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Kwak M, Sun X, Wi Y, Nah K, Kim Y, Jin H. A novel indicator in epidemic monitoring through a case study of Ebola in West Africa (2014-2016). Sci Rep 2024; 14:12147. [PMID: 38802461 PMCID: PMC11130319 DOI: 10.1038/s41598-024-62719-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Accepted: 05/21/2024] [Indexed: 05/29/2024] Open
Abstract
The E/S (exposed/susceptible) ratio is analyzed in the SEIR model. The ratio plays a key role in understanding epidemic dynamics during the 2014-2016 Ebola outbreak in Sierra Leone and Guinea. The maximum value of the ratio occurs immediately before or after the time-dependent reproduction number (Rt) equals 1, depending on the initial susceptible population (S(0)). It is demonstrated that transmission rate curves corresponding to various incubation periods intersect at a single point referred to as the Cross Point (CP). At this point, the E/S ratio reaches an extremum, signifying a critical shift in transmission dynamics and aligning with the time when Rt approaches 1. By plotting transmission rate curves, β(t), for any two arbitrary incubation periods and tracking their intersections, we can trace CP over time. CP serves as an indicator of epidemic status, especially when Rt is close to 1. It provides a practical means of monitoring epidemics without prior knowledge of the incubation period. Through a case study, we estimate the transmission rate and reproduction number, identifying CP and Rt = 1 while examining the E/S ratio across various values of S(0).
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Affiliation(s)
- Minkyu Kwak
- Department of Mathematics and Statistics, Chonnam National University, Gwangju, South Korea
| | - Xiuxiu Sun
- Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Henan, China
| | - Yunju Wi
- Department of Mathematics and Statistics, Chonnam National University, Gwangju, South Korea
| | - Kyeongah Nah
- Busan Center for Medical Mathematics, National Institute of Mathematical Sciences, Busan, South Korea
| | - Yongkuk Kim
- Department of Mathematics, Kyungpook National University, Daegu, South Korea
| | - Hongsung Jin
- Department of Mathematics and Statistics, Chonnam National University, Gwangju, South Korea.
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Dall’Amico L, Kleynhans J, Gauvin L, Tizzoni M, Ozella L, Makhasi M, Wolter N, Language B, Wagner RG, Cohen C, Tempia S, Cattuto C. Estimating household contact matrices structure from easily collectable metadata. PLoS One 2024; 19:e0296810. [PMID: 38483886 PMCID: PMC10939291 DOI: 10.1371/journal.pone.0296810] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 12/18/2023] [Indexed: 03/17/2024] Open
Abstract
Contact matrices are a commonly adopted data representation, used to develop compartmental models for epidemic spreading, accounting for the contact heterogeneities across age groups. Their estimation, however, is generally time and effort consuming and model-driven strategies to quantify the contacts are often needed. In this article we focus on household contact matrices, describing the contacts among the members of a family and develop a parametric model to describe them. This model combines demographic and easily quantifiable survey-based data and is tested on high resolution proximity data collected in two sites in South Africa. Given its simplicity and interpretability, we expect our method to be easily applied to other contexts as well and we identify relevant questions that need to be addressed during the data collection procedure.
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Affiliation(s)
| | - Jackie Kleynhans
- National Institute for Communicable Diseases of the National Health Laboratory Service, Johannesburg, South Africa
- School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa
| | - Laetitia Gauvin
- ISI Foundation, Turin, Italy
- Institute for Research on sustainable Development, UMR215 PRODIG, Aubervilliers, France
| | - Michele Tizzoni
- ISI Foundation, Turin, Italy
- Department of Sociology and Social Research, University of Trento, Trento, Italy
| | | | - Mvuyo Makhasi
- National Institute for Communicable Diseases of the National Health Laboratory Service, Johannesburg, South Africa
| | - Nicole Wolter
- National Institute for Communicable Diseases of the National Health Laboratory Service, Johannesburg, South Africa
- School of Pathology, University of the Witwatersrand, Johannesburg, South Africa
| | - Brigitte Language
- Unit for Environmental Science and Management, Climatology Research Group, North-West University, Potchefstroom, South Africa
| | - Ryan G. Wagner
- MRC/Wits Rural Public Health and Health Transitions Research Unit (Agincourt), Agincourt, South Africa
| | - Cheryl Cohen
- National Institute for Communicable Diseases of the National Health Laboratory Service, Johannesburg, South Africa
- School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa
| | - Stefano Tempia
- National Institute for Communicable Diseases of the National Health Laboratory Service, Johannesburg, South Africa
- School of Public Health, Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, South Africa
| | - Ciro Cattuto
- ISI Foundation, Turin, Italy
- Department of Informatics, University of Turin, Turin, Italy
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Banholzer N, Lison A, Özcelik D, Stadler T, Feuerriegel S, Vach W. The methodologies to assess the effectiveness of non-pharmaceutical interventions during COVID-19: a systematic review. Eur J Epidemiol 2022; 37:1003-1024. [PMID: 36152133 PMCID: PMC9510554 DOI: 10.1007/s10654-022-00908-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2022] [Accepted: 07/15/2022] [Indexed: 11/26/2022]
Abstract
Non-pharmaceutical interventions, such as school closures and stay-at-home orders, have been implemented around the world to control the spread of SARS-CoV-2. Their effectiveness in improving health-related outcomes has been the subject of numerous empirical studies. However, these studies show fairly large variation among methodologies in use, reflecting the absence of an established methodological framework. On the one hand, variation in methodologies may be desirable to assess the robustness of results; on the other hand, a lack of common standards can impede comparability among studies. To establish a comprehensive overview over the methodologies in use, we conducted a systematic review of studies assessing the effectiveness of non-pharmaceutical interventions between January 1, 2020 and January 12, 2021 (n = 248). We identified substantial variation in methodologies with respect to study setting, outcome, intervention, methodological approach, and effectiveness assessment. On this basis, we point to shortcomings of existing studies and make recommendations for the design of future studies.
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Affiliation(s)
- Nicolas Banholzer
- Department of Management, Technology, and Economics, ETH Zurich, Zurich, Switzerland.
| | - Adrian Lison
- Department of Biosystems Science and Engineering, ETH Zurich, Zurich, Switzerland.
| | - Dennis Özcelik
- Chemistry | Biology | Pharmacy Information Center, ETH Zurich, Zurich, Switzerland
| | - Tanja Stadler
- Department of Biosystems Science and Engineering, ETH Zurich, Zurich, Switzerland
| | - Stefan Feuerriegel
- Department of Management, Technology, and Economics, ETH Zurich, Zurich, Switzerland
- LMU Munich School of Management, LMU Munich, Munich, Germany
| | - Werner Vach
- Basel Academy for Quality and Research in Medicine, Basel, Switzerland
- Department of Environmental Sciences, University of Basel, Basel, Switzerland
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Wang X, Han Q, Kong JD. Studying the mixed transmission in a community with age heterogeneity: COVID-19 as a case study. Infect Dis Model 2022; 7:250-260. [PMID: 35665302 PMCID: PMC9142179 DOI: 10.1016/j.idm.2022.05.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2022] [Revised: 05/22/2022] [Accepted: 05/22/2022] [Indexed: 11/02/2022] Open
Abstract
COVID-19 has been prevalent worldwide for about 2 years now and has brought unprecedented challenges to our society. Before vaccines were available, the main disease intervention strategies were non-pharmaceutical. Starting December 2020, in Ontario, Canada, vaccines were approved for administering to vulnerable individuals and gradually expanded to all individuals above the age of 12. As the vaccine coverage reached a satisfactory level among the eligible population, normal social activities resumed and schools reopened starting September 2021. However, when schools reopen for in-person learning, children under the age of 12 are unvaccinated and are at higher risks of contracting the virus. We propose an age-stratified model based on the age and vaccine eligibility of the individuals. We fit our model to the data in Ontario, Canada and obtain a good fitting result. The results show that a relaxed between-group contact rate may trigger future epidemic waves more easily than an increased within-group contact rate. An increasing mixed contact rate of the older group quickly amplifies the daily incidence numbers for both groups whereas an increasing mixed contact rate of the younger group mainly leads to future waves in the younger group alone. The results indicate the importance of accelerating vaccine rollout for younger individuals in mitigating disease spread.
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David J, Bragazzi NL, Scarabel F, McCarthy Z, Wu J. Non-pharmaceutical intervention levels to reduce the COVID-19 attack ratio among children. ROYAL SOCIETY OPEN SCIENCE 2022; 9:211863. [PMID: 35308622 PMCID: PMC8924746 DOI: 10.1098/rsos.211863] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 02/25/2022] [Indexed: 05/03/2023]
Abstract
The attack ratio in a subpopulation is defined as the total number of infections over the total number of individuals in this subpopulation. Using a methodology based on an age-stratified transmission dynamics model, we estimated the attack ratio of COVID-19 among children (individuals 0-11 years) when a large proportion of individuals eligible for vaccination (age 12 and above) are vaccinated to contain the epidemic among this subpopulation, or the effective herd immunity (with additional physical distancing measures). We describe the relationship between the attack ratio among children, the time to remove infected individuals from the transmission chain and the children-to-children daily contact rate while considering the increased transmissibility of virus variants (using the Delta variant as an example). We illustrate the generality and applicability of the methodology established by performing an analysis of the attack ratio of COVID-19 among children in the population of Canada and in its province of Ontario. The clinical attack ratio, defined as the number of symptomatic infections over the total population, can be informed from the attack ratio and both can be reduced substantially via a combination of reduced social mixing and rapid testing and isolation of the children.
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Affiliation(s)
- Jummy David
- Fields-CQAM Laboratory of Mathematics for Public Health (MfPH), York University, Toronto, Ontario, Canada
- Laboratory for Industrial and Applied Mathematics, York University, Toronto, Ontario, Canada
| | - Nicola Luigi Bragazzi
- Fields-CQAM Laboratory of Mathematics for Public Health (MfPH), York University, Toronto, Ontario, Canada
- Laboratory for Industrial and Applied Mathematics, York University, Toronto, Ontario, Canada
| | - Francesca Scarabel
- Department of Mathematics, The University of Manchester, Manchester, UK
- Joint UNIversities Pandemic and Epidemiological Research (JUNIPER), UK
- CDLab - Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Italy
| | - Zachary McCarthy
- Fields-CQAM Laboratory of Mathematics for Public Health (MfPH), York University, Toronto, Ontario, Canada
- Laboratory for Industrial and Applied Mathematics, York University, Toronto, Ontario, Canada
| | - Jianhong Wu
- Fields-CQAM Laboratory of Mathematics for Public Health (MfPH), York University, Toronto, Ontario, Canada
- Laboratory for Industrial and Applied Mathematics, York University, Toronto, Ontario, Canada
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Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models. ENTROPY 2022; 24:e24020216. [PMID: 35205511 PMCID: PMC8871447 DOI: 10.3390/e24020216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/07/2022] [Revised: 01/21/2022] [Accepted: 01/25/2022] [Indexed: 11/17/2022]
Abstract
The spread of the COVID-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modeling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated, resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth distribution based on binary wealth exchanges. The interplay between wealth exchanges and the progress of the infectious disease is realized by assuming, on the one hand, that individuals in different compartments act differently in the economic process and, on the other hand, that the epidemic affects risk in economic transactions. Using the mathematical tools of kinetic theory, it is possible to identify the equilibrium states of the system and the formation of inequalities due to the pandemic in the wealth distribution of the population. Numerical experiments highlight the importance of the vaccination campaign and its positive effects in reducing economic inequalities in the multi-agent society.
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Silk MJ, Carrignon S, Bentley RA, Fefferman NH. Observations and conversations: how communities learn about infection risk can impact the success of non-pharmaceutical interventions against epidemics. BMC Public Health 2022; 22:13. [PMID: 34986810 PMCID: PMC8729323 DOI: 10.1186/s12889-021-12353-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Accepted: 11/24/2021] [Indexed: 12/24/2022] Open
Abstract
BACKGROUND Individual behavioural decisions are responses to a person's perceived social norms that could be shaped by both their physical and social environment. In the context of the COVID-19 pandemic, these environments correspond to epidemiological risk from contacts and the social construction of risk by communication within networks of friends. Understanding the circumstances under which the influence of these different social networks can promote the acceptance of non-pharmaceutical interventions and consequently the adoption of protective behaviours is critical for guiding useful, practical public health messaging. METHODS We explore how information from both physical contact and social communication layers of a multiplex network can contribute to flattening the epidemic curve in a community. Connections in the physical contact layer represent opportunities for transmission, while connections in the communication layer represent social interactions through which individuals may gain information, e.g. messaging friends. RESULTS We show that maintaining focus on awareness of risk among each individual's physical contacts promotes the greatest reduction in disease spread, but only when an individual is aware of the symptoms of a non-trivial proportion of their physical contacts (~ ≥ 20%). Information from the social communication layer without was less useful when these connections matched less well with physical contacts and contributed little in combination with accurate information from physical contacts. CONCLUSIONS We conclude that maintaining social focus on local outbreak status will allow individuals to structure their perceived social norms appropriately and respond more rapidly when risk increases. Finding ways to relay accurate local information from trusted community leaders could improve mitigation even where more intrusive/costly strategies, such as contact-tracing, are not possible.
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Affiliation(s)
- Matthew J Silk
- Centre for Ecology and Conservation, University of Exeter Penryn Campus, Penryn, UK
- Environment and Sustainability Institute, University of Exeter, Exeter, UK
- National Institute for Mathematical and Biological Synthesis (NIMBioS), University of Tennessee, Knoxville, TN, USA
| | - Simon Carrignon
- Center for the Dynamics of Social Complexity (DySoC), University of Tennessee, Knoxville, TN, USA
- Department of Anthropology, University of Tennessee, Knoxville, TN, USA
- School of Information Science, University of Tennessee, Knoxville, TN, USA
| | - R Alexander Bentley
- Center for the Dynamics of Social Complexity (DySoC), University of Tennessee, Knoxville, TN, USA
- Department of Anthropology, University of Tennessee, Knoxville, TN, USA
| | - Nina H Fefferman
- National Institute for Mathematical and Biological Synthesis (NIMBioS), University of Tennessee, Knoxville, TN, USA.
- Department of Ecology and Evolutionary Biology & Mathematics, University of Tennessee, 447 Hesler Biology Building, Knoxville, TN, 37996, USA.
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Xiao Y, Chen S, Zhu Y, McCarthy Z, Bragazzi NL, Asgary A, Wu J. Optimal Reopening Pathways With COVID-19 Vaccine Rollout and Emerging Variants of Concern. Front Public Health 2021; 9:729141. [PMID: 34557471 PMCID: PMC8452896 DOI: 10.3389/fpubh.2021.729141] [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: 06/22/2021] [Accepted: 08/04/2021] [Indexed: 12/03/2022] Open
Abstract
We developed a stochastic optimization technology based on a COVID-19 transmission dynamics model to determine optimal pathways from lockdown toward reopening with different scales and speeds of mass vaccine rollout in order to maximize social economical activities while not overwhelming the health system capacity in general, hospitalization beds, and intensive care units in particular. We used the Province of Ontario, Canada as a case study to demonstrate the methodology and the optimal decision trees; but our method and algorithm are generic and can be adapted to other settings. Our model framework and optimization strategies take into account the likely range of social contacts during different phases of a gradual reopening process and consider the uncertainties of these contact rates due to variations of individual behaviors and compliance. The results show that, without a mass vaccination rollout, there would be multiple optimal pathways should this strategy be adopted right after the Province's lockdown and stay-at-home order; however, once reopening has started earlier than the timing determined in the optimal pathway, an optimal pathway with similar constraints no longer exists, and sub-optimal pathways with increased demand for intensive care units can be found, but the choice is limited and the pathway is narrow. We also simulated the situation when the reopening starts after the mass vaccination has been rolled out, and we concluded that optimal pathways toward near pre-pandemic activity level is feasible given an accelerated vaccination rollout plan, with the final activity level being determined by the vaccine coverage and the transmissibility of the dominating strain.
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Affiliation(s)
- Yanyu Xiao
- Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, United States
| | - Shengyuan Chen
- Department of Mathematics and Statistics, York University, Toronto, ON, Canada
| | - Yi Zhu
- Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, ON, Canada
| | - Zachary McCarthy
- Department of Mathematics and Statistics, York University, Toronto, ON, Canada
- Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, ON, Canada
| | - Nicola Luigi Bragazzi
- Department of Mathematics and Statistics, York University, Toronto, ON, Canada
- Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, ON, Canada
| | - Ali Asgary
- Disaster and Emergency Management, School of Administrative Studies and Advanced Disaster and Emergency Rapid-Response Simulation, York University, Toronto, ON, Canada
| | - Jianhong Wu
- Department of Mathematics and Statistics, York University, Toronto, ON, Canada
- Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, Toronto, ON, Canada
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A window of opportunity for intensifying testing and tracing efforts to prevent new COVID-19 outbreaks due to more transmissible variants. CANADA COMMUNICABLE DISEASE REPORT = RELEVÉ DES MALADIES TRANSMISSIBLES AU CANADA 2021; 47:329-338. [PMID: 34667443 DOI: 10.14745/ccdr.v47i78a06] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Background When public health interventions are being loosened after several days of decline in the number of coronavirus disease 2019 (COVID-19) cases, it is of critical importance to identify potential strategies to ease restrictions while mitigating a new wave of more transmissible variants of concern (VOCs). We estimated the necessary enhancements to public health interventions for a partial reopening of the economy while avoiding the worst consequences of a new outbreak, associated with more transmissible VOCs. Methods We used a transmission dynamics model to quantify conditions that combined public health interventions must meet to reopen the economy without a large outbreak. These conditions are those that maintain the control reproduction number below unity, while accounting for an increase in transmissibility due to VOC. Results We identified combinations of the proportion of individuals exposed to the virus who are traced and quarantined before becoming infectious, the proportion of symptomatic individuals confirmed and isolated, and individual daily contact rates needed to ensure the control reproduction number remains below unity. Conclusion Our analysis indicates that the success of restrictive measures including lockdown and stay-at-home orders, as reflected by a reduction in number of cases, provides a narrow window of opportunity to intensify case detection and contact tracing efforts to prevent a new wave associated with circulation of more transmissible VOCs.
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