regression model to fit a combination of the quadratic out-of-home duration and temperature to the COVID-19 growth multiplier. We finally demonstrate that many other models, when brought to the same scale, give similar reductions of the effective R-value, but that none of these models extend plausibly to an out-of-home duration of zero.
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Affiliation(s)
- Sydney Paltra
- Technische Universität Berlin, FG Verkehrssystemplanung und Verkehrstelematik, 10623, Berlin, Germany.
| | | | - Kai Nagel
- Technische Universität Berlin, FG Verkehrssystemplanung und Verkehrstelematik, 10623, Berlin, Germany
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Schmidt PW. Inference under superspreading: Determinants of SARS-CoV-2 transmission in Germany. Stat Med 2024; 43:1933-1954. [PMID: 38422989 DOI: 10.1002/sim.10046] [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: 08/03/2022] [Revised: 01/11/2024] [Accepted: 02/10/2024] [Indexed: 03/02/2024]
Abstract
Superspreading, under-reporting, reporting delay, and confounding complicate statistical inference on determinants of disease transmission. A model that accounts for these factors within a Bayesian framework is estimated using German Covid-19 surveillance data. Compartments based on date of symptom onset, location, and age group allow to identify age-specific changes in transmission, adjusting for weather, reported prevalence, and testing and tracing. Several factors were associated with a reduction in transmission: public awareness rising, information on local prevalence, testing and tracing, high temperature, stay-at-home orders, and restaurant closures. However, substantial uncertainty remains for other interventions including school closures and mandatory face coverings. The challenge of disentangling the effects of different determinants is discussed and examined through a simulation study. On a broader perspective, the study illustrates the potential of surveillance data with demographic information and date of symptom onset to improve inference in the presence of under-reporting and reporting delay.
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Khazaei Y, Küchenhoff H, Hoffmann S, Syliqi D, Rehms R. Using a Bayesian hierarchical approach to study the association between non-pharmaceutical interventions and the spread of Covid-19 in Germany. Sci Rep 2023; 13:18900. [PMID: 37919336 PMCID: PMC10622568 DOI: 10.1038/s41598-023-45950-2] [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: 06/20/2023] [Accepted: 10/26/2023] [Indexed: 11/04/2023] Open
Abstract
Non-Pharmaceutical Interventions (NPIs) are community mitigation strategies, aimed at reducing the spread of illnesses like the coronavirus pandemic, without relying on pharmaceutical drug treatments. This study aims to evaluate the effectiveness of different NPIs across sixteen states of Germany, for a time period of 21 months of the pandemic. We used a Bayesian hierarchical approach that combines different sub-models and merges information from complementary sources, to estimate the true and unknown number of infections. In this framework, we used data on reported cases, hospitalizations, intensive care unit occupancy, and deaths to estimate the effect of NPIs. The list of NPIs includes: "contact restriction (up to 5 people)", "strict contact restriction", "curfew", "events permitted up to 100 people", "mask requirement in shopping malls", "restaurant closure", "restaurants permitted only with test", "school closure" and "general behavioral changes". We found a considerable reduction in the instantaneous reproduction number by "general behavioral changes", "strict contact restriction", "restaurants permitted only with test", "contact restriction (up to 5 people)", "restaurant closure" and "curfew". No association with school closures could be found. This study suggests that some public health measures, including general behavioral changes, strict contact restrictions, and restaurants permitted only with tests are associated with containing the Covid-19 pandemic. Future research is needed to better understand the effectiveness of NPIs in the context of Covid-19 vaccination.
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Affiliation(s)
- Yeganeh Khazaei
- Statistical Consulting Unit StaBLab, Department of Statistics, Ludwig-Maximilians-Universität, Munich, Germany.
| | - Helmut Küchenhoff
- Statistical Consulting Unit StaBLab, Department of Statistics, Ludwig-Maximilians-Universität, Munich, Germany
| | - Sabine Hoffmann
- Department of Statistics, Ludwig-Maximilians-Universität, Munich, Germany
- Institute of Medical Data Processing, Biometrics and Epidemiology (IBE), Faculty of Medicine, Ludwig-Maximilians-Universität, Munich, Germany
| | - Diella Syliqi
- Statistical Consulting Unit StaBLab, Department of Statistics, Ludwig-Maximilians-Universität, Munich, Germany
| | - Raphael Rehms
- Department of Statistics, Ludwig-Maximilians-Universität, Munich, Germany
- Institute of Medical Data Processing, Biometrics and Epidemiology (IBE), Faculty of Medicine, Ludwig-Maximilians-Universität, Munich, Germany
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Wood AJ, Sanchez AR, Bessell PR, Wightman R, Kao RR. Assessing the importance of demographic risk factors across two waves of SARS-CoV-2 using fine-scale case data. PLoS Comput Biol 2023; 19:e1011611. [PMID: 38011282 PMCID: PMC10703279 DOI: 10.1371/journal.pcbi.1011611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2023] [Revised: 12/07/2023] [Accepted: 10/17/2023] [Indexed: 11/29/2023] Open
Abstract
For the long term control of an infectious disease such as COVID-19, it is crucial to identify the most likely individuals to become infected and the role that differences in demographic characteristics play in the observed patterns of infection. As high-volume surveillance winds down, testing data from earlier periods are invaluable for studying risk factors for infection in detail. Observed changes in time during these periods may then inform how stable the pattern will be in the long term. To this end we analyse the distribution of cases of COVID-19 across Scotland in 2021, where the location (census areas of order 500-1,000 residents) and reporting date of cases are known. We consider over 450,000 individually recorded cases, in two infection waves triggered by different lineages: B.1.1.529 ("Omicron") and B.1.617.2 ("Delta"). We use random forests, informed by measures of geography, demography, testing and vaccination. We show that the distributions are only adequately explained when considering multiple explanatory variables, implying that case heterogeneity arose from a combination of individual behaviour, immunity, and testing frequency. Despite differences in virus lineage, time of year, and interventions in place, we find the risk factors remained broadly consistent between the two waves. Many of the observed smaller differences could be reasonably explained by changes in control measures.
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Affiliation(s)
- Anthony J. Wood
- Roslin Institute, University of Edinburgh, Midlothian, United Kingdom
| | - Aeron R. Sanchez
- Roslin Institute, University of Edinburgh, Midlothian, United Kingdom
| | - Paul R. Bessell
- Roslin Institute, University of Edinburgh, Midlothian, United Kingdom
| | - Rebecca Wightman
- Edinburgh Medical School, University of Edinburgh, Edinburgh, United Kingdom
| | - Rowland R. Kao
- Roslin Institute, University of Edinburgh, Midlothian, United Kingdom
- Royal (Dick) School of Veterinary Studies, University of Edinburgh, Midlothian, United Kingdom
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Colston JM, Hinson P, Nguyen NLH, Chen YT, Badr HS, Kerr GH, Gardner LM, Martin DN, Quispe AM, Schiaffino F, Kosek MN, Zaitchik BF. Effects of hydrometeorological and other factors on SARS-CoV-2 reproduction number in three contiguous countries of tropical Andean South America: a spatiotemporally disaggregated time series analysis. IJID REGIONS 2023; 6:29-41. [PMID: 36437857 PMCID: PMC9675637 DOI: 10.1016/j.ijregi.2022.11.007] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Revised: 11/14/2022] [Accepted: 11/15/2022] [Indexed: 06/09/2023]
Abstract
Background The COVID-19 pandemic has caused societal disruption globally, and South America has been hit harder than other lower-income regions. This study modeled the effects of six weather variables on district-level SARS-CoV-2 reproduction numbers (Rt ) in three contiguous countries of tropical Andean South America (Colombia, Ecuador, and Peru), adjusting for environmental, policy, healthcare infrastructural and other factors. Methods Daily time-series data on SARS-CoV-2 infections were sourced from the health authorities of the three countries at the smallest available administrative level. Rt values were calculated and merged by date and unit ID with variables from a unified COVID-19 dataset and other publicly available sources for May-December, 2020. Generalized additive models were fitted. Findings Relative humidity and solar radiation were inversely associated with SARS-CoV-2 Rt . Days with radiation above 1000 kJ/m2 saw a 1.3% reduction in Rt , and those with humidity above 50% recorded a 0.9% reduction in Rt . Transmission was highest in densely populated districts, and lowest in districts with poor healthcare access and on days with lowest population mobility. Wind speed, temperature, region, aggregate government policy response, and population age structure had little impact. The fully adjusted model explained 4.3% of Rt variance. Interpretation Dry atmospheric conditions of low humidity increase district-level SARS-CoV-2 reproduction numbers, while higher levels of solar radiation decrease district-level SARS-CoV-2 reproduction numbers - effects that are comparable in magnitude to population factors like lockdown compliance. Weather monitoring could be incorporated into disease surveillance and early warning systems in conjunction with more established risk indicators and surveillance measures. Funding NASA's Group on Earth Observations Work Programme (16-GEO16-0047).
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Affiliation(s)
- Josh M. Colston
- Division of Infectious Diseases and International Health, University of Virginia School of Medicine, Charlottesville, VA, 22903, USA
| | - Patrick Hinson
- College of Arts and Sciences, University of Virginia, VA, USA
| | | | - Yen Ting Chen
- Department of Emergency Medicine, Chi-Mei Medical Center, Tainan, Taiwan
| | - Hamada S. Badr
- Department of Earth and Planetary Sciences, Johns Hopkins Krieger School of Arts and Sciences, Baltimore, MD, 21218, USA
| | - Gaige H. Kerr
- Department of Environmental and Occupational Health, Milken Institute School of Public Health, George Washington University, Washington, DC, USA
| | - Lauren M. Gardner
- Department of Civil and Systems Engineering, Johns Hopkins University, Baltimore, MD, USA
| | - David N. Martin
- Claude Moore Health Sciences Library, University of Virginia School of Medicine, VA, USA
| | | | - Francesca Schiaffino
- Faculty of Veterinary Medicine, Universidad Peruana Cayetano Heredia, Lima, Peru
- Division of Infectious Diseases and International Health and Public Health Sciences, University of Virginia School of Medicine, Charlottesville, VA, 22903, USA
| | - Margaret N. Kosek
- Division of Infectious Diseases and International Health and Public Health Sciences, University of Virginia School of Medicine, Charlottesville, VA, 22903, USA
| | - Benjamin F. Zaitchik
- Department of Environmental and Occupational Health, Milken Institute School of Public Health, George Washington University, Washington, DC, USA
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Bicher M, Zuba M, Rainer L, Bachner F, Rippinger C, Ostermann H, Popper N, Thurner S, Klimek P. Supporting COVID-19 policy-making with a predictive epidemiological multi-model warning system. COMMUNICATIONS MEDICINE 2022; 2:157. [PMID: 36476987 PMCID: PMC9729177 DOI: 10.1038/s43856-022-00219-z] [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: 06/08/2021] [Accepted: 11/17/2022] [Indexed: 12/13/2022] Open
Abstract
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.
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Affiliation(s)
- Martin Bicher
- grid.5329.d0000 0001 2348 4034Institute of Information Systems Engineering, TU Wien, Favoritenstraße 8-11, A-1040 Vienna, Austria ,dwh simulation services, dwh GmbH, Neustiftgasse 57-59, A-1070 Vienna, Austria
| | - Martin Zuba
- Austrian National Public Health Institute, Stubenring 6, A-1010 Vienna, Austria
| | - Lukas Rainer
- Austrian National Public Health Institute, Stubenring 6, A-1010 Vienna, Austria
| | - Florian Bachner
- Austrian National Public Health Institute, Stubenring 6, A-1010 Vienna, Austria
| | - Claire Rippinger
- dwh simulation services, dwh GmbH, Neustiftgasse 57-59, A-1070 Vienna, Austria
| | - Herwig Ostermann
- Austrian National Public Health Institute, Stubenring 6, A-1010 Vienna, Austria ,grid.41719.3a0000 0000 9734 7019Private University for Health Sciences, Medical Informatics and Technology GmbH, UMIT, Eduard-Wallnöfer-Zentrum 1, A-6060 Hall in Tirol, Austria
| | - Nikolas Popper
- grid.5329.d0000 0001 2348 4034Institute of Information Systems Engineering, TU Wien, Favoritenstraße 8-11, A-1040 Vienna, Austria ,dwh simulation services, dwh GmbH, Neustiftgasse 57-59, A-1070 Vienna, Austria ,Association for Decision Support Policy and Planning, DEXHELPP, Neustiftgasse 57-59, A-1070 Vienna, Austria
| | - Stefan Thurner
- grid.22937.3d0000 0000 9259 8492Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, A-1090 Vienna, Austria ,grid.484678.1Complexity Science Hub Vienna, Josefstädterstraße 39, A-1080 Vienna, Austria ,grid.209665.e0000 0001 1941 1940Santa Fe Institute, 1399 Hyde Park road, Santa Fe, NM 87501 USA
| | - Peter Klimek
- grid.22937.3d0000 0000 9259 8492Section for Science of Complex Systems, Medical University of Vienna, Spitalgasse 23, A-1090 Vienna, Austria ,grid.484678.1Complexity Science Hub Vienna, Josefstädterstraße 39, A-1080 Vienna, Austria
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