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Bosman M, Esteve A, Gabbanelli L, Jordan X, López-Gay A, Manera M, Martínez M, Masjuan P, Mir L, Paradells J, Pignatelli A, Riu I, Vitagliano V. Stochastic simulation of successive waves of COVID-19 in the province of Barcelona. Infect Dis Model 2023; 8:145-158. [PMID: 36589597 PMCID: PMC9792425 DOI: 10.1016/j.idm.2022.12.005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2022] [Revised: 12/21/2022] [Accepted: 12/22/2022] [Indexed: 12/29/2022] Open
Abstract
Analytic compartmental models are currently used in mathematical epidemiology to forecast the COVID-19 pandemic evolution and explore the impact of mitigation strategies. In general, such models treat the population as a single entity, losing the social, cultural and economical specificities. We present a network model that uses socio-demographic datasets with the highest available granularity to predict the spread of COVID-19 in the province of Barcelona. The model is flexible enough to incorporate the effect of containment policies, such as lockdowns or the use of protective masks, and can be easily adapted to future epidemics. We follow a stochastic approach that combines a compartmental model with detailed individual microdata from the population census, including social determinants and age-dependent strata, and time-dependent mobility information. We show that our model reproduces the dynamical features of the disease across two waves and demonstrates its capability to become a powerful tool for simulating epidemic events.
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Affiliation(s)
- M. Bosman
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
- Corresponding author.
| | - A. Esteve
- Centre d’Estudis Demogràfics (CED-CERCA), Barcelona, Spain
- Serra Húnter Fellow, Departament de Ciències Polítiques i Socials, Universitat Pompeu Fabra, Barcelona, Spain
| | - L. Gabbanelli
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
| | - X. Jordan
- i2CAT Foundation, Edifici Nexus (Campus Nord UPC), Barcelona, Spain
| | - A. López-Gay
- Centre d’Estudis Demogràfics (CED-CERCA), Barcelona, Spain
- Departament de Geografia, Universitat Autònoma de Barcelona, Bellaterra, Spain
| | - M. Manera
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
- Serra Húnter Fellow, Departament de Física, Universitat Autònoma de Barcelona, Bellaterra, Spain
| | - M. Martínez
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
- Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain
| | - P. Masjuan
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
- Departament de Física, Universitat Autònoma de Barcelona, Bellaterra, Spain
| | - Ll.M. Mir
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
| | - J. Paradells
- i2CAT Foundation, Edifici Nexus (Campus Nord UPC), Barcelona, Spain
- Departament d’Enginyeria Telemàtica, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - A. Pignatelli
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
| | - I. Riu
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
| | - V. Vitagliano
- Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
- DIME, University of Genova, Via all’Opera Pia 15, 16145, Genova, Italy
- INFN, Sezione di Genova, via Dodecaneso 33, 16146, Genoa, Italy
- Department of Mathematics and Physics, University of Hull, Kingston upon Hull, HU6 7RX, UK
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Mohammadi Z, Cojocaru MG, Thommes EW. Human behaviour, NPI and mobility reduction effects on COVID-19 transmission in different countries of the world. BMC Public Health 2022; 22:1594. [PMID: 35996132 PMCID: PMC9394048 DOI: 10.1186/s12889-022-13921-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2021] [Accepted: 08/01/2022] [Indexed: 11/13/2022] Open
Abstract
Background The outbreak of Coronavirus disease, which originated in Wuhan, China in 2019, has affected the lives of billions of people globally. Throughout 2020, the reproduction number of COVID-19 was widely used by decision-makers to explain their strategies to control the pandemic. Methods In this work, we deduce and analyze both initial and effective reproduction numbers for 12 diverse world regions between February and December of 2020. We consider mobility reductions, mask wearing and compliance with masks, mask efficacy values alongside other non-pharmaceutical interventions (NPIs) in each region to get further insights in how each of the above factored into each region’s SARS-COV-2 transmission dynamic. Results We quantify in each region the following reductions in the observed effective reproduction numbers of the pandemic: i) reduction due to decrease in mobility (as captured in Google mobility reports); ii) reduction due to mask wearing and mask compliance; iii) reduction due to other NPI’s, over and above the ones identified in i) and ii). Conclusion In most cases mobility reduction coming from nationwide lockdown measures has helped stave off the initial wave in countries who took these types of measures. Beyond the first waves, mask mandates and compliance, together with social-distancing measures (which we refer to as other NPI’s) have allowed some control of subsequent disease spread. The methodology we propose here is novel and can be applied to other respiratory diseases such as influenza or RSV. Supplementary Information The online version contains supplementary material available at (10.1186/s12889-022-13921-3).
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Affiliation(s)
- Zahra Mohammadi
- Department of Mathematics & Statistics, University of Guelph, 50 Stone Road E., Guelph, N1G 2W1, Canada.
| | - Monica Gabriela Cojocaru
- Department of Mathematics & Statistics, University of Guelph, 50 Stone Road E., Guelph, N1G 2W1, Canada
| | - Edward Wolfgang Thommes
- Department of Mathematics & Statistics, University of Guelph, 50 Stone Road E., Guelph, N1G 2W1, Canada.,Modeling, Epidemiology and Data Science, Sanofi Pasteur, Toronto, Canada
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Bodenstein M, Corsetti G, Guerrieri L. Social distancing and supply disruptions in a pandemic. QUANTITATIVE ECONOMICS 2022; 13:681-721. [PMID: 35942438 PMCID: PMC9348191 DOI: 10.3982/qe1618] [Citation(s) in RCA: 21] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Revised: 07/28/2021] [Accepted: 12/02/2021] [Indexed: 05/04/2023]
Abstract
We integrate an epidemiological model, augmented with contact and mobility analyses, with a two-sector macroeconomic model, to assess the economic costs of labor supply disruptions in a pandemic. The model is designed to capture key characteristics of the U.S. input-output tables with a core sector that produces intermediate inputs not easily replaceable by the other sectors, possibly subject to minimum-scale requirements. Using epidemiological and mobility data to inform our exercises, we show that the reduction in labor services due to the observed social distancing (spontaneous and mandatory) could explain up to 6-8 percentage points of the roughly 12% U.S. GDP contraction in the second quarter of 2020. We show that public measures designed to protect workers in core industries and occupations with tasks that cannot be performed from home, can flatten the epidemiological curve at reduced economic costs-and contain vulnerabilities to supply disruptions, namely a new surge of infections. Using state-level data for the United States, we provide econometric evidence that spontaneous social distancing was no less costly than mandated social distancing.
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Wu JT, Mei S, Luo S, Leung K, Liu D, Lv Q, Liu J, Li Y, Prem K, Jit M, Weng J, Feng T, Zheng X, Leung GM. A global assessment of the impact of school closure in reducing COVID-19 spread. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210124. [PMID: 34802277 PMCID: PMC8607143 DOI: 10.1098/rsta.2021.0124] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
Prolonged school closure has been adopted worldwide to control COVID-19. Indeed, UN Educational, Scientific and Cultural Organization figures show that two-thirds of an academic year was lost on average worldwide due to COVID-19 school closures. Such pre-emptive implementation was predicated on the premise that school children are a core group for COVID-19 transmission. Using surveillance data from the Chinese cities of Shenzhen and Anqing together, we inferred that compared with the elderly aged 60 and over, children aged 18 and under and adults aged 19-59 were 75% and 32% less susceptible to infection, respectively. Using transmission models parametrized with synthetic contact matrices for 177 jurisdictions around the world, we showed that the lower susceptibility of school children substantially limited the effectiveness of school closure in reducing COVID-19 transmissibility. Our results, together with recent findings that clinical severity of COVID-19 in children is lower, suggest that school closure may not be ideal as a sustained, primary intervention for controlling COVID-19. This article is part of the theme issue 'Data science approach to infectious disease surveillance'.
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Affiliation(s)
- Joseph T. Wu
- WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, LKS Faculty of Medicine, The University of Hong Kong, Hong Kong
- Laboratory of Data Discovery for Health (D4H), Hong Kong Science Park, New Territories, Hong Kong
| | - Shujiang Mei
- Department of Communicable Diseases Control and Prevention, Shenzhen Center for Disease Control and Prevention, Shenzhen 518055, People's Republic of China
| | - Sihui Luo
- The First Affiliated Hospital of USTC, Division of Life Science and Medicine, University of Science and Technology of China, Hefei, People's Republic of China
- Clinical Research Hospital (Hefei) of Chinese Academy of Science, Hefei, People's Republic of China
| | - Kathy Leung
- WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, LKS Faculty of Medicine, The University of Hong Kong, Hong Kong
- Laboratory of Data Discovery for Health (D4H), Hong Kong Science Park, New Territories, Hong Kong
| | - Di Liu
- WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, LKS Faculty of Medicine, The University of Hong Kong, Hong Kong
- Laboratory of Data Discovery for Health (D4H), Hong Kong Science Park, New Territories, Hong Kong
| | - Qiuying Lv
- Department of Communicable Diseases Control and Prevention, Shenzhen Center for Disease Control and Prevention, Shenzhen 518055, People's Republic of China
| | - Jian Liu
- Anqing Hospital Affiliated to Anhui Medical University (Anqing Municipal Hospital), Anqing, People's Republic of China
| | - Yuan Li
- Department of Communicable Diseases Control and Prevention, Shenzhen Center for Disease Control and Prevention, Shenzhen 518055, People's Republic of China
| | - Kiesha Prem
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - Mark Jit
- WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, LKS Faculty of Medicine, The University of Hong Kong, Hong Kong
- Laboratory of Data Discovery for Health (D4H), Hong Kong Science Park, New Territories, Hong Kong
- Centre for Mathematical Modelling of Infectious Diseases, Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK
| | - Jianping Weng
- The First Affiliated Hospital of USTC, Division of Life Science and Medicine, University of Science and Technology of China, Hefei, People's Republic of China
- Clinical Research Hospital (Hefei) of Chinese Academy of Science, Hefei, People's Republic of China
| | - Tiejian Feng
- Department of Communicable Diseases Control and Prevention, Shenzhen Center for Disease Control and Prevention, Shenzhen 518055, People's Republic of China
| | - Xueying Zheng
- The First Affiliated Hospital of USTC, Division of Life Science and Medicine, University of Science and Technology of China, Hefei, People's Republic of China
- Clinical Research Hospital (Hefei) of Chinese Academy of Science, Hefei, People's Republic of China
| | - Gabriel M. Leung
- WHO Collaborating Centre for Infectious Disease Epidemiology and Control, School of Public Health, LKS Faculty of Medicine, The University of Hong Kong, Hong Kong
- Laboratory of Data Discovery for Health (D4H), Hong Kong Science Park, New Territories, Hong Kong
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Liu Y, Sandmann FG, Barnard RC, Pearson CA, Pastore R, Pebody R, Flasche S, Jit M. Optimising health and economic impacts of COVID-19 vaccine prioritisation strategies in the WHO European Region. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2021:2021.07.09.21260272. [PMID: 34282421 PMCID: PMC8288152 DOI: 10.1101/2021.07.09.21260272] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
BACKGROUND Countries in the World Health Organization (WHO) European Region differ in terms of the COVID-19 vaccine roll-out speed. We evaluated the health and economic impact of different age-based vaccine prioritisation strategies across this demographically and socio-economically diverse region. METHODS We fitted country-specific age-stratified compartmental transmission models to reported COVID-19 mortality in the WHO European Region to inform the immunity level before vaccine roll-out. Building upon broad recommendations from the WHO Strategic Advisory Group of Experts on Immunisation (SAGE), we examined four strategies that prioritise: all adults (V+), younger (20-59 year-olds) followed by older adults (60+) (V20), older followed by younger adults (V60), and the oldest adults (75+) (V75) followed by incremental expansion to successively younger five-year age groups. We explored four roll-out scenarios based on projections or recent observations (R1-4) - the slowest scenario (R1) covers 30% of the total population by December 2022 and the fastest (R4) 80% by December 2021. Five decision-making metrics were summarised over 2021-22: mortality, morbidity, and losses in comorbidity-adjusted life expectancy (cLE), comorbidity- and quality-adjusted life years (cQALY), and the value of human capital (HC). Six sets of infection-blocking and disease-reducing vaccine efficacies were considered. FINDINGS The optimal age-based vaccine prioritisation strategies were sensitive to country characteristics, decision-making metrics and roll-out speeds. Overall, V60 consistently performed better than or comparably to V75. There were greater benefits in prioritising older adults when roll-out is slow and when VE is low. Under faster roll-out, V+ was the most desirable option. INTERPRETATION A prioritisation strategy involving more age-based stages (V75) does not necessarily lead to better health and economic outcomes than targeting broad age groups (V60). Countries expecting a slow vaccine roll-out may particularly benefit from prioritising older adults. FUNDING World Health Organization, Bill and Melinda Gates Foundation, the Medical Research Council (United Kingdom), the National Institute of Health Research (United Kingdom), the European Commission, the Foreign, Commonwealth and Development Office (United Kingdom), Wellcome Trust. RESEARCH IN CONTEXT Evidence before this study: We searched PubMed and medRxiv for articles published in English from inception to 9 Jun 2021, with the search terms: ("COVID-19" OR "SARS-CoV-2") AND ("priorit*) AND ("model*") AND ("vaccin*") and identified 66 studies on vaccine prioritization strategies. Of the 25 studies that compared two or more age-based prioritisation strategies, 12 found that targeting younger adults minimised infections while targeting older adults minimised mortality; an additional handful of studies found similar outcomes between different age-based prioritisation strategies where large outbreaks had already occurred. However, only two studies have explored age-based vaccine prioritisation using models calibrated to observed outbreaks in more than one country, and no study has explored the effectiveness of vaccine prioritisation strategies across settings with different population structures, contact patterns, and outbreak history.Added-value of this study: We evaluated various age-based vaccine prioritisation strategies for 38 countries in the WHO European Region using various health and economic outcomes for decision-making, by parameterising models using observed outbreak history, known epidemiologic and vaccine characteristics, and a range of realistic vaccine roll-out scenarios. We showed that while targeting older adults was generally advantageous, broadly targeting everyone above 60 years might perform better than or comparably to a more detailed strategy that targeted the oldest age group above 75 years followed by those in the next younger five-year age band. Rapid vaccine roll-out has only been observed in a small number of countries. If vaccine coverage can reach 80% by the end of 2021, prioritising older adults may not be optimal in terms of health and economic impact. Lower vaccine efficacy was associated with greater relative benefits only under relatively slow roll-out scenarios considered.Implication of all the available evidence: COVID-19 vaccine prioritization strategies that require more precise targeting of individuals of a specific and narrow age range may not necessarily lead to better outcomes compared to strategies that prioritise populations across broader age ranges. In the WHO European Region, prioritising all adults equally or younger adults first will only optimise health and economic impact when roll-out is rapid, which may raise between-country equity issues given the global demand for COVID-19 vaccines.
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Affiliation(s)
- Yang Liu
- Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, United Kingdom
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine London, United Kingdom
| | - Frank G. Sandmann
- Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, United Kingdom
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine London, United Kingdom
- Statistics, Modelling and Economics Department, National Infection Service, Public Health England, London, United Kingdom
| | - Rosanna C. Barnard
- Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, United Kingdom
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine London, United Kingdom
| | - Carl A.B. Pearson
- Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, United Kingdom
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine London, United Kingdom
| | | | - Roberta Pastore
- World Health Organization (WHO) Regional Office for Europe, Copenhagen, Denmark
| | - Richard Pebody
- World Health Organization (WHO) Regional Office for Europe, Copenhagen, Denmark
| | - Stefan Flasche
- Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, United Kingdom
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine London, United Kingdom
| | - Mark Jit
- Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, United Kingdom
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine London, United Kingdom
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Li R, Bjørnstad ON, Stenseth NC. Switching vaccination among target groups to achieve improved long-lasting benefits. ROYAL SOCIETY OPEN SCIENCE 2021; 8:210292. [PMID: 34150317 PMCID: PMC8206705 DOI: 10.1098/rsos.210292] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 06/04/2021] [Indexed: 05/15/2023]
Abstract
The development of vaccines has opened a way to lower the public health and societal burden of COVID-19 pandemic. To achieve sustainable gains in the long term, switching the vaccination from one target group to a more diverse portfolio should be planned appropriately. We lay out a general mathematical framework for comparing alternative vaccination roll-out strategies for the year to come: single focus groups: (i-a) the high-risk older age groups and (i-b) the core-sociable groups; and two focus groups: (ii-a) mixed vaccination of both the high-risk and core-sociable groups simultaneously and (ii-b) cyclic vaccination switching between groups. Featuring analyses of all relevant data including age pyramids for 15 representative countries with diverse social mixing patterns shows that mixed strategies that result in both direct and indirect protection of high-risk groups may be better for the overall societal health impact of COVID-19 vaccine roll-out. Of note, over time switching the priority from high-risk older age groups to core-sociable groups responsible for heightened circulation and thus indirect risk may be increasingly advantageous.
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Affiliation(s)
- Ruiyun Li
- Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biosciences, University of Oslo, 0316 Oslo, Norway
| | - Ottar N. Bjørnstad
- Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biosciences, University of Oslo, 0316 Oslo, Norway
- Department of Biology, Center for Infectious Disease Dynamics, The Pennsylvania State University, University Park, PA, USA
| | - Nils Chr. Stenseth
- Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biosciences, University of Oslo, 0316 Oslo, Norway
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Menkir TF, Jbaily A, Verguet S. Incorporating equity in infectious disease modeling: Case study of a distributional impact framework for measles transmission. Vaccine 2021; 39:2894-2900. [PMID: 33863575 PMCID: PMC8117973 DOI: 10.1016/j.vaccine.2021.03.023] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Revised: 02/22/2021] [Accepted: 03/04/2021] [Indexed: 11/21/2022]
Abstract
INTRODUCTION Deterministic compartmental models of infectious diseases like measles typically reflect biological heterogeneities in the risk of infection and severity to characterize transmission dynamics. Given the known association of socioeconomic status and increased vulnerability to infection and mortality, it is also critical that such models further incorporate social heterogeneities. METHODS Here, we aimed to explore the influence of integrating income-associated differences in parameters of traditional dynamic transmission models. We developed a measles SIR model, in which the Susceptible, Infected and Recovered classes were stratified by income quintile, with income-specific transmission rates, disease-induced mortality rates, and vaccination coverage levels. We further provided a stylized illustration with secondary data from Ethiopia, where we examined various scenarios demonstrating differences in transmission patterns by income and in distributional vaccination coverage, and quantified impacts on disparities in measles mortality. RESULTS The income-stratified SIR model exhibited similar dynamics to that of the traditional SIR model, with amplified outbreak peaks and measles mortality among the poorest income group. All vaccination coverage strategies were found to substantially curb the overall number of measles deaths, yet most considerably for the poorest, with select strategies yielding clear reductions in measles mortality disparities. DISCUSSION The incorporation of income-specific differences can reveal distinct outbreak patterns across income groups and important differences in the subsequent effects of preventative interventions like vaccination. Our case study highlights the need to extend traditional modeling frameworks (e.g. SIR models) to be stratified by socioeconomic factors like income and to consider ensuing income-associated differences in disease-related morbidity and mortality. In so doing, we build on existing tools and characterize ongoing challenges in achieving health equity.
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Affiliation(s)
- Tigist Ferede Menkir
- Center for Communicable Disease Dynamics, Department of Epidemiology, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, USA
| | - Abdulrahman Jbaily
- Department of Global Health and Population, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, USA
| | - Stéphane Verguet
- Department of Global Health and Population, Harvard T.H. Chan School of Public Health, Harvard University, Boston, MA, USA.
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The influence of social and economic ties to the spread of COVID-19 in Europe. JOURNAL OF POPULATION RESEARCH 2021; 39:495-511. [PMID: 33841047 PMCID: PMC8021302 DOI: 10.1007/s12546-021-09257-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/04/2021] [Indexed: 12/21/2022]
Abstract
By late January 2020, the 2019 novel coronavirus (SARS-CoV-2) had reached Europe and most European countries had registered cases by March 1. However, the spread of the virus has been uneven in both prevalence and speed of propagation. We analyse the association of social, economic, and demographic factors in the initial spread of the coronavirus disease COVID-19 across 23 European countries between March 1 and April 30, 2020. Diagnosed COVID-19 cases from Johns Hopkins University and data from the European Social Survey and other sources were used to estimate bivariate associations between cumulative reported case numbers at ten-day intervals and nine social, demographic, and economic variables. To avoid overfitting, we first reduce these variables to three factors by factor analysis before conducting a multiple regression analysis. We also perform a sensitivity analysis using rates and new cases between two time periods. Results showed that social and economic factors are strongly and positively associated with COVID-19 throughout the studied period, while the association with population density and cultural factors was initially low, but by April, was higher than the earlier mentioned factors. For future influenza-like pandemics, implementing strict movement restrictions from early on will be crucial to curb the spread of such diseases in economically, socially, and culturally vibrant and densely populated countries.
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Monod M, Blenkinsop A, Xi X, Hebert D, Bershan S, Tietze S, Baguelin M, Bradley VC, Chen Y, Coupland H, Filippi S, Ish-Horowicz J, McManus M, Mellan T, Gandy A, Hutchinson M, Unwin HJT, van Elsland SL, Vollmer MAC, Weber S, Zhu H, Bezancon A, Ferguson NM, Mishra S, Flaxman S, Bhatt S, Ratmann O. Age groups that sustain resurging COVID-19 epidemics in the United States. Science 2021; 371:eabe8372. [PMID: 33531384 PMCID: PMC8101272 DOI: 10.1126/science.abe8372] [Citation(s) in RCA: 177] [Impact Index Per Article: 59.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2020] [Accepted: 01/27/2021] [Indexed: 12/12/2022]
Abstract
After initial declines, in mid-2020 a resurgence in transmission of novel coronavirus disease (COVID-19) occurred in the United States and Europe. As efforts to control COVID-19 disease are reintensified, understanding the age demographics driving transmission and how these affect the loosening of interventions is crucial. We analyze aggregated, age-specific mobility trends from more than 10 million individuals in the United States and link these mechanistically to age-specific COVID-19 mortality data. We estimate that as of October 2020, individuals aged 20 to 49 are the only age groups sustaining resurgent SARS-CoV-2 transmission with reproduction numbers well above one and that at least 65 of 100 COVID-19 infections originate from individuals aged 20 to 49 in the United States. Targeting interventions-including transmission-blocking vaccines-to adults aged 20 to 49 is an important consideration in halting resurgent epidemics and preventing COVID-19-attributable deaths.
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Affiliation(s)
- Mélodie Monod
- Department of Mathematics, Imperial College London, London, UK
| | | | - Xiaoyue Xi
- Department of Mathematics, Imperial College London, London, UK
| | | | | | | | - Marc Baguelin
- MRC Centre for Global Infectious Disease Analysis; and the Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), School of Public Health, Imperial College London, London, UK
| | | | - Yu Chen
- Department of Mathematics, Imperial College London, London, UK
| | - Helen Coupland
- MRC Centre for Global Infectious Disease Analysis; and the Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), School of Public Health, Imperial College London, London, UK
| | - Sarah Filippi
- Department of Mathematics, Imperial College London, London, UK
| | | | - Martin McManus
- Department of Mathematics, Imperial College London, London, UK
| | - Thomas Mellan
- MRC Centre for Global Infectious Disease Analysis; and the Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), School of Public Health, Imperial College London, London, UK
| | - Axel Gandy
- Department of Mathematics, Imperial College London, London, UK
| | | | - H Juliette T Unwin
- MRC Centre for Global Infectious Disease Analysis; and the Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), School of Public Health, Imperial College London, London, UK
| | - Sabine L van Elsland
- MRC Centre for Global Infectious Disease Analysis; and the Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), School of Public Health, Imperial College London, London, UK
| | - Michaela A C Vollmer
- MRC Centre for Global Infectious Disease Analysis; and the Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), School of Public Health, Imperial College London, London, UK
| | | | - Harrison Zhu
- Department of Mathematics, Imperial College London, London, UK
| | | | - Neil M Ferguson
- MRC Centre for Global Infectious Disease Analysis; and the Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), School of Public Health, Imperial College London, London, UK
| | - Swapnil Mishra
- MRC Centre for Global Infectious Disease Analysis; and the Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), School of Public Health, Imperial College London, London, UK
| | - Seth Flaxman
- Department of Mathematics, Imperial College London, London, UK.
| | - Samir Bhatt
- MRC Centre for Global Infectious Disease Analysis; and the Abdul Latif Jameel Institute for Disease and Emergency Analytics (J-IDEA), School of Public Health, Imperial College London, London, UK.
- Section of Epidemiology, Department of Public Health, University of Copenhagen, Denmark
| | - Oliver Ratmann
- Department of Mathematics, Imperial College London, London, UK.
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Singh DE, Marinescu MC, Guzmán-Merino M, Durán C, Delgado-Sanz C, Gomez-Barroso D, Carretero J. Simulation of COVID-19 Propagation Scenarios in the Madrid Metropolitan Area. Front Public Health 2021; 9:636023. [PMID: 33796497 PMCID: PMC8007867 DOI: 10.3389/fpubh.2021.636023] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 02/11/2021] [Indexed: 12/23/2022] Open
Abstract
This work presents simulation results for different mitigation and confinement scenarios for the propagation of COVID-19 in the metropolitan area of Madrid. These scenarios were implemented and tested using EpiGraph, an epidemic simulator which has been extended to simulate COVID-19 propagation. EpiGraph implements a social interaction model, which realistically captures a large number of characteristics of individuals and groups, as well as their individual interconnections, which are extracted from connection patterns in social networks. Besides the epidemiological and social interaction components, it also models people's short and long-distance movements as part of a transportation model. These features, together with the capacity to simulate scenarios with millions of individuals and apply different contention and mitigation measures, gives EpiGraph the potential to reproduce the COVID-19 evolution and study medium-term effects of the virus when applying mitigation methods. EpiGraph, obtains closely aligned infected and death curves related to the first wave in the Madrid metropolitan area, achieving similar seroprevalence values. We also show that selective lockdown for people over 60 would reduce the number of deaths. In addition, evaluate the effect of the use of face masks after the first wave, which shows that the percentage of people that comply with mask use is a crucial factor for mitigating the infection's spread.
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Affiliation(s)
- David E Singh
- Department Computer Science, Universidad Carlos III de Madrid, Leganés, Spain
| | | | | | - Christian Durán
- Department Computer Science, Universidad Carlos III de Madrid, Leganés, Spain
| | - Concepción Delgado-Sanz
- CIBER en Epidemiología y Salud Pública (CIBERESP), Madrid, Spain.,National Centre for Epidemiology, Carlos III Institute of Health, Madrid, Spain
| | - Diana Gomez-Barroso
- CIBER en Epidemiología y Salud Pública (CIBERESP), Madrid, Spain.,National Centre for Epidemiology, Carlos III Institute of Health, Madrid, Spain
| | - Jesus Carretero
- Department Computer Science, Universidad Carlos III de Madrid, Leganés, Spain
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11
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Crawford FW, Jones SA, Cartter M, Dean SG, Warren JL, Li ZR, Barbieri J, Campbell J, Kenney P, Valleau T, Morozova O. Impact of close interpersonal contact on COVID-19 incidence: evidence from one year of mobile device data. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2021:2021.03.10.21253282. [PMID: 33758869 PMCID: PMC7987027 DOI: 10.1101/2021.03.10.21253282] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Abstract
Close contact between people is the primary route for transmission of SARS-CoV-2, the virus that causes coronavirus disease 2019 (COVID-19). We sought to quantify interpersonal contact at the population-level by using anonymized mobile device geolocation data. We computed the frequency of contact (within six feet) between people in Connecticut during February 2020 - January 2021. Then we aggregated counts of contact events by area of residence to obtain an estimate of the total intensity of interpersonal contact experienced by residents of each town for each day. When incorporated into a susceptible-exposed-infective-removed (SEIR) model of COVID-19 transmission, the contact rate accurately predicted COVID-19 cases in Connecticut towns during the timespan. The pattern of contact rate in Connecticut explains the large initial wave of infections during March-April, the subsequent drop in cases during June-August, local outbreaks during August-September, broad statewide resurgence during September-December, and decline in January 2021. Contact rate data can help guide public health messaging campaigns to encourage social distancing and in the allocation of testing resources to detect or prevent emerging local outbreaks more quickly than traditional case investigation. ONE SENTENCE SUMMARY Close interpersonal contact measured using mobile device location data explains dynamics of COVID-19 transmission in Connecticut during the first year of the pandemic.
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Affiliation(s)
- Forrest W Crawford
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
- Department of Statistics & Data Science, Yale University, New Haven, CT, USA
- Department of Ecology & Evolutionary Biology, Yale University, New Haven, CT, USA
- Yale School of Management, New Haven, CT, USA
| | - Sydney A Jones
- Epidemic Intelligence Service, Centers for Disease Control & Prevention, Atlanta, GA, USA
- Infectious Diseases Section, Connecticut Department of Public Health, New Haven, CT, USA
| | - Matthew Cartter
- Infectious Diseases Section, Connecticut Department of Public Health, New Haven, CT, USA
| | - Samantha G Dean
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
| | - Joshua L Warren
- Department of Biostatistics, Yale School of Public Health, New Haven, CT, USA
| | - Zehang Richard Li
- Department of Statistics, University of California, Santa Cruz, Santa Cruz, CA, USA
| | | | | | | | | | - Olga Morozova
- Program in Public Health and Department of Family, Population and Preventive Medicine, Stony Brook University, NY, USA
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12
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Bubar KM, Reinholt K, Kissler SM, Lipsitch M, Cobey S, Grad YH, Larremore DB. Model-informed COVID-19 vaccine prioritization strategies by age and serostatus. Science 2021; 371:916-921. [PMID: 33479118 DOI: 10.1126/science:abe6959] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Accepted: 01/12/2021] [Indexed: 05/25/2023]
Abstract
Limited initial supply of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine raises the question of how to prioritize available doses. We used a mathematical model to compare five age-stratified prioritization strategies. A highly effective transmission-blocking vaccine prioritized to adults ages 20 to 49 years minimized cumulative incidence, but mortality and years of life lost were minimized in most scenarios when the vaccine was prioritized to adults greater than 60 years old. Use of individual-level serological tests to redirect doses to seronegative individuals improved the marginal impact of each dose while potentially reducing existing inequities in COVID-19 impact. Although maximum impact prioritization strategies were broadly consistent across countries, transmission rates, vaccination rollout speeds, and estimates of naturally acquired immunity, this framework can be used to compare impacts of prioritization strategies across contexts.
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Affiliation(s)
- Kate M Bubar
- Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO 80309, USA.
- IQ Biology Program, University of Colorado Boulder, Boulder, CO 80303, USA
| | - Kyle Reinholt
- Department of Computer Science, University of Colorado Boulder, Boulder, CO 80309, USA
| | - Stephen M Kissler
- Department of Immunology and Infectious Diseases, Harvard T. H. Chan School of Public Health, Boston, MA 02115, USA
| | - Marc Lipsitch
- Department of Immunology and Infectious Diseases, Harvard T. H. Chan School of Public Health, Boston, MA 02115, USA
- Center for Communicable Disease Dynamics, Harvard T. H. Chan School of Public Health, Boston, MA 02115, USA
| | - Sarah Cobey
- Department of Ecology and Evolution, University of Chicago, Chicago, IL 60637, USA
| | - Yonatan H Grad
- Department of Immunology and Infectious Diseases, Harvard T. H. Chan School of Public Health, Boston, MA 02115, USA
| | - Daniel B Larremore
- Department of Computer Science, University of Colorado Boulder, Boulder, CO 80309, USA.
- BioFrontiers Institute, University of Colorado Boulder, Boulder, CO 80303, USA
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13
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Bubar KM, Reinholt K, Kissler SM, Lipsitch M, Cobey S, Grad YH, Larremore DB. Model-informed COVID-19 vaccine prioritization strategies by age and serostatus. Science 2021; 371:916-921. [PMID: 33479118 PMCID: PMC7963218 DOI: 10.1126/science.abe6959] [Citation(s) in RCA: 407] [Impact Index Per Article: 135.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Accepted: 01/12/2021] [Indexed: 12/12/2022]
Abstract
Limited initial supply of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine raises the question of how to prioritize available doses. We used a mathematical model to compare five age-stratified prioritization strategies. A highly effective transmission-blocking vaccine prioritized to adults ages 20 to 49 years minimized cumulative incidence, but mortality and years of life lost were minimized in most scenarios when the vaccine was prioritized to adults greater than 60 years old. Use of individual-level serological tests to redirect doses to seronegative individuals improved the marginal impact of each dose while potentially reducing existing inequities in COVID-19 impact. Although maximum impact prioritization strategies were broadly consistent across countries, transmission rates, vaccination rollout speeds, and estimates of naturally acquired immunity, this framework can be used to compare impacts of prioritization strategies across contexts.
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Affiliation(s)
- Kate M Bubar
- Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO 80309, USA.
- IQ Biology Program, University of Colorado Boulder, Boulder, CO 80303, USA
| | - Kyle Reinholt
- Department of Computer Science, University of Colorado Boulder, Boulder, CO 80309, USA
| | - Stephen M Kissler
- Department of Immunology and Infectious Diseases, Harvard T. H. Chan School of Public Health, Boston, MA 02115, USA
| | - Marc Lipsitch
- Department of Immunology and Infectious Diseases, Harvard T. H. Chan School of Public Health, Boston, MA 02115, USA
- Center for Communicable Disease Dynamics, Harvard T. H. Chan School of Public Health, Boston, MA 02115, USA
| | - Sarah Cobey
- Department of Ecology and Evolution, University of Chicago, Chicago, IL 60637, USA
| | - Yonatan H Grad
- Department of Immunology and Infectious Diseases, Harvard T. H. Chan School of Public Health, Boston, MA 02115, USA
| | - Daniel B Larremore
- Department of Computer Science, University of Colorado Boulder, Boulder, CO 80309, USA.
- BioFrontiers Institute, University of Colorado Boulder, Boulder, CO 80303, USA
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14
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Bubar KM, Reinholt K, Kissler SM, Lipsitch M, Cobey S, Grad YH, Larremore DB. Model-informed COVID-19 vaccine prioritization strategies by age and serostatus. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2021:2020.09.08.20190629. [PMID: 33330882 PMCID: PMC7743091 DOI: 10.1101/2020.09.08.20190629] [Citation(s) in RCA: 57] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Limited initial supply of SARS-CoV-2 vaccine raises the question of how to prioritize available doses. Here, we used a mathematical model to compare five age-stratified prioritization strategies. A highly effective transmission-blocking vaccine prioritized to adults ages 20-49 years minimized cumulative incidence, but mortality and years of life lost were minimized in most scenarios when the vaccine was prioritized to adults over 60 years old. Use of individual-level serological tests to redirect doses to seronegative individuals improved the marginal impact of each dose while potentially reducing existing inequities in COVID-19 impact. While maximum impact prioritization strategies were broadly consistent across countries, transmission rates, vaccination rollout speeds, and estimates of naturally acquired immunity, this framework can be used to compare impacts of prioritization strategies across contexts.
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Affiliation(s)
- Kate M. Bubar
- Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO, 80303, USA
- IQ Biology Program, University of Colorado Boulder, Boulder, CO, 80309, USA
| | - Kyle Reinholt
- Department of Computer Science, University of Colorado Boulder, Boulder, CO, 80309, USA
| | - Stephen M. Kissler
- Department of Immunology and Infectious Diseases, Harvard T.H. Chan School of Public Health, Boston, MA, 02115, USA
| | - Marc Lipsitch
- Department of Immunology and Infectious Diseases, Harvard T.H. Chan School of Public Health, Boston, MA, 02115, USA
- Center for Communicable Disease Dynamics, Harvard T.H. Chan School of Public Health, Boston, MA, 02115, USA
| | - Sarah Cobey
- Department of Ecology and Evolution, University of Chicago, Chicago, IL, 60637, USA
| | - Yonatan H. Grad
- Department of Immunology and Infectious Diseases, Harvard T.H. Chan School of Public Health, Boston, MA, 02115, USA
| | - Daniel B. Larremore
- Department of Computer Science, University of Colorado Boulder, Boulder, CO, 80309, USA
- BioFrontiers Institute, University of Colorado Boulder, Boulder, CO, 80303, USA
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15
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Eggo RM, Dawa J, Kucharski AJ, Cucunuba ZM. The importance of local context in COVID-19 models. NATURE COMPUTATIONAL SCIENCE 2021; 1:6-8. [PMID: 38217154 DOI: 10.1038/s43588-020-00014-7] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Affiliation(s)
- Rosalind M Eggo
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK.
| | - Jeanette Dawa
- College of Health Sciences, University of Nairobi, Nairobi, Kenya
- Washington State University, Global Health Programs, Nairobi, Kenya
| | - Adam J Kucharski
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, London, UK
| | - Zulma M Cucunuba
- MRC Centre for Global Infectious Disease Analysis, School of Public Health, Imperial College London, London, UK
- Faculty of Medicine, Pontificia Universidad Javeriana, Bogotá, Colombia
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16
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van Zandvoort K, Jarvis CI, Pearson CAB, Davies NG, Ratnayake R, Russell TW, Kucharski AJ, Jit M, Flasche S, Eggo RM, Checchi F. Response strategies for COVID-19 epidemics in African settings: a mathematical modelling study. BMC Med 2020; 18:324. [PMID: 33050951 PMCID: PMC7553800 DOI: 10.1186/s12916-020-01789-2] [Citation(s) in RCA: 44] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/26/2020] [Accepted: 09/22/2020] [Indexed: 12/26/2022] Open
Abstract
BACKGROUND The health impact of COVID-19 may differ in African settings as compared to countries in Europe or China due to demographic, epidemiological, environmental and socio-economic factors. We evaluated strategies to reduce SARS-CoV-2 burden in African countries, so as to support decisions that balance minimising mortality, protecting health services and safeguarding livelihoods. METHODS We used a Susceptible-Exposed-Infectious-Recovered mathematical model, stratified by age, to predict the evolution of COVID-19 epidemics in three countries representing a range of age distributions in Africa (from oldest to youngest average age: Mauritius, Nigeria and Niger), under various effectiveness assumptions for combinations of different non-pharmaceutical interventions: self-isolation of symptomatic people, physical distancing and 'shielding' (physical isolation) of the high-risk population. We adapted model parameters to better represent uncertainty about what might be expected in African populations, in particular by shifting the distribution of severity risk towards younger ages and increasing the case-fatality ratio. We also present sensitivity analyses for key model parameters subject to uncertainty. RESULTS We predicted median symptomatic attack rates over the first 12 months of 23% (Niger) to 42% (Mauritius), peaking at 2-4 months, if epidemics were unmitigated. Self-isolation while symptomatic had a maximum impact of about 30% on reducing severe cases, while the impact of physical distancing varied widely depending on percent contact reduction and R0. The effect of shielding high-risk people, e.g. by rehousing them in physical isolation, was sensitive mainly to residual contact with low-risk people, and to a lesser extent to contact among shielded individuals. Mitigation strategies incorporating self-isolation of symptomatic individuals, moderate physical distancing and high uptake of shielding reduced predicted peak bed demand and mortality by around 50%. Lockdowns delayed epidemics by about 3 months. Estimates were sensitive to differences in age-specific social mixing patterns, as published in the literature, and assumptions on transmissibility, infectiousness of asymptomatic cases and risk of severe disease or death by age. CONCLUSIONS In African settings, as elsewhere, current evidence suggests large COVID-19 epidemics are expected. However, African countries have fewer means to suppress transmission and manage cases. We found that self-isolation of symptomatic persons and general physical distancing are unlikely to avert very large epidemics, unless distancing takes the form of stringent lockdown measures. However, both interventions help to mitigate the epidemic. Shielding of high-risk individuals can reduce health service demand and, even more markedly, mortality if it features high uptake and low contact of shielded and unshielded people, with no increase in contact among shielded people. Strategies combining self-isolation, moderate physical distancing and shielding could achieve substantial reductions in mortality in African countries. Temporary lockdowns, where socioeconomically acceptable, can help gain crucial time for planning and expanding health service capacity.
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Affiliation(s)
- Kevin van Zandvoort
- Department of Infectious Disease Epidemiology, Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, Keppel Street,, London, WC1E 7HT, UK.
| | - Christopher I Jarvis
- Department of Infectious Disease Epidemiology, Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, Keppel Street,, London, WC1E 7HT, UK
| | - Carl A B Pearson
- Department of Infectious Disease Epidemiology, Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, Keppel Street,, London, WC1E 7HT, UK
- South African Centre for Epidemiological Modelling and Analysis, Stellenbosch University, Stellenbosch, Republic of South Africa
| | - Nicholas G Davies
- Department of Infectious Disease Epidemiology, Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, Keppel Street,, London, WC1E 7HT, UK
| | - Ruwan Ratnayake
- Department of Infectious Disease Epidemiology, Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, Keppel Street,, London, WC1E 7HT, UK
| | - Timothy W Russell
- Department of Infectious Disease Epidemiology, Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, Keppel Street,, London, WC1E 7HT, UK
| | - Adam J Kucharski
- Department of Infectious Disease Epidemiology, Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, Keppel Street,, London, WC1E 7HT, UK
| | - Mark Jit
- Department of Infectious Disease Epidemiology, Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, Keppel Street,, London, WC1E 7HT, UK
| | - Stefan Flasche
- Department of Infectious Disease Epidemiology, Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, Keppel Street,, London, WC1E 7HT, UK
| | - Rosalind M Eggo
- Department of Infectious Disease Epidemiology, Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene and Tropical Medicine, Keppel Street,, London, WC1E 7HT, UK
| | - Francesco Checchi
- Department of Infectious Disease Epidemiology, Health in Humanitarian Crises Centre, London School of Hygiene & Tropical Medicine, Keppel Street, London, WC1E 7HT, UK
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