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Jang G, Kim J, Lee Y, Son C, Ko KT, Lee H. Analysis of the impact of COVID-19 variants and vaccination on the time-varying reproduction number: statistical methods. Front Public Health 2024; 12:1353441. [PMID: 39022412 PMCID: PMC11253806 DOI: 10.3389/fpubh.2024.1353441] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2023] [Accepted: 06/07/2024] [Indexed: 07/20/2024] Open
Abstract
Introduction The COVID-19 pandemic has profoundly impacted global health systems, requiring the monitoring of infection waves and strategies to control transmission. Estimating the time-varying reproduction number is crucial for understanding the epidemic and guiding interventions. Methods Probability distributions of serial interval are estimated for Pre-Delta and Delta periods. We conducted a comparative analysis of time-varying reproduction numbers, taking into account population immunity and variant differences. We incorporated the regional heterogeneity and age distribution of the population, as well as the evolving variants and vaccination rates over time. COVID-19 transmission dynamics were analyzed with variants and vaccination. Results The reproduction number is computed with and without considering variant-based immunity. In addition, values of reproduction number significantly differed by variants, emphasizing immunity's importance. Enhanced vaccination efforts and stringent control measures were effective in reducing the transmission of the Delta variant. Conversely, Pre-Delta variant appeared less influenced by immunity levels, due to lower vaccination rates. Furthermore, during the Pre-Delta period, there was a significant difference between the region-specific and the non-region-specific reproduction numbers, with particularly distinct pattern differences observed in Gangwon, Gyeongbuk, and Jeju in Korea. Discussion This research elucidates the dynamics of COVID-19 transmission concerning the dominance of the Delta variant, the efficacy of vaccinations, and the influence of immunity levels. It highlights the necessity for targeted interventions and extensive vaccination coverage. This study makes a significant contribution to the understanding of disease transmission mechanisms and informs public health strategies.
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Affiliation(s)
- Geunsoo Jang
- Nonlinear Dynamics and Mathematical Application Center, Kyungpook National University, Daegu, Republic of Korea
| | - Jihyeon Kim
- Department of Statistics, Kyungpook National University, Daegu, Republic of Korea
| | - Yeonsu Lee
- Department of Statistics, Kyungpook National University, Daegu, Republic of Korea
| | - Changdae Son
- Department of Statistics, Kyungpook National University, Daegu, Republic of Korea
| | - Kyeong Tae Ko
- Department of Statistics, Kyungpook National University, Daegu, Republic of Korea
| | - Hyojung Lee
- Department of Statistics, Kyungpook National University, Daegu, Republic of Korea
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von Rhein M, Chaouch A, Oros V, Manzano S, Gualco G, Sidler M, Laasner U, Dey M, Dratva J, Seiler M. The effect of the COVID-19 pandemic on pediatric emergency department utilization in three regions in Switzerland. Int J Emerg Med 2024; 17:64. [PMID: 38755579 PMCID: PMC11097595 DOI: 10.1186/s12245-024-00640-2] [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: 11/22/2023] [Accepted: 05/04/2024] [Indexed: 05/18/2024] Open
Abstract
PURPOSE The COVID-19 pandemic was associated with a decrease in emergency department (ED) visits. However, contradictory, and sparse data regarding children could not yet answer the question, how pediatric ED utilization evolved throughout the pandemic. Our objectives were to investigate the impact of the pandemic in three language regions of Switzerland by analyzing trends over time, describe regional differences, and address implications for future healthcare. METHODS We conducted a retrospective, longitudinal cohort study at three Swiss tertiary pediatric EDs (March 1st, 2018-February 28th, 2022), analyzing the numbers of ED visits (including patients` age, triage categories, and urgent vs. non-urgent cases). The impact of COVID-19 related non-pharmaceutical interventions (NPIs) on pediatric ED utilization was assessed by interrupted time series (ITS) modelling. RESULTS Based on 304'438 ED visits, we found a drop of nearly 50% at the onset of NPIs, followed by a gradual recovery. This primarily affected children 0-4 years, and both non-urgent and urgent cases. However, the decline in urgent visits appeared to be more pronounced in two centers compared to a third, where also hospitalization rates did not decrease significantly during the pandemic. A subgroup analysis showed a significant decrease in respiratory and gastrointestinal diseases, and an increase in the proportion of trauma patients during the pandemic. CONCLUSIONS The COVID-19 pandemic had substantial effects on number and reasons for pediatric ED visits, particularly among children 0-4 years. Despite equal regulatory conditions, the utilization dynamics varied markedly between the three regions, highlighting the multifactorial modification of pediatric ED utilization during the pandemic. Furthermore, future policy decisions should take regional differences into account.
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Affiliation(s)
- Michael von Rhein
- Child Development Center, University Children`s Hospital Zurich, University of Zurich, Zurich, Switzerland.
| | - Aziz Chaouch
- Department of Epidemiology and Health Systems, Center for Primary Care and Public Health (Unisanté), University of Lausanne, Lausanne, Switzerland
| | - Vivian Oros
- University Children`S Hospital Zurich, University of Zurich, Zurich, Switzerland
| | - Sergio Manzano
- Pediatric Emergency Department, Geneva University Hospitals, University of Geneva, Geneva, Switzerland
| | - Gianluca Gualco
- Pediatric Emergency Departement, Clinics of Pediatrics, Institute of Pediatrics of Southern Switzerland, EOC, Bellinzona, Switzerland
| | | | | | - Michelle Dey
- School of Health Science, ZHAW Zurich University of Applied Sciences, Winterthur, Switzerland
| | - Julia Dratva
- School of Health Science, ZHAW Zurich University of Applied Sciences, Winterthur, Switzerland
- Medical Faculty, University of Basel, Basel, Switzerland
| | - Michelle Seiler
- Pediatric Emergency Department, University Children`S Hospital Zurich, University of Zurich, Zurich, Switzerland
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Corradi-Dell'Acqua C, Horisberger G, Caillet-Bois D, Toraldo A, Christ M, Santa VD, Frochaux V, Mols P, Penaloza A, Rezzonico S, Tagliabue L, Hugli O. Perceived Hospital Preparedness Is Negatively Associated With Pandemic-Induced Psychological Vulnerability in Primary Care Employees: A Multicentre Cross-Sectional Observational Study. Clin Psychol Psychother 2024; 31:e2969. [PMID: 38600791 DOI: 10.1002/cpp.2969] [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: 07/03/2023] [Revised: 03/01/2024] [Accepted: 03/04/2024] [Indexed: 04/12/2024]
Abstract
OBJECTIVE The COVID-19 pandemic had a profound negative impact on the psychological wellbeing of healthcare providers (HPs), but little is known about the factors that positively predict mental health of primary care staff during these dire situations. METHODS We conducted an online questionnaire survey among 702 emergency department workers across 10 hospitals in Switzerland and Belgium following the first COVID-19 wave in 2020, to explore their psychological vulnerability, perceived concerns, self-reported impact and level of pandemic workplace preparedness. Participants included physicians, nurses, psychologists and nondirect care employees (administrative staff). We tested for predictors of psychological vulnerability through both an exploratory cross-correlation with rigorous correction for multiple comparisons and model-based path modelling. RESULTS Findings showed that the self-reported impact of COVID-19 at work, concerns about contracting COVID-19 at work, and a lack of personal protective equipment were strong positive predictors of Depression, Anxiety, and Stress, and low Resilience. Instead, knowledge of the degree of preparedness of the hospital/department, especially in the presence of a predetermined contingency plan for an epidemic and training sessions about protective measures, showed the opposite effect, and were associated with lower psychological vulnerability. All effects were confirmed after accounting for confounding factors related to gender, age, geographical location and the role played by HPs in the hospital/department. CONCLUSIONS Difficult working conditions during the pandemic had a major impact on the psychological wellbeing of emergency department HPs, but this effect might have been lessened if they had been informed about adequate measures for minimizing the risk of exposure.
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Affiliation(s)
- Corrado Corradi-Dell'Acqua
- Center for Mind/Brain Sciences (CIMeC), University of Trento, Trento, Italy
- Faculty of Psychology and Educational Sciences, University of Geneva, Geneva, Switzerland
| | - Garance Horisberger
- Faculty of Biology and Medicine, University of Lausanne, Lausanne, Switzerland
| | - David Caillet-Bois
- Emergency Department, University Hospital of Lausanne, Lausanne, Switzerland
| | - Alessio Toraldo
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
- Milan Center for Neuroscience (NeuroMI), Milan, Italy
| | - Michael Christ
- Emergency Department, Kantonsspital Luzern, Luzern, Switzerland
| | - Vincent Della Santa
- Emergency Department, Réseau hospitalier neuchâtelois, Neuchâtel, Switzerland
| | | | - Pierre Mols
- Emergency Department, St. Pierre University Hospital, Université Libre de Bruxelles, Brussels, Belgium
| | - Andrea Penaloza
- Emergency Department, Cliniques Universitaires Saint-Luc, Université Catholique de Louvain, Brussels, Belgium
| | - Sara Rezzonico
- Emergency Department, Faculty of Biology and Medicine, Bellinzona Hospital, Bellinzona, Switzerland
| | - Luca Tagliabue
- Emergency Department, Faculty of Biology and Medicine, Bellinzona Hospital, Bellinzona, Switzerland
| | - Olivier Hugli
- Faculty of Biology and Medicine, University of Lausanne, Lausanne, Switzerland
- Emergency Department, University Hospital of Lausanne, Lausanne, Switzerland
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Vaughan TG, Scire J, Nadeau SA, Stadler T. Estimates of early outbreak-specific SARS-CoV-2 epidemiological parameters from genomic data. Proc Natl Acad Sci U S A 2024; 121:e2308125121. [PMID: 38175864 PMCID: PMC10786264 DOI: 10.1073/pnas.2308125121] [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: 05/15/2023] [Accepted: 12/02/2023] [Indexed: 01/06/2024] Open
Abstract
We estimate the basic reproductive number and case counts for 15 distinct Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) outbreaks, distributed across 11 populations (10 countries and one cruise ship), based solely on phylodynamic analyses of genomic data. Our results indicate that, prior to significant public health interventions, the reproductive numbers for 10 (out of 15) of these outbreaks are similar, with median posterior estimates ranging between 1.4 and 2.8. These estimates provide a view which is complementary to that provided by those based on traditional line listing data. The genomic-based view is arguably less susceptible to biases resulting from differences in testing protocols, testing intensity, and import of cases into the community of interest. In the analyses reported here, the genomic data primarily provide information regarding which samples belong to a particular outbreak. We observe that once these outbreaks are identified, the sampling dates carry the majority of the information regarding the reproductive number. Finally, we provide genome-based estimates of the cumulative number of infections for each outbreak. For 7 out of 11 of the populations studied, the number of confirmed cases is much bigger than the cumulative number of infections estimated from the sequence data, a possible explanation being the presence of unsequenced outbreaks in these populations.
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Affiliation(s)
- Timothy G. Vaughan
- Department of Biosystems Science and Engineering, Eidgenössiche Technische Hochschule Zurich, Basel4058, Switzerland
- Computational Evolution Group, Swiss Institute of Bioinformatics, Lausanne1015, Switzerland
| | - Jérémie Scire
- Department of Biosystems Science and Engineering, Eidgenössiche Technische Hochschule Zurich, Basel4058, Switzerland
- Computational Evolution Group, Swiss Institute of Bioinformatics, Lausanne1015, Switzerland
| | - Sarah A. Nadeau
- Department of Biosystems Science and Engineering, Eidgenössiche Technische Hochschule Zurich, Basel4058, Switzerland
- Computational Evolution Group, Swiss Institute of Bioinformatics, Lausanne1015, Switzerland
| | - Tanja Stadler
- Department of Biosystems Science and Engineering, Eidgenössiche Technische Hochschule Zurich, Basel4058, Switzerland
- Computational Evolution Group, Swiss Institute of Bioinformatics, Lausanne1015, Switzerland
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Bonaldi C, Fouillet A, Sommen C, Lévy-Bruhl D, Paireau J. Monitoring the reproductive number of COVID-19 in France: Comparative estimates from three datasets. PLoS One 2023; 18:e0293585. [PMID: 37906577 PMCID: PMC10617725 DOI: 10.1371/journal.pone.0293585] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Accepted: 10/17/2023] [Indexed: 11/02/2023] Open
Abstract
BACKGROUND The effective reproduction number (Rt) quantifies the average number of secondary cases caused by one person with an infectious disease. Near-real-time monitoring of Rt during an outbreak is a major indicator used to monitor changes in disease transmission and assess the effectiveness of interventions. The estimation of Rt usually requires the identification of infected cases in the population, which can prove challenging with the available data, especially when asymptomatic people or with mild symptoms are not usually screened. The purpose of this study was to perform sensitivity analysis of Rt estimates for COVID-19 surveillance in France based on three data sources with different sensitivities and specificities for identifying infected cases. METHODS We applied a statistical method developed by Cori et al. to estimate Rt using (1) confirmed cases identified from positive virological tests in the population, (2) suspected cases recorded by a national network of emergency departments, and (3) COVID-19 hospital admissions recorded by a national administrative system to manage hospital organization. RESULTS Rt estimates in France from May 27, 2020, to August 12, 2022, showed similar temporal trends regardless of the dataset. Estimates based on the daily number of confirmed cases provided an earlier signal than the two other sources, with an average lag of 3 and 6 days for estimates based on emergency department visits and hospital admissions, respectively. CONCLUSION The COVID-19 experience confirmed that monitoring temporal changes in Rt was a key indicator to help the public health authorities control the outbreak in real time. However, gaining access to data on all infected people in the population in order to estimate Rt is not straightforward in practice. As this analysis has shown, the opportunity to use more readily available data to estimate Rt trends, provided that it is highly correlated with the spread of infection, provides a practical solution for monitoring the COVID-19 pandemic and indeed any other epidemic.
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Affiliation(s)
- Christophe Bonaldi
- Data Science Division, Santé Publique France, The French Public Health Agency, Saint Maurice, France
| | - Anne Fouillet
- Data Science Division, Santé Publique France, The French Public Health Agency, Saint Maurice, France
| | - Cécile Sommen
- Data Science Division, Santé Publique France, The French Public Health Agency, Saint Maurice, France
| | - Daniel Lévy-Bruhl
- Infectious Diseases Division, Santé Publique France, The French Public Health Agency, Saint Maurice, France
| | - Juliette Paireau
- Infectious Diseases Division, Santé Publique France, The French Public Health Agency, Saint Maurice, France
- Mathematical Modelling of Infectious Diseases Unit, Institut Pasteur, Université de Paris Cité, CNRS UMR 2000, Paris, France
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Scire J, Huisman JS, Grosu A, Angst DC, Lison A, Li J, Maathuis MH, Bonhoeffer S, Stadler T. estimateR: an R package to estimate and monitor the effective reproductive number. BMC Bioinformatics 2023; 24:310. [PMID: 37568078 PMCID: PMC10416499 DOI: 10.1186/s12859-023-05428-4] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2022] [Accepted: 07/24/2023] [Indexed: 08/13/2023] Open
Abstract
BACKGROUND Accurate estimation of the effective reproductive number ([Formula: see text]) of epidemic outbreaks is of central relevance to public health policy and decision making. We present estimateR, an R package for the estimation of the reproductive number through time from delayed observations of infection events. Such delayed observations include confirmed cases, hospitalizations or deaths. The package implements the methodology of Huisman et al. but modularizes the [Formula: see text] estimation procedure to allow easy implementation of new alternatives to the currently available methods. Users can tailor their analyses according to their particular use case by choosing among implemented options. RESULTS The estimateR R package allows users to estimate the effective reproductive number of an epidemic outbreak based on observed cases, hospitalization, death or any other type of event documenting past infections, in a fast and timely fashion. We validated the implementation with a simulation study: estimateR yielded estimates comparable to alternative publicly available methods while being around two orders of magnitude faster. We then applied estimateR to empirical case-confirmation incidence data for COVID-19 in nine countries and for dengue fever in Brazil; in parallel, estimateR is already being applied (i) to SARS-CoV-2 measurements in wastewater data and (ii) to study influenza transmission based on wastewater and clinical data in other studies. In summary, this R package provides a fast and flexible implementation to estimate the effective reproductive number for various diseases and datasets. CONCLUSIONS The estimateR R package is a modular and extendable tool designed for outbreak surveillance and retrospective outbreak investigation. It extends the method developed for COVID-19 by Huisman et al. and makes it available for a variety of pathogens, outbreak scenarios, and observation types. Estimates obtained with estimateR can be interpreted directly or used to inform more complex epidemic models (e.g. for forecasting) on the value of [Formula: see text].
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Affiliation(s)
- Jérémie Scire
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland.
- Swiss Institute of Bioinformatics, Lausanne, Switzerland.
| | - Jana S Huisman
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland
- Swiss Institute of Bioinformatics, Lausanne, Switzerland
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
- Department of Physics, Massachusetts Institute of Technology, Cambridge, USA
| | - Ana Grosu
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland
| | - Daniel C Angst
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Adrian Lison
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland
| | - Jinzhou Li
- Department of Mathematics, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Marloes H Maathuis
- Department of Mathematics, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Sebastian Bonhoeffer
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Tanja Stadler
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland.
- Swiss Institute of Bioinformatics, Lausanne, Switzerland.
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SARS-CoV-2 Seroprevalence in Employees of Four Essential Non-Health Care Sectors at Moderate/High Risk of Exposure to Coronavirus Infection: Data From the "First Wave". J Occup Environ Med 2023; 65:10-15. [PMID: 36094075 PMCID: PMC9835238 DOI: 10.1097/jom.0000000000002690] [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] [Indexed: 01/22/2023]
Abstract
OBJECTIVE The aim of this study was to evaluate severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) seroprevalence in Swiss non-health care employees at a moderate to high risk of exposure: bus drivers and supermarket, laundry service, and mail-sorting center employees. METHODS Data on 455 essential workers included demographics, SARS-CoV-2 exposure and use of protective measures. Anti-SARS-CoV-2 immunoglobulins G and A targeting the spike protein were measured between May and July 2020. RESULTS The overall crude seroprevalence estimate (15.9%; 95% confidence interval [CI], 12.6% to 19.7%) among essential workers was not significantly higher than that of the general working-age population (11.2%; 95% CI, 7.1% to 15.2%). Seroprevalence ranged from 11.9% (95% CI, 6.3% to 19.8%) among bus drivers to 22.0% (95% CI, 12.6% to 19.7%) among food supermarket employees. CONCLUSIONS We found no significant difference in seroprevalence between our sample of essential workers and local working-age population during the first lockdown phase of the COVID-19 pandemic. Having a seropositive housemate was the strongest predictor of SARS-CoV-2 seropositivity.
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Rickards CG, Kilpatrick AM. Age-specific SARS-CoV-2 infection fatality rates derived from serological data vary with income and income inequality. PLoS One 2023; 18:e0285612. [PMID: 37196049 DOI: 10.1371/journal.pone.0285612] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Accepted: 04/26/2023] [Indexed: 05/19/2023] Open
Abstract
The ongoing COVID-19 pandemic has killed at least 1.1 million people in the United States and over 6.7 million globally. Accurately estimating the age-specific infection fatality rate (IFR) of SARS-CoV-2 for different populations is crucial for assessing and understanding the impact of COVID-19 and for appropriately allocating vaccines and treatments to at-risk groups. We estimated age-specific IFRs of wild-type SARS-CoV-2 using published seroprevalence, case, and death data from New York City (NYC) from March to May 2020, using a Bayesian framework that accounted for delays between key epidemiological events. IFRs increased 3-4-fold with every 20 years of age, from 0.06% in individuals between 18-45 years old to 4.7% in individuals over 75. We then compared IFRs in NYC to several city- and country-wide estimates including England, Switzerland (Geneva), Sweden (Stockholm), Belgium, Mexico, and Brazil, as well as a global estimate. IFRs in NYC were higher for individuals younger than 65 years old than most other populations, but similar for older individuals. IFRs for age groups less than 65 decreased with income and increased with income inequality measured using the Gini index. These results demonstrate that the age-specific fatality of COVID-19 differs among developed countries and raises questions about factors underlying these differences, including underlying health conditions and healthcare access.
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Affiliation(s)
- Chloe G Rickards
- Department of Ecology and Evolutionary Biology, University of California Santa Cruz, Santa Cruz, CA, United States of America
| | - A Marm Kilpatrick
- Department of Ecology and Evolutionary Biology, University of California Santa Cruz, Santa Cruz, CA, United States of America
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Huisman JS, Scire J, Angst DC, Li J, Neher RA, Maathuis MH, Bonhoeffer S, Stadler T. Estimation and worldwide monitoring of the effective reproductive number of SARS-CoV-2. eLife 2022; 11:71345. [PMID: 35938911 DOI: 10.1101/2020.11.26.20239368] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 07/01/2022] [Indexed: 05/28/2023] Open
Abstract
The effective reproductive number Re is a key indicator of the growth of an epidemic. Since the start of the SARS-CoV-2 pandemic, many methods and online dashboards have sprung up to monitor this number through time. However, these methods are not always thoroughly tested, correctly placed in time, or are overly confident during high incidence periods. Here, we present a method for timely estimation of Re, applied to COVID-19 epidemic data from 170 countries. We thoroughly evaluate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that, in early 2020, in the majority of countries the estimated Re dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe the implementation of non-pharmaceutical interventions was broadly associated with reductions in the estimated Re. Globally though, relaxing non-pharmaceutical interventions had more varied effects on subsequent Re estimates. Our framework is useful to inform governments and the general public on the status of epidemics in their country, and is used as the official source of Re estimates for SARS-CoV-2 in Switzerland. It further allows detailed comparison between countries and in relation to covariates such as implemented public health policies, mobility, behaviour, or weather data.
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Affiliation(s)
- Jana S Huisman
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
- Swiss Institute of Bioinformatics, Lausanne, Switzerland
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland
| | - Jérémie Scire
- Swiss Institute of Bioinformatics, Lausanne, Switzerland
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland
| | - Daniel C Angst
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Jinzhou Li
- Department of Mathematics, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Richard A Neher
- Swiss Institute of Bioinformatics, Lausanne, Switzerland
- Biozentrum, University of Basel, Basel, Switzerland
| | - Marloes H Maathuis
- Department of Mathematics, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Sebastian Bonhoeffer
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of Technology, Zurich, Switzerland
| | - Tanja Stadler
- Swiss Institute of Bioinformatics, Lausanne, Switzerland
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of Technology, Basel, Switzerland
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Huisman JS, Scire J, Angst DC, Li J, Neher RA, Maathuis MH, Bonhoeffer S, Stadler T. Estimation and worldwide monitoring of the effective reproductive number of SARS-CoV-2. eLife 2022; 11:e71345. [PMID: 35938911 PMCID: PMC9467515 DOI: 10.7554/elife.71345] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 07/01/2022] [Indexed: 11/20/2022] Open
Abstract
The effective reproductive number Re is a key indicator of the growth of an epidemic. Since the start of the SARS-CoV-2 pandemic, many methods and online dashboards have sprung up to monitor this number through time. However, these methods are not always thoroughly tested, correctly placed in time, or are overly confident during high incidence periods. Here, we present a method for timely estimation of Re, applied to COVID-19 epidemic data from 170 countries. We thoroughly evaluate the method on simulated data, and present an intuitive web interface for interactive data exploration. We show that, in early 2020, in the majority of countries the estimated Re dropped below 1 only after the introduction of major non-pharmaceutical interventions. For Europe the implementation of non-pharmaceutical interventions was broadly associated with reductions in the estimated Re. Globally though, relaxing non-pharmaceutical interventions had more varied effects on subsequent Re estimates. Our framework is useful to inform governments and the general public on the status of epidemics in their country, and is used as the official source of Re estimates for SARS-CoV-2 in Switzerland. It further allows detailed comparison between countries and in relation to covariates such as implemented public health policies, mobility, behaviour, or weather data.
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Affiliation(s)
- Jana S Huisman
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of TechnologyZurichSwitzerland
- Swiss Institute of BioinformaticsLausanneSwitzerland
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of TechnologyBaselSwitzerland
| | - Jérémie Scire
- Swiss Institute of BioinformaticsLausanneSwitzerland
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of TechnologyBaselSwitzerland
| | - Daniel C Angst
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of TechnologyZurichSwitzerland
| | - Jinzhou Li
- Department of Mathematics, ETH Zurich, Swiss Federal Institute of TechnologyZurichSwitzerland
| | - Richard A Neher
- Swiss Institute of BioinformaticsLausanneSwitzerland
- Biozentrum, University of BaselBaselSwitzerland
| | - Marloes H Maathuis
- Department of Mathematics, ETH Zurich, Swiss Federal Institute of TechnologyZurichSwitzerland
| | - Sebastian Bonhoeffer
- Department of Environmental Systems Science, ETH Zurich, Swiss Federal Institute of TechnologyZurichSwitzerland
| | - Tanja Stadler
- Swiss Institute of BioinformaticsLausanneSwitzerland
- Department of Biosystems Science and Engineering, ETH Zurich, Swiss Federal Institute of TechnologyBaselSwitzerland
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Griette Q, Demongeot J, Magal P. What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases? MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:537-594. [PMID: 34903002 DOI: 10.3934/mbe.2022025] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The COVID-19 outbreak, which started in late December 2019 and rapidly spread around the world, has been accompanied by an unprecedented release of data on reported cases. Our objective is to offer a fresh look at these data by coupling a phenomenological description to the epidemiological dynamics. We use a phenomenological model to describe and regularize the reported cases data. This phenomenological model is combined with an epidemic model having a time-dependent transmission rate. The time-dependent rate of transmission involves changes in social interactions between people as well as changes in host-pathogen interactions. Our method is applied to cumulative data of reported cases for eight different geographic areas. In the eight geographic areas considered, successive epidemic waves are matched with a phenomenological model and are connected to each other. We find a single epidemic model that coincides with the best fit to the data of the phenomenological model. By reconstructing the transmission rate from the data, we can understand the contributions of the changes in social interactions (contacts between individuals) on the one hand and the contributions of the epidemiological dynamics on the other hand. Our study provides a new method to compute the instantaneous reproduction number that turns out to stay below 3.5 from the early beginning of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important factor in understanding the epidemic wave dynamics for COVID-19. The instantaneous reproduction number stays below 3.5, which implies that it is sufficient to vaccinate 71% of the population in each state or country considered in our study. Therefore, assuming the vaccines will remain efficient against the new variants and adjusting for higher confidence, it is sufficient to vaccinate 75-80% to eliminate COVID-19 in each state or country.
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Affiliation(s)
- Quentin Griette
- Université de Bordeaux, IMB, UMR 5251, Talence F-33400, France CNRS, IMB, UMR 5251, Talence F-33400, France
| | | | - Pierre Magal
- Université de Bordeaux, IMB, UMR 5251, Talence F-33400, France CNRS, IMB, UMR 5251, Talence F-33400, France
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12
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Gorji H, Arnoldini M, Jenny DF, Hardt WD, Jenny P. Smart investment of virus RNA testing resources to enhance Covid-19 mitigation. PLoS One 2021; 16:e0259018. [PMID: 34847176 PMCID: PMC8631684 DOI: 10.1371/journal.pone.0259018] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 10/11/2021] [Indexed: 01/12/2023] Open
Abstract
A variety of mitigation strategies have been employed against the Covid-19 pandemic. Social distancing is still one of the main methods to reduce spread, but it entails a high toll on personal freedom and economic life. Alternative mitigation strategies that do not come with the same problems but are effective at preventing disease spread are therefore needed. Repetitive mass-testing using PCR assays for viral RNA has been suggested, but as a stand-alone strategy this would be prohibitively resource intensive. Here, we suggest a strategy that aims at targeting the limited resources available for viral RNA testing to subgroups that are more likely than the average population to yield a positive test result. Importantly, these pre-selected subgroups include symptom-free people. By testing everyone in these subgroups, in addition to symptomatic cases, large fractions of pre- and asymptomatic people can be identified, which is only possible by testing-based mitigation. We call this strategy smart testing (ST). In principle, pre-selected subgroups can be found in different ways, but for the purpose of this study we analyze a pre-selection procedure based on cheap and fast virus antigen tests. We quantify the potential reduction of the epidemic reproduction number by such a two-stage ST strategy. In addition to a scenario where such a strategy is available to the whole population, we analyze local applications, e.g. in a country, company, or school, where the tested subgroups are also in exchange with the untested population. Our results suggest that a two-stage ST strategy can be effective to curb pandemic spread, at costs that are clearly outweighed by the economic benefit. It is technically and logistically feasible to employ such a strategy, and our model predicts that it is even effective when applied only within local groups. We therefore recommend adding two-stage ST to the portfolio of available mitigation strategies, which allow easing social distancing measures without compromising public health.
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Affiliation(s)
- Hossein Gorji
- Laboratory of Multiscale Studies in Building Physics, Empa, Dübendorf, Switzerland
| | - Markus Arnoldini
- Department of Health Sciences and Technology, Swiss Federal Institute of Technology, Zürich, Switzerland
| | - David F. Jenny
- Department of Mathematics, Swiss Federal Institute of Technology, Zürich, Switzerland
| | - Wolf-Dietrich Hardt
- Institute of Microbiology, D-BIOL, Swiss Federal Institute of Technology, Zürich, Switzerland
| | - Patrick Jenny
- Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology, IFD, Zürich, Switzerland
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13
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Abstract
(1) Background: The estimation of daily reproduction numbers throughout the contagiousness period is rarely considered, and only their sum R0 is calculated to quantify the contagiousness level of an infectious disease. (2) Methods: We provide the equation of the discrete dynamics of the epidemic’s growth and obtain an estimation of the daily reproduction numbers by using a deconvolution technique on a series of new COVID-19 cases. (3) Results: We provide both simulation results and estimations for several countries and waves of the COVID-19 outbreak. (4) Discussion: We discuss the role of noise on the stability of the epidemic’s dynamics. (5) Conclusions: We consider the possibility of improving the estimation of the distribution of daily reproduction numbers during the contagiousness period by taking into account the heterogeneity due to several host age classes.
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14
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Nawaz SA, Li J, Bhatti UA, Bazai SU, Zafar A, Bhatti MA, Mehmood A, Ain QU, Shoukat MU. A hybrid approach to forecast the COVID-19 epidemic trend. PLoS One 2021; 16:e0256971. [PMID: 34606503 PMCID: PMC8489714 DOI: 10.1371/journal.pone.0256971] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 08/19/2021] [Indexed: 12/02/2022] Open
Abstract
Studying the progress and trend of the novel coronavirus pneumonia (COVID-19) transmission mode will help effectively curb its spread. Some commonly used infectious disease prediction models are introduced. The hybrid model is proposed, which overcomes the disadvantages of the logistic model's inability to predict the number of confirmed diagnoses and the drawbacks of too many tuning parameters of the SEIR (Susceptible, Exposed, Infectious, Recovered) model. The realization and superiority of the prediction of the proposed model are proven through experiments. At the same time, the influence of different initial values of the parameters that need to be debugged on the hybrid model is further studied, and the mean error is used to quantify the prediction effect. By forecasting epidemic size and peak time and simulating the effects of public health interventions, this paper aims to clarify the transmission dynamics of COVID-19 and recommend operation suggestions to slow down the epidemic. It is suggested that the quick detection of cases, sufficient implementation of quarantine and public self-protection behaviours are critical to slow down the epidemic.
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Affiliation(s)
- Saqib Ali Nawaz
- College of Information and Communication Engineering, Hainan University, Haikou, China
- State Key Laboratory of Marine Resource Utilization in the South China Sea, Hainan University, Haikou, China
| | - Jingbing Li
- College of Information and Communication Engineering, Hainan University, Haikou, China
- State Key Laboratory of Marine Resource Utilization in the South China Sea, Hainan University, Haikou, China
| | - Uzair Aslam Bhatti
- School of Geography (Remote Sensing), Nanjing Normal University, Nanjing, Jiangsu, China
| | | | - Asmat Zafar
- General Nursing College DHQ Hospital, Jhang, Pakistan
| | - Mughair Aslam Bhatti
- School of Geography (Remote Sensing), Nanjing Normal University, Nanjing, Jiangsu, China
| | - Anum Mehmood
- Medical School of Southeast University, Nanjing, P.R. China
| | - Qurat ul Ain
- School of Geography (Remote Sensing), Nanjing Normal University, Nanjing, Jiangsu, China
| | - Muhammad Usman Shoukat
- School of Automation and Information, Sichuan University of Science and Engineering, Yibin, China
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15
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Radev ST, Graw F, Chen S, Mutters NT, Eichel VM, Bärnighausen T, Köthe U. OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany. PLoS Comput Biol 2021; 17:e1009472. [PMID: 34695111 PMCID: PMC8584772 DOI: 10.1371/journal.pcbi.1009472] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2021] [Revised: 11/11/2021] [Accepted: 09/23/2021] [Indexed: 01/08/2023] Open
Abstract
Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and interventional measures during an ongoing outbreak. However, reliably inferring the epidemical dynamics by connecting complex models to real data is still hard and requires either laborious manual parameter fitting or expensive optimization methods which have to be repeated from scratch for every application of a given model. In this work, we address this problem with a novel combination of epidemiological modeling with specialized neural networks. Our approach entails two computational phases: In an initial training phase, a mathematical model describing the epidemic is used as a coach for a neural network, which acquires global knowledge about the full range of possible disease dynamics. In the subsequent inference phase, the trained neural network processes the observed data of an actual outbreak and infers the parameters of the model in order to realistically reproduce the observed dynamics and reliably predict future progression. With its flexible framework, our simulation-based approach is applicable to a variety of epidemiological models. Moreover, since our method is fully Bayesian, it is designed to incorporate all available prior knowledge about plausible parameter values and returns complete joint posterior distributions over these parameters. Application of our method to the early Covid-19 outbreak phase in Germany demonstrates that we are able to obtain reliable probabilistic estimates for important disease characteristics, such as generation time, fraction of undetected infections, likelihood of transmission before symptom onset, and reporting delays using a very moderate amount of real-world observations.
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Affiliation(s)
- Stefan T. Radev
- Institute of Psychology, Heidelberg University, Heidelberg, Germany
| | - Frederik Graw
- BioQuant - Center for Quantitative Biology, Heidelberg University, Heidelberg, Germany
| | - Simiao Chen
- Heidelberg Institute of Global Health, Heidelberg, Germany
- Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing, China
| | - Nico T. Mutters
- Institute for Hygiene and Public Health, University Hospital Bonn, Bonn, Germany
| | - Vanessa M. Eichel
- Center of Infectious Diseases, University Hospital Heidelberg, Heidelberg, Germany
| | - Till Bärnighausen
- Heidelberg Institute of Global Health, Heidelberg, Germany
- Harvard T.H. Chan School of Public Health, Boston, Massachusetts, United States of America
- Africa Health Research Institute, Durban, South Africa
| | - Ullrich Köthe
- Computer Vision and Learning Lab, Heidelberg University, Heidelberg, Germany
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16
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A simple method to describe the COVID-19 trajectory and dynamics in any country based on Johnson cumulative density function fitting. Sci Rep 2021; 11:17744. [PMID: 34493760 PMCID: PMC8423734 DOI: 10.1038/s41598-021-97285-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Accepted: 08/20/2021] [Indexed: 11/26/2022] Open
Abstract
A simple method is utilised to study and compare COVID-19 infection dynamics between countries based on curve fitting to publicly shared data of confirmed COVID-19 infections. The method was tested using data from 80 countries from 6 continents. We found that Johnson cumulative density functions (CDFs) were extremely well fitted to the data (R2 > 0.99) and that Johnson CDFs were much better fitted to the tails of the data than either the commonly used normal or lognormal CDFs. Fitted Johnson CDFs can be used to obtain basic parameters of the infection wave, such as the percentage of the population infected during an infection wave, the days of the start, peak and end of the infection wave, and the duration of the wave’s increase and decrease. These parameters can be easily interpreted biologically and used both for describing infection wave dynamics and in further statistical analysis. The usefulness of the parameters obtained was analysed with respect to the relation between the gross domestic product (GDP) per capita, the population density, the percentage of the population infected during an infection wave, the starting day and the duration of the infection wave in the 80 countries. We found that all the above parameters were significantly associated with GDP per capita, but only the percentage of the population infected was significantly associated with population density. If used with caution, this method has a limited ability to predict the future trajectory and parameters of an ongoing infection wave.
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17
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Righolt CH, Zhang G, Sever E, Wilkinson K, Mahmud SM. Patterns and descriptors of COVID-19 testing and lab-confirmed COVID-19 incidence in Manitoba, Canada, March 2020-May 2021: A population-based study. ACTA ACUST UNITED AC 2021; 2:100038. [PMID: 34409400 PMCID: PMC8360706 DOI: 10.1016/j.lana.2021.100038] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Revised: 07/27/2021] [Accepted: 07/27/2021] [Indexed: 11/20/2022]
Abstract
Background We studied lab-confirmed COVID-19 infection (LCCI) testing, incidence, and severity. Methods We included all Manitoba residents and limited our severity analysis to LCCI patients. We calculated testing, incidence and vaccination rates between March 8, 2020 and June 1, 2021. We estimated the association between patient characteristics and testing (rate ratio [RR]; Poisson regression), including the reason for testing (screening, symptomatic, contact/outbreak asymptomatic), incidence (hazard ratio [HR]; Cox regression), and severity (prevalence ratio [PR], Cox regression). Findings The overall testing rate during the second/third wave was 570/1,000 person-years, with an LCCI rate of 50/1,000 person-years. The secondary attack rate during the second/third wave was 16%. Across regions, young children (<10) had the lowest positivity for symptomatic testing, the highest positivity for asymptomatic testing, and the highest risk of LCCI as asymptomatic contact. People in the lowest income quintile had the highest risk of LCCI, 1.3-6x the hazard of those in the highest income quintile. Long-term care (LTC) residents were particularly affected in the second wave with HRs>10 for asymptomatic residents. Interpretation Although the severity of LCCI in children was low, they have a high risk of asymptomatic positivity. The groups most vulnerable to LCCI, who should remain a focus of public health, were residents of Manitoba's North, LTC facilities, and low-income neighbourhoods. Funding Canada Research Chair Program
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Affiliation(s)
| | | | | | | | - Salaheddin M. Mahmud
- Correspondence Author: Dr. Salaheddin Mahmud, MD PhD FRCPC, Professor and Director, Vaccine and Drug Evaluation Centre, Department of Community Health Sciences, University of Manitoba, 337 - 750 McDermot Avenue, Winnipeg, Manitoba, R3E 0T5 Canada
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18
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Deopa N, Fortunato P. Coronagraben in Switzerland: culture and social distancing in times of COVID-19. JOURNAL OF POPULATION ECONOMICS 2021; 34:1355-1383. [PMID: 34334956 PMCID: PMC8315728 DOI: 10.1007/s00148-021-00865-y] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 06/25/2021] [Indexed: 05/20/2023]
Abstract
Social distancing measures help contain the spread of COVID-19, but actual compliance has varied substantially across space and time. We ask whether cultural differences underlie this heterogeneity using mobility data across Switzerland between February and December 2020. We find that German-speaking cantons decreased their mobility for non-essential activities significantly less than French-speaking cantons. However, we find no such significant differences for bilingual cantons. Contrary to the evidence in the literature, we find that within the Swiss context, high trusting areas exhibited a smaller decline in mobility. Additionally, cantons supporting a limited role of the state in matters of welfare also experienced a smaller reduction in mobility.
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Affiliation(s)
- Neha Deopa
- The Graduate Institute of International and Development Studies, Geneva, Switzerland
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19
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Davahli MR, Karwowski W, Fiok K. Optimizing COVID-19 vaccine distribution across the United States using deterministic and stochastic recurrent neural networks. PLoS One 2021; 16:e0253925. [PMID: 34228740 PMCID: PMC8259963 DOI: 10.1371/journal.pone.0253925] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2020] [Accepted: 06/15/2021] [Indexed: 11/18/2022] Open
Abstract
Optimizing COVID-19 vaccine distribution can help plan around the limited production and distribution of vaccination, particularly in early stages. One of the main criteria for equitable vaccine distribution is predicting the geographic distribution of active virus at the time of vaccination. This research developed sequence-learning models to predict the behavior of the COVID-19 pandemic across the US, based on previously reported information. For this objective, we used two time-series datasets of confirmed COVID-19 cases and COVID-19 effective reproduction numbers from January 22, 2020 to November 26, 2020 for all states in the US. The datasets have 310 time-steps (days) and 50 features (US states). To avoid training the models for all states, we categorized US states on the basis of their similarity to previously reported COVID-19 behavior. For this purpose, we used an unsupervised self-organizing map to categorize all states of the US into four groups on the basis of the similarity of their effective reproduction numbers. After selecting a leading state (the state with earliest outbreaks) in each group, we developed deterministic and stochastic Long Short Term Memory (LSTM) and Mixture Density Network (MDN) models. We trained the models with data from each leading state to make predictions, then compared the models with a baseline linear regression model. We also remove seasonality and trends from a dataset of non-stationary COVID-19 cases to determine the effects on prediction. We showed that the deterministic LSTM model trained on the COVID-19 effective reproduction numbers outperforms other prediction methods.
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Affiliation(s)
- Mohammad Reza Davahli
- Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, Florida, United States of America
| | - Waldemar Karwowski
- Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, Florida, United States of America
| | - Krzysztof Fiok
- Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, Florida, United States of America
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20
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Seiler M, Staubli G, Hoeffe J, Gualco G, Manzano S, Goldman RD. A tale of two parts of Switzerland: regional differences in the impact of the COVID-19 pandemic on parents. BMC Public Health 2021; 21:1275. [PMID: 34193102 PMCID: PMC8242280 DOI: 10.1186/s12889-021-11315-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 06/18/2021] [Indexed: 01/22/2023] Open
Abstract
BACKGROUND We aimed to document the impact of the coronavirus disease 2019 (COVID-19) pandemic on regions within a European country. METHODS Parents arriving at two pediatric emergency departments (EDs) in North of Switzerland and two in South of Switzerland completed an online survey during the first peak of the pandemic (April-June 2020). They were asked to rate their concern about their children or themselves having COVID-19. RESULTS A total of 662 respondents completed the survey. Parents in the South were significantly more exposed to someone tested positive for COVID-19 than in the North (13.9 and 4.7%, respectively; P < 0.001). Parents in the South were much more concerned than in the North that they (mean 4.61 and 3.32, respectively; P < 0.001) or their child (mean 4.79 and 3.17, respectively; P < 0.001) had COVID-19. Parents reported their children wore facemasks significantly more often in the South than in the North (71.5 and 23.5%, respectively; P < 0.001). CONCLUSION The COVID-19 pandemic resulted in significant regional differences among families arriving at EDs in Switzerland. Public health agencies should consider regional strategies, rather than country-wide guidelines, in future pandemics and for vaccination against COVID-19 for children.
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Affiliation(s)
- Michelle Seiler
- Pediatric Emergency Department, University Children's Hospital Zurich, Steinwiesstrasse 75, 8032, Zurich, Switzerland.
| | - Georg Staubli
- Pediatric Emergency Department, University Children's Hospital Zurich, Steinwiesstrasse 75, 8032, Zurich, Switzerland
| | - Julia Hoeffe
- Pediatric Emergency Department, Inselspital University Hospital of Bern, Bern, Switzerland
| | - Gianluca Gualco
- Pediatric Emergency Department, Pediatric Institute of Italian part of Switzerland, Bellinzona, Switzerland
| | - Sergio Manzano
- Pediatric Emergency Department, Geneva University Hospitals and Faculty of Medicine, University of Geneva, Geneva, Switzerland
| | - Ran D Goldman
- The Pediatric Research in Emergency Therapeutics (PRETx) Program, Division of Emergency Medicine, Department of Pediatrics, University of British Columbia, and BC Children's Hospital Research Institute, Vancouver, BC, Canada
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21
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Champredon D, Fazil A, Ogden NH. Simple mathematical modelling approaches to assessing the transmission risk of SARS-CoV-2 at gatherings. CANADA COMMUNICABLE DISEASE REPORT = RELEVE DES MALADIES TRANSMISSIBLES AU CANADA 2021; 47:184-194. [PMID: 34035664 PMCID: PMC8127697 DOI: 10.14745/ccdr.v47i04a02] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
BACKGROUND Gatherings may contribute significantly to the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). For this reason, public health interventions have sought to constrain unrepeated or recurrent gatherings to curb the coronavirus disease 2019 (COVID-19) pandemic. Unfortunately, the range of different types of gatherings hinders specific guidance from setting limiting parameters (e.g. total size, number of cohorts, the extent of physical distancing). METHODS We used a generic modelling framework, based on fundamental probability principles, to derive simple formulas to assess introduction and transmission risks associated with gatherings, as well as the potential efficiency of some testing strategies to mitigate these risks. RESULTS Introduction risk can be broadly assessed with the population prevalence and the size of the gathering, while transmission risk at a gathering is mainly driven by the gathering size. For recurrent gatherings, the cohort structure does not have a significant impact on transmission between cohorts. Testing strategies can mitigate risk, but frequency of testing and test performance are factors in finding a balance between detection and false positives. CONCLUSION The generality of the modelling framework used here helps to disentangle the various factors affecting transmission risk at gatherings and may be useful for public health decision-making.
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Affiliation(s)
- David Champredon
- Public Health Risk Sciences Division, National Microbiology Laboratory, Public Health Agency of Canada, Guelph, ON
| | - Aamir Fazil
- Public Health Risk Sciences Division, National Microbiology Laboratory, Public Health Agency of Canada, Guelph, ON
| | - Nicholas H Ogden
- Public Health Risk Sciences Division, National Microbiology Laboratory, Public Health Agency of Canada, St.-Hyacinthe, QC and Guelph, ON
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22
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Davahli MR, Fiok K, Karwowski W, Aljuaid AM, Taiar R. Predicting the Dynamics of the COVID-19 Pandemic in the United States Using Graph Theory-Based Neural Networks. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2021; 18:3834. [PMID: 33917544 PMCID: PMC8038789 DOI: 10.3390/ijerph18073834] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Revised: 03/28/2021] [Accepted: 04/03/2021] [Indexed: 12/03/2022]
Abstract
The COVID-19 pandemic has had unprecedented social and economic consequences in the United States. Therefore, accurately predicting the dynamics of the pandemic can be very beneficial. Two main elements required for developing reliable predictions include: (1) a predictive model and (2) an indicator of the current condition and status of the pandemic. As a pandemic indicator, we used the effective reproduction number (Rt), which is defined as the number of new infections transmitted by a single contagious individual in a population that may no longer be fully susceptible. To bring the pandemic under control, Rt must be less than one. To eliminate the pandemic, Rt should be close to zero. Therefore, this value may serve as a strong indicator of the current status of the pandemic. For a predictive model, we used graph neural networks (GNNs), a method that combines graphical analysis with the structure of neural networks. We developed two types of GNN models, including: (1) graph-theory-based neural networks (GTNN) and (2) neighborhood-based neural networks (NGNN). The nodes in both graphs indicated individual states in the United States. While the GTNN model's edges document functional connectivity between states, those in the NGNN model link neighboring states to one another. We trained both models with Rt numbers collected over the previous four days and asked them to predict the following day for all states in the United States. The performance of these models was evaluated with the datasets that included Rt values reflecting conditions from 22 January through 26 November 2020 (before the start of COVID-19 vaccination in the United States). To determine the efficiency, we compared the results of two models with each other and with those generated by a baseline Long short-term memory (LSTM) model. The results indicated that the GTNN model outperformed both the NGNN and LSTM models for predicting Rt.
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Affiliation(s)
- Mohammad Reza Davahli
- Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, FL 32816, USA; (K.F.); (W.K.)
| | - Krzysztof Fiok
- Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, FL 32816, USA; (K.F.); (W.K.)
| | - Waldemar Karwowski
- Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, FL 32816, USA; (K.F.); (W.K.)
| | - Awad M. Aljuaid
- Department of Industrial Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia;
| | - Redha Taiar
- Department of Sports Sciences, MATIM, Université de Reims Champagne-Ardenne, 51100 Reims, France;
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23
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Fung ICH, Hung YW, Ofori SK, Muniz-Rodriguez K, Lai PY, Chowell G. SARS-CoV-2 Transmission in Alberta, British Columbia, and Ontario, Canada, December 25, 2019, to December 1, 2020. Disaster Med Public Health Prep 2021; 16:1-10. [PMID: 33762027 PMCID: PMC8134904 DOI: 10.1017/dmp.2021.78] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Revised: 01/19/2021] [Accepted: 02/07/2021] [Indexed: 12/20/2022]
Abstract
OBJECTIVE This study aimed to investigate coronavirus disease (COVID-19) epidemiology in Alberta, British Columbia, and Ontario, Canada. METHODS Using data through December 1, 2020, we estimated time-varying reproduction number, Rt, using EpiEstim package in R, and calculated incidence rate ratios (IRR) across the 3 provinces. RESULTS In Ontario, 76% (92 745/121 745) of cases were in Toronto, Peel, York, Ottawa, and Durham; in Alberta, 82% (49 878/61 169) in Calgary and Edmonton; in British Columbia, 90% (31 142/34 699) in Fraser and Vancouver Coastal. Across 3 provinces, Rt dropped to ≤ 1 after April. In Ontario, Rt would remain < 1 in April if congregate-setting-associated cases were excluded. Over summer, Rt maintained < 1 in Ontario, ~1 in British Columbia, and ~1 in Alberta, except early July when Rt was > 1. In all 3 provinces, Rt was > 1, reflecting surges in case count from September through November. Compared with British Columbia (684.2 cases per 100 000), Alberta (IRR = 2.0; 1399.3 cases per 100 000) and Ontario (IRR = 1.2; 835.8 cases per 100 000) had a higher cumulative case count per 100 000 population. CONCLUSIONS Alberta and Ontario had a higher incidence rate than British Columbia, but Rt trajectories were similar across all 3 provinces.
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Affiliation(s)
- Isaac Chun-Hai Fung
- Department of Biostatistics, Epidemiology and Environmental Health Sciences, Jiann-Ping Hsu College of Public Health, Georgia Southern University, Statesboro, GA, USA
| | - Yuen Wai Hung
- Department of Health Sciences, Wilfrid Laurier University, Waterloo, ON, Canada
| | - Sylvia K. Ofori
- Department of Biostatistics, Epidemiology and Environmental Health Sciences, Jiann-Ping Hsu College of Public Health, Georgia Southern University, Statesboro, GA, USA
| | - Kamalich Muniz-Rodriguez
- Department of Biostatistics, Epidemiology and Environmental Health Sciences, Jiann-Ping Hsu College of Public Health, Georgia Southern University, Statesboro, GA, USA
| | - Po-Ying Lai
- Department of Biostatistics, School of Public Health, Boston University, Boston, MA, USA
| | - Gerardo Chowell
- Department of Population Health Sciences, School of Public Health, Georgia State University, Atlanta, GA, USA
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24
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Nakajo K, Nishiura H. Assessing Interventions against Coronavirus Disease 2019 (COVID-19) in Osaka, Japan: A Modeling Study. J Clin Med 2021; 10:jcm10061256. [PMID: 33803634 PMCID: PMC8003080 DOI: 10.3390/jcm10061256] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Revised: 03/16/2021] [Accepted: 03/17/2021] [Indexed: 12/13/2022] Open
Abstract
Estimation of the effective reproduction number, R(t), of coronavirus disease (COVID-19) in real-time is a continuing challenge. R(t) reflects the epidemic dynamics based on readily available illness onset data, and is useful for the planning and implementation of public health and social measures. In the present study, we proposed a method for computing the R(t) of COVID-19, and applied this method to the epidemic in Osaka prefecture from February to September 2020. We estimated R(t) as a function of the time of infection using the date of illness onset. The epidemic in Osaka came under control around 2 April during the first wave, and 26 July during the second wave. R(t) did not decline drastically following any single intervention. However, when multiple interventions were combined, the relative reductions in R(t) during the first and second waves were 70% and 51%, respectively. Although the second wave was brought under control without declaring a state of emergency, our model comparison indicated that relying on a single intervention would not be sufficient to reduce R(t) < 1. The outcome of the COVID-19 pandemic continues to rely on political leadership to swiftly design and implement combined interventions capable of broadly and appropriately reducing contacts.
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Affiliation(s)
- Ko Nakajo
- Kyoto University School of Public Health, Yoshida-Konoe-cho, Sakyo-ku, Kyoto 606-8501, Japan;
- Graduate School of Medicine, Hokkaido University, Kita 15 Jo Nishi 7 Chome, Kita-ku, Sapporo-shi, Hokkaido 060-8638, Japan
- Sanofi K.K. Tokyo Opera City Tower, 3-20-2, Nishi Shinjuku, Shinjuku-ku, Tokyo 163-1488, Japan
| | - Hiroshi Nishiura
- Kyoto University School of Public Health, Yoshida-Konoe-cho, Sakyo-ku, Kyoto 606-8501, Japan;
- Correspondence: ; Tel.: +81-75-753-4490
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Baj J, Ciesielka M, Buszewicz G, Maciejewski R, Budzyńska B, Listos P, Teresiński G. COVID-19 in the autopsy room-requirements, safety, recommendations and pathological findings. Forensic Sci Med Pathol 2021; 17:101-113. [PMID: 33394313 PMCID: PMC7780078 DOI: 10.1007/s12024-020-00341-1] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/05/2020] [Indexed: 12/20/2022]
Abstract
Modern technologies enable the exchange of information about the expansion of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection and the continually increasing number of the coronavirus disease 2019 (COVID-19) cases almost in real time. The gravity of a current epidemiological situation is represented by the mortality rates, which are scrupulously updated daily. Performing autopsies on patients with either suspected or confirmed COVID-19 is of high importance since these might not only improve clinical management but also reduce the risk of SARS-CoV-2 infection expansion. The following paper aimed to present the most crucial aspects of SARS-CoV-2 infection from the point of view of forensic experts and pathologists, recommendations and safety precautions regarding autopsies, autopsy room requirements, possible techniques, examinations used for effective viral detection, recommendations regarding burials, and gross and microscopic pathological findings of the deceased who died due to SARS-CoV-2 infection. Autopsies remain the gold standard for determining the cause of death. Therefore, it would be beneficial to perform autopsies on patients with both suspected and confirmed COVID-19, especially those with coexisting comorbidities.
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Affiliation(s)
- Jacek Baj
- Chair and Department of Anatomy, Medical University of Lublin, 20-090 Lublin, Poland
| | - Marzanna Ciesielka
- Chair and Department of Forensic Medicine, Medical University of Lublin, 20-090 Lublin, Poland
| | - Grzegorz Buszewicz
- Chair and Department of Forensic Medicine, Medical University of Lublin, 20-090 Lublin, Poland
| | - Ryszard Maciejewski
- Chair and Department of Anatomy, Medical University of Lublin, 20-090 Lublin, Poland
| | - Barbara Budzyńska
- Independent Laboratory of Behavioral Studies, Medical University of Lublin, 20-090 Lublin, Poland
| | - Piotr Listos
- Department and Clinic of Animal Internal Diseases, Sub-Department of Pathomorphology and ForensicMedicine, Faculty of Veterinary Medicine, University of Life Sciences in Lublin, Lubin, Poland
| | - Grzegorz Teresiński
- Chair and Department of Forensic Medicine, Medical University of Lublin, 20-090 Lublin, Poland
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26
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Riguzzi M, Gashi S. Lessons From the First Wave of COVID-19: Work-Related Consequences, Clinical Knowledge, Emotional Distress, and Safety-Conscious Behavior in Healthcare Workers in Switzerland. Front Psychol 2021; 12:628033. [PMID: 33633652 PMCID: PMC7899962 DOI: 10.3389/fpsyg.2021.628033] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 01/06/2021] [Indexed: 12/18/2022] Open
Abstract
The coronavirus disease (COVID-19) imposes an unusual risk to the physical and mental health of healthcare workers and thereby to the functioning of healthcare systems during the crisis. This study investigates the clinical knowledge of healthcare workers about COVID-19, their ways of acquiring information, their emotional distress and risk perception, their adherence to preventive guidelines, their changed work situation due to the pandemic, and their perception of how the healthcare system has coped with the pandemic. It is based on a quantitative cross-sectional survey of 185 Swiss healthcare workers directly attending to patients during the pandemic, with 22% (n = 40) of them being assigned to COVID-19-infected patients. The participants answered between 16th June and 15th July 2020, shortly after the first wave of COVID-19 had been overcome and the national government had relaxed its preventive regulations to a great extent. The questionnaire incorporated parts of the "Standard questionnaire on risk perception of an infectious disease outbreak" (version 2015), which were adapted to the case of COVID-19. Clinical knowledge was lowest regarding the effectiveness of standard hygiene (p < 0.05). Knowledge of infectiousness, incubation time, and life-threatening disease progression was higher, however still significantly lower than regarding asymptomatic cases and transmission without physical contact (p < 0.001). 70% (95%-confidence interval: 64-77%) of the healthcare workers reported considerable emotional distress on at least one of the measured dimensions. They worried significantly more strongly about patients, elderly people, and family members, than about their own health (p < 0.001). Adherence to (not legally binding) preventive guidelines by the government displayed patterns such that not all guidelines were followed equally. Most of the participants were faced with a lack of protective materials, personnel, structures, processes, and contingency plans. An increase in stress level was the most prevalent among the diverse effects the pandemic had on their work situation. Better medical equipment (including drugs), better protection for their own mental and physical health, more (assigned) personnel, more comprehensive information about the symptoms of the disease, and a system of earlier warning were the primary lessons to be learned in view of upcoming waves of the pandemic.
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27
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Pasetto D, Lemaitre JC, Bertuzzo E, Gatto M, Rinaldo A. Range of reproduction number estimates for COVID-19 spread. Biochem Biophys Res Commun 2021; 538:253-258. [PMID: 33342517 PMCID: PMC7723757 DOI: 10.1016/j.bbrc.2020.12.003] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2020] [Accepted: 12/01/2020] [Indexed: 12/15/2022]
Abstract
To monitor local and global COVID-19 outbreaks, and to plan containment measures, accessible and comprehensible decision-making tools need to be based on the growth rates of new confirmed infections, hospitalization or case fatality rates. Growth rates of new cases form the empirical basis for estimates of a variety of reproduction numbers, dimensionless numbers whose value, when larger than unity, describes surging infections and generally worsening epidemiological conditions. Typically, these determinations rely on noisy or incomplete data gained over limited periods of time, and on many parameters to estimate. This paper examines how estimates from data and models of time-evolving reproduction numbers of national COVID-19 infection spread change by using different techniques and assumptions. Given the importance acquired by reproduction numbers as diagnostic tools, assessing their range of possible variations obtainable from the same epidemiological data is relevant. We compute control reproduction numbers from Swiss and Italian COVID-19 time series adopting both data convolution (renewal equation) and a SEIR-type model. Within these two paradigms we run a comparative analysis of the possible inferences obtained through approximations of the distributions typically used to describe serial intervals, generation, latency and incubation times, and the delays between onset of symptoms and notification. Our results suggest that estimates of reproduction numbers under these different assumptions may show significant temporal differences, while the actual variability range of computed values is rather small.
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Affiliation(s)
- Damiano Pasetto
- Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca’ Foscari Venezia, 30172, Venezia-Mestre, (IT), Italy,Corresponding author
| | - Joseph C. Lemaitre
- Laboratory of Ecohydrology, School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, (CH), Switzerland
| | - Enrico Bertuzzo
- Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Ca’ Foscari Venezia, 30172, Venezia-Mestre, (IT), Italy
| | - Marino Gatto
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133, Milan, (IT), Italy
| | - Andrea Rinaldo
- Laboratory of Ecohydrology, School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, (CH), Switzerland,Dipartimento di Ingegneria Civile Edile ed Ambientale, Università di Padova, I-35131, Padua, (IT), Italy
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28
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Mansouri Daneshvar MR, Ebrahimi M, Sadeghi A, Mahmoudzadeh A. Climate effects on the COVID-19 outbreak: a comparative analysis between the UAE and Switzerland. MODELING EARTH SYSTEMS AND ENVIRONMENT 2021; 8:469-482. [PMID: 33521243 PMCID: PMC7822754 DOI: 10.1007/s40808-021-01110-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 01/05/2021] [Indexed: 02/06/2023]
Abstract
The main aim of the present study is to disclose the similarities or differences of the climate effects on the COVID-19 outbreak in two countries, which have different climatic conditions. Using the correlation modeling, the results revealed that some climatic factors, such as the ULR, temperature, and CH4 in the UAE and aerosol index and NO2 in Switzerland have positive lagged correlations with the outburst of COVID-19 by intensifying role within - 9, - 7, and - 2 days. The mitigating role was also observed for ozone/solar radiation and temperature/long-wave radiation in the UAE and Switzerland, respectively. The initial hypotheses of the research have confirmed the correlations between new cases of COVID-19 and ULR and aerosol indices in the UAE and Switzerland. However, the main finding revealed that the climate effects on the COVID-19 outbreak show different roles in the different countries, locating in dissimilar climatic zones. Accordingly, the COVID-19 can be intensified by increases of the ULR and temperature in an arid region, while it can be exactly mitigated by increases of these factors in a temperate area. This finding may be useful for future researches for identifying the essential influencing factors for the mitigating COVID-19 outbreak.
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Affiliation(s)
- M. R. Mansouri Daneshvar
- Department of Geography and Natural Hazards, Research Institute of Shakhes Pajouh, Isfahan, Iran
| | - M. Ebrahimi
- Department of Physical Geography, Hakim Sabzevari University, Sabzevar, Iran
| | - A. Sadeghi
- Department of Humanities and Social Science, Farhangian University, Tehran, Iran
| | - A. Mahmoudzadeh
- Head of Departments and Chancellor, Research Institute of Shakhes Pajouh, Isfahan, Iran
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Turbé H, Bjelogrlic M, Robert A, Gaudet-Blavignac C, Goldman JP, Lovis C. Adaptive Time-Dependent Priors and Bayesian Inference to Evaluate SARS-CoV-2 Public Health Measures Validated on 31 Countries. Front Public Health 2021; 8:583401. [PMID: 33553088 PMCID: PMC7862946 DOI: 10.3389/fpubh.2020.583401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2020] [Accepted: 12/03/2020] [Indexed: 01/19/2023] Open
Abstract
With the rapid spread of the SARS-CoV-2 virus since the end of 2019, public health confinement measures to contain the propagation of the pandemic have been implemented. Our method to estimate the reproduction number using Bayesian inference with time-dependent priors enhances previous approaches by considering a dynamic prior continuously updated as restrictive measures and comportments within the society evolve. In addition, to allow direct comparison between reproduction number and introduction of public health measures in a specific country, the infection dates are inferred from daily confirmed cases and confirmed death. The evolution of this reproduction number in combination with the stringency index is analyzed on 31 European countries. We show that most countries required tough state interventions with a stringency index equal to 79.6 out of 100 to reduce their reproduction number below one and control the progression of the pandemic. In addition, we show a direct correlation between the time taken to introduce restrictive measures and the time required to contain the spread of the pandemic with a median time of 8 days. This analysis is validated by comparing the excess deaths and the time taken to implement restrictive measures. Our analysis reinforces the importance of having a fast response with a coherent and comprehensive set of confinement measures to control the pandemic. Only restrictions or combinations of those have shown to effectively control the pandemic.
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Affiliation(s)
- Hugues Turbé
- Medical Information Sciences Division, Department of Radiology and Medical Informatics, University of Geneva, Geneva, Switzerland
- Medical Information Sciences Division, Diagnostic Department, University Hospitals of Geneva, Geneva, Switzerland
| | - Mina Bjelogrlic
- Medical Information Sciences Division, Department of Radiology and Medical Informatics, University of Geneva, Geneva, Switzerland
- Medical Information Sciences Division, Diagnostic Department, University Hospitals of Geneva, Geneva, Switzerland
| | - Arnaud Robert
- Medical Information Sciences Division, Department of Radiology and Medical Informatics, University of Geneva, Geneva, Switzerland
- Medical Information Sciences Division, Diagnostic Department, University Hospitals of Geneva, Geneva, Switzerland
| | - Christophe Gaudet-Blavignac
- Medical Information Sciences Division, Department of Radiology and Medical Informatics, University of Geneva, Geneva, Switzerland
- Medical Information Sciences Division, Diagnostic Department, University Hospitals of Geneva, Geneva, Switzerland
| | - Jean-Philippe Goldman
- Medical Information Sciences Division, Department of Radiology and Medical Informatics, University of Geneva, Geneva, Switzerland
- Medical Information Sciences Division, Diagnostic Department, University Hospitals of Geneva, Geneva, Switzerland
| | - Christian Lovis
- Medical Information Sciences Division, Department of Radiology and Medical Informatics, University of Geneva, Geneva, Switzerland
- Medical Information Sciences Division, Diagnostic Department, University Hospitals of Geneva, Geneva, Switzerland
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Ives AR, Bozzuto C. Estimating and explaining the spread of COVID-19 at the county level in the USA. Commun Biol 2021; 4:60. [PMID: 33402722 PMCID: PMC7785728 DOI: 10.1038/s42003-020-01609-6] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2020] [Accepted: 12/15/2020] [Indexed: 11/25/2022] Open
Abstract
The basic reproduction number, R0, determines the rate of spread of a communicable disease and therefore gives fundamental information needed to plan public health interventions. Using mortality records, we estimated the rate of spread of COVID-19 among 160 counties and county-aggregates in the USA at the start of the epidemic. We show that most of the high among-county variance is explained by four factors (R2 = 0.70): the timing of outbreak, population size, population density, and spatial location. For predictions of future spread, population density and spatial location are important, and for the latter we show that SARS-CoV-2 strains containing the G614 mutation to the spike gene are associated with higher rates of spread. Finally, the high predictability of R0 allows extending estimates to all 3109 counties in the conterminous 48 states. The high variation of R0 argues for public health policies enacted at the county level for controlling COVID-19.
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Affiliation(s)
- Anthony R Ives
- Department of Integrative Biology, University of Wisconsin-Madison, Madison, WI, 53706, USA.
| | - Claudio Bozzuto
- Wildlife Analysis GmbH, Oetlisbergstrasse 38, 8053, Zurich, Switzerland
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Balabdaoui F, Mohr D. Age-stratified discrete compartment model of the COVID-19 epidemic with application to Switzerland. Sci Rep 2020; 10:21306. [PMID: 33277545 PMCID: PMC7718912 DOI: 10.1038/s41598-020-77420-4] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Accepted: 11/04/2020] [Indexed: 01/08/2023] Open
Abstract
Compartmental models enable the analysis and prediction of an epidemic including the number of infected, hospitalized and deceased individuals in a population. They allow for computational case studies on non-pharmaceutical interventions thereby providing an important basis for policy makers. While research is ongoing on the transmission dynamics of the SARS-CoV-2 coronavirus, it is important to come up with epidemic models that can describe the main stages of the progression of the associated COVID-19 respiratory disease. We propose an age-stratified discrete compartment model as an alternative to differential equation based S-I-R type of models. The model captures the highly age-dependent progression of COVID-19 and is able to describe the day-by-day advancement of an infected individual in a modern health care system. The fully-identified model for Switzerland not only predicts the overall histories of the number of infected, hospitalized and deceased, but also the corresponding age-distributions. The model-based analysis of the outbreak reveals an average infection fatality ratio of 0.4% with a pronounced maximum of 9.5% for those aged ≥ 80 years. The predictions for different scenarios of relaxing the soft lockdown indicate a low risk of overloading the hospitals through a second wave of infections. However, there is a hidden risk of a significant increase in the total fatalities (by up to 200%) in case schools reopen with insufficient containment measures in place.
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Affiliation(s)
- Fadoua Balabdaoui
- Seminar of Statistics, Department of Mathematics, Swiss Federal Institute of Technology (ETH), Rämistrasse 101, 8092, Zurich, Switzerland
| | - Dirk Mohr
- Department of Mechanical and Process Engineering, Swiss Federal Institute of Technology (ETH), Tannenstrasse 3, 8092, Zurich, Switzerland.
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32
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Gostic KM, McGough L, Baskerville EB, Abbott S, Joshi K, Tedijanto C, Kahn R, Niehus R, Hay JA, De Salazar PM, Hellewell J, Meakin S, Munday JD, Bosse NI, Sherrat K, Thompson RN, White LF, Huisman JS, Scire J, Bonhoeffer S, Stadler T, Wallinga J, Funk S, Lipsitch M, Cobey S. Practical considerations for measuring the effective reproductive number, Rt. PLoS Comput Biol 2020; 16:e1008409. [PMID: 33301457 PMCID: PMC7728287 DOI: 10.1371/journal.pcbi.1008409] [Citation(s) in RCA: 257] [Impact Index Per Article: 64.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
Estimation of the effective reproductive number Rt is important for detecting changes in disease transmission over time. During the Coronavirus Disease 2019 (COVID-19) pandemic, policy makers and public health officials are using Rt to assess the effectiveness of interventions and to inform policy. However, estimation of Rt from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of Rt, we recommend the approach of Cori and colleagues, which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis, are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to the spread. We advise caution when using methods derived from the approach of Bettencourt and Ribeiro, as the resulting Rt estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in Rt estimation.
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Affiliation(s)
- Katelyn M. Gostic
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America
| | - Lauren McGough
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America
| | - Edward B. Baskerville
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America
| | - Sam Abbott
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Keya Joshi
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Christine Tedijanto
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Rebecca Kahn
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Rene Niehus
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - James A. Hay
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Pablo M. De Salazar
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Joel Hellewell
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Sophie Meakin
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - James D. Munday
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Nikos I. Bosse
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Katharine Sherrat
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Robin N. Thompson
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Mathematical Institute, University of Oxford, Oxford, United Kingdom
| | - Laura F. White
- Department of Biostatistics, Boston University School of Public Health, Boston, MA, United States of America
| | - Jana S. Huisman
- Department of Environmental Systems Science, ETH Zürich, Zürich, Switzerland
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
| | - Jérémie Scire
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
- Swiss Institute of Bioinformatics, Basel, Switzerland
| | | | - Tanja Stadler
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
- Swiss Institute of Bioinformatics, Basel, Switzerland
| | - Jacco Wallinga
- Centre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, the Netherlands
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, the Netherlands
| | - Sebastian Funk
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Marc Lipsitch
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, United States of America
| | - Sarah Cobey
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, United States of America
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Haslbauer JD, Perrina V, Matter M, Dellas A, Mihatsch MJ, Tzankov A. Retrospective Post-mortem SARS-CoV-2 RT-PCR of Autopsies with COVID-19-Suggestive Pathology Supports the Absence of Lethal Community Spread in Basel, Switzerland, before February 2020. Pathobiology 2020; 88:95-105. [PMID: 33161409 DOI: 10.1159/000512563] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2020] [Accepted: 09/30/2020] [Indexed: 12/15/2022] Open
Abstract
INTRODUCTION Coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has rapidly spread around the world. While the first case was recorded in Hubei in December 2019, the extent of early community spread in Central Europe before this period is unknown. A high proportion of asymptomatic cases and undocumented infections, high transmissibility, and phylogenetic genomic diversity have engendered the controversial possibility of early international community spread of SARS-CoV-2 before its emergence in China. METHODS To assess the early presence of lethal COVID-19 in Switzerland, we retrospectively performed an analysis of deaths at University Hospital Basel between October 2019 and February 2020 (n = 310), comparing the incidence of clinical causes of death with March 2020 (n = 72), the month during which the first lethal COVID-19 cases in Basel were reported. Trends of COVID-19-suggestive sequelae, such as bronchopneumonia with organization, acute respiratory distress syndrome (ARDS), or pulmonary embolisms (PE) were evaluated. In cases where autopsy was performed (n = 71), analogous analyses were conducted on the cause of death and pulmonary histological findings. Eight cases with a COVID-19-suggestive clinical history and histopathology between October 2019 and February 2020, and 3 cases before October 2019, were selected for SARS-CoV-2 RT-PCR. RESULTS A statistically significant rise in pulmonary causes of death was observed in March 2020 (p = 0.03), consistent with the reported emergence of lethal COVID-19 in Switzerland. A rise in lethal bronchopneumonia was observed between December 2019 and January 2020, which was likely seasonal. The incidence of lethal ARDS and PE was uniformly low between October 2019 and February 2020. All autopsy cases analyzed by means of SARS-CoV-2 RT-PCR yielded negative results. CONCLUSION Our data suggest the absence of early lethal community spread of COVID-19 in Basel before its initial reported emergence in Switzerland in March 2020.
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Affiliation(s)
- Jasmin Dionne Haslbauer
- Pathology, Institute of Medical Genetics and Pathology, University Hospital Basel, University of Basel, Basel, Switzerland
| | - Valeria Perrina
- Pathology, Institute of Medical Genetics and Pathology, University Hospital Basel, University of Basel, Basel, Switzerland
| | - Matthias Matter
- Pathology, Institute of Medical Genetics and Pathology, University Hospital Basel, University of Basel, Basel, Switzerland
| | - Athanassios Dellas
- Department of Clinical Research, University Hospital Basel, University of Basel, Basel, Switzerland
| | - Michael J Mihatsch
- Pathology, Institute of Medical Genetics and Pathology, University Hospital Basel, University of Basel, Basel, Switzerland
| | - Alexandar Tzankov
- Pathology, Institute of Medical Genetics and Pathology, University Hospital Basel, University of Basel, Basel, Switzerland,
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34
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Zenk L, Steiner G, Pina e Cunha M, Laubichler MD, Bertau M, Kainz MJ, Jäger C, Schernhammer ES. Fast Response to Superspreading: Uncertainty and Complexity in the Context of COVID-19. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2020; 17:E7884. [PMID: 33121161 PMCID: PMC7663466 DOI: 10.3390/ijerph17217884] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 09/10/2020] [Revised: 10/13/2020] [Accepted: 10/21/2020] [Indexed: 12/11/2022]
Abstract
Although the first coronavirus disease 2019 (COVID-19) wave has peaked with the second wave underway, the world is still struggling to manage potential systemic risks and unpredictability of the pandemic. A particular challenge is the "superspreading" of the virus, which starts abruptly, is difficult to predict, and can quickly escalate into medical and socio-economic emergencies that contribute to long-lasting crises challenging our current ways of life. In these uncertain times, organizations and societies worldwide are faced with the need to develop appropriate strategies and intervention portfolios that require fast understanding of the complex interdependencies in our world and rapid, flexible action to contain the spread of the virus as quickly as possible, thus preventing further disastrous consequences of the pandemic. We integrate perspectives from systems sciences, epidemiology, biology, social networks, and organizational research in the context of the superspreading phenomenon to understand the complex system of COVID-19 pandemic and develop suggestions for interventions aimed at rapid responses.
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Affiliation(s)
- Lukas Zenk
- Department of Knowledge and Communication Management, Faculty of Business and Globalization, Danube University Krems, 3500 Krems an der Donau, Austria;
| | - Gerald Steiner
- Department of Knowledge and Communication Management, Faculty of Business and Globalization, Danube University Krems, 3500 Krems an der Donau, Austria;
- Complexity Science Hub Vienna, 1090 Vienna, Austria; (M.D.L.); (C.J.)
| | - Miguel Pina e Cunha
- Nova School of Business and Economics, Universidade Nova de Lisboa, 2775-405 Carcavelos, Portugal;
| | - Manfred D. Laubichler
- Complexity Science Hub Vienna, 1090 Vienna, Austria; (M.D.L.); (C.J.)
- School of Complex Adaptive Systems Tempe, Arizona State University, Tempe, AZ 85287-2701, USA
- Santa Fe Institute, Santa Fe, NM 87501, USA
- Global Climate Forum, 10178 Berlin, Germany
| | - Martin Bertau
- Institute of Chemical Technology, Freiberg University of Mining and Technology, 09599 Freiberg, Germany;
| | - Martin J. Kainz
- WasserCluster Lunz-Inter-University Center for Aquatic Ecosystem Research, 3293 Lunz am See, Austria;
| | - Carlo Jäger
- Complexity Science Hub Vienna, 1090 Vienna, Austria; (M.D.L.); (C.J.)
- School of Complex Adaptive Systems Tempe, Arizona State University, Tempe, AZ 85287-2701, USA
- Global Climate Forum, 10178 Berlin, Germany
- Academy of Disaster Reduction and Emergency Management, Beijing Normal University, Beijing 100875, China
| | - Eva S. Schernhammer
- Complexity Science Hub Vienna, 1090 Vienna, Austria; (M.D.L.); (C.J.)
- Department of Epidemiology, Center for Public Health, Medical University of Vienna, 1090 Vienna, Austria
- Channing Division of Network Medicine, Harvard Medical School, Boston, MA 02115, USA
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35
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Gostic KM, McGough L, Baskerville EB, Abbott S, Joshi K, Tedijanto C, Kahn R, Niehus R, Hay J, De Salazar PM, Hellewell J, Meakin S, Munday J, Bosse NI, Sherrat K, Thompson RN, White LF, Huisman JS, Scire J, Bonhoeffer S, Stadler T, Wallinga J, Funk S, Lipsitch M, Cobey S. Practical considerations for measuring the effective reproductive number, R t. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2020:2020.06.18.20134858. [PMID: 32607522 PMCID: PMC7325187 DOI: 10.1101/2020.06.18.20134858] [Citation(s) in RCA: 50] [Impact Index Per Article: 12.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Estimation of the effective reproductive number, R t , is important for detecting changes in disease transmission over time. During the COVID-19 pandemic, policymakers and public health officials are using R t to assess the effectiveness of interventions and to inform policy. However, estimation of R t from available data presents several challenges, with critical implications for the interpretation of the course of the pandemic. The purpose of this document is to summarize these challenges, illustrate them with examples from synthetic data, and, where possible, make recommendations. For near real-time estimation of R t , we recommend the approach of Cori et al. (2013), which uses data from before time t and empirical estimates of the distribution of time between infections. Methods that require data from after time t, such as Wallinga and Teunis (2004), are conceptually and methodologically less suited for near real-time estimation, but may be appropriate for retrospective analyses of how individuals infected at different time points contributed to spread. We advise against using methods derived from Bettencourt and Ribeiro (2008), as the resulting R t estimates may be biased if the underlying structural assumptions are not met. Two key challenges common to all approaches are accurate specification of the generation interval and reconstruction of the time series of new infections from observations occurring long after the moment of transmission. Naive approaches for dealing with observation delays, such as subtracting delays sampled from a distribution, can introduce bias. We provide suggestions for how to mitigate this and other technical challenges and highlight open problems in R t estimation.
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Affiliation(s)
- Katelyn M. Gostic
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, USA
| | - Lauren McGough
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, USA
| | | | - Sam Abbott
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Keya Joshi
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Christine Tedijanto
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Rebecca Kahn
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Rene Niehus
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - James Hay
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Pablo M. De Salazar
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Joel Hellewell
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Sophie Meakin
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - James Munday
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Nikos I. Bosse
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Katharine Sherrat
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Robin N. Thompson
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
- Mathematical Institute, University of Oxford, Oxford, UK
| | - Laura F. White
- Department of Biostatistics, Boston University School of Public Health, Boston, MA, USA
| | - Jana S. Huisman
- Department of Environmental Systems Science, ETH Zürich, Zürich, Switzerland
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
| | - Jérémie Scire
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
- Swiss Institute of Bioinformatics, Basel, Switzerland
| | | | - Tanja Stadler
- Department of Biosystems Science and Engineering, ETH Zürich, Switzerland
- Swiss Institute of Bioinformatics, Basel, Switzerland
| | - Jacco Wallinga
- Centre for Infectious Disease Control, National Institute for Public Health and the Environment, Bilthoven, The Netherlands
- Department of Biomedical Data Sciences, Leiden University Medical Centre, Leiden, The Netherlands
| | - Sebastian Funk
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene & Tropical Medicine, London, UK
| | - Marc Lipsitch
- Center for Communicable Disease Dynamics, Department of Epidemiology, T.H. Chan School of Public Health, Harvard University, Cambridge, MA, USA
| | - Sarah Cobey
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, USA
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