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Corchis-Scott R, Beach M, Geng Q, Podadera A, Corchis-Scott O, Norton J, Busch A, Faust RA, McFarlane S, Withington S, Irwin B, Aloosh M, Ng KKS, McKay RM. Wastewater Surveillance to Confirm Differences in Influenza A Infection between Michigan, USA, and Ontario, Canada, September 2022-March 2023. Emerg Infect Dis 2024; 30:1580-1588. [PMID: 39043398 PMCID: PMC11286066 DOI: 10.3201/eid3008.240225] [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] [Indexed: 07/25/2024] Open
Abstract
Wastewater surveillance is an effective way to track the prevalence of infectious agents within a community and, potentially, the spread of pathogens between jurisdictions. We conducted a retrospective wastewater surveillance study of the 2022-23 influenza season in 2 communities, Detroit, Michigan, USA, and Windsor-Essex, Ontario, Canada, that form North America's largest cross-border conurbation. We observed a positive relationship between influenza-related hospitalizations and the influenza A virus (IAV) wastewater signal in Windsor-Essex (ρ = 0.785; p<0.001) and an association between influenza-related hospitalizations in Michigan and the IAV wastewater signal for Detroit (ρ = 0.769; p<0.001). Time-lagged cross correlation and qualitative examination of wastewater signal in the monitored sewersheds showed the peak of the IAV season in Detroit was delayed behind Windsor-Essex by 3 weeks. Wastewater surveillance for IAV reflects regional differences in infection dynamics which may be influenced by many factors, including the timing of vaccine administration between jurisdictions.
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Espinosa O, Mora L, Sanabria C, Ramos A, Rincón D, Bejarano V, Rodríguez J, Barrera N, Álvarez-Moreno C, Cortés J, Saavedra C, Robayo A, Franco OH. Predictive models for health outcomes due to SARS-CoV-2, including the effect of vaccination: a systematic review. Syst Rev 2024; 13:30. [PMID: 38229123 PMCID: PMC10790449 DOI: 10.1186/s13643-023-02411-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Accepted: 12/04/2023] [Indexed: 01/18/2024] Open
Abstract
BACKGROUND The interaction between modelers and policymakers is becoming more common due to the increase in computing speed seen in recent decades. The recent pandemic caused by the SARS-CoV-2 virus was no exception. Thus, this study aims to identify and assess epidemiological mathematical models of SARS-CoV-2 applied to real-world data, including immunization for coronavirus 2019 (COVID-19). METHODOLOGY PubMed, JSTOR, medRxiv, LILACS, EconLit, and other databases were searched for studies employing epidemiological mathematical models of SARS-CoV-2 applied to real-world data. We summarized the information qualitatively, and each article included was assessed for bias risk using the Joanna Briggs Institute (JBI) and PROBAST checklist tool. The PROSPERO registration number is CRD42022344542. FINDINGS In total, 5646 articles were retrieved, of which 411 were included. Most of the information was published in 2021. The countries with the highest number of studies were the United States, Canada, China, and the United Kingdom; no studies were found in low-income countries. The SEIR model (susceptible, exposed, infectious, and recovered) was the most frequently used approach, followed by agent-based modeling. Moreover, the most commonly used software were R, Matlab, and Python, with the most recurring health outcomes being death and recovery. According to the JBI assessment, 61.4% of articles were considered to have a low risk of bias. INTERPRETATION The utilization of mathematical models increased following the onset of the SARS-CoV-2 pandemic. Stakeholders have begun to incorporate these analytical tools more extensively into public policy, enabling the construction of various scenarios for public health. This contribution adds value to informed decision-making. Therefore, understanding their advancements, strengths, and limitations is essential.
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Affiliation(s)
- Oscar Espinosa
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS) & Economic Models and Quantitative Methods Research Group, Centro de Investigaciones para el Desarrollo, Universidad Nacional de Colombia, Bogotá, D.C., Colombia.
| | - Laura Mora
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS), Bogotá, Colombia
| | - Cristian Sanabria
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS), Bogotá, Colombia
| | - Antonio Ramos
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS) & Economic Models and Quantitative Methods Research Group, Centro de Investigaciones para el Desarrollo, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Duván Rincón
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS), Bogotá, Colombia
| | - Valeria Bejarano
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS) & Economic Models and Quantitative Methods Research Group, Centro de Investigaciones para el Desarrollo, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Jhonathan Rodríguez
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS) & Economic Models and Quantitative Methods Research Group, Centro de Investigaciones para el Desarrollo, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Nicolás Barrera
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS), Bogotá, Colombia
| | | | - Jorge Cortés
- Faculty of Medicine, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Carlos Saavedra
- Faculty of Medicine, Universidad Nacional de Colombia, Bogotá, D.C., Colombia
| | - Adriana Robayo
- Directorate of Analytical, Economic and Actuarial Studies in Health, Instituto de Evaluación Tecnológica en Salud (IETS), Bogotá, Colombia
| | - Oscar H Franco
- University Medical Center Utrecht, Utrecht University & Harvard T.H. Chan School of Public Health, Harvard University, Cambridge, USA
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Noh E, Hong J, Yoo J, Jung J. Inference and forecasting phase shift regime of COVID-19 sub-lineages with a Markov-switching model. Microbiol Spectr 2023; 11:e0166923. [PMID: 37811981 PMCID: PMC10714866 DOI: 10.1128/spectrum.01669-23] [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: 04/20/2023] [Accepted: 08/23/2023] [Indexed: 10/10/2023] Open
Abstract
IMPORTANCE Using regime-switching models, we attempted to determine whether there is a link between changes in severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2) variants and infection waves, as well as forecasting new SARS-Cov-2 variants. We believe that our study makes a significant contribution to the field because it proposes a new approach for forecasting the ongoing pandemic, and the spread of other infectious diseases, using a statistical model which incorporates unpredictable factors such as human behavior, political factors, and cultural beliefs.
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Affiliation(s)
- Eul Noh
- Freddie Mac, Tysons Corner, Virginia, USA
| | - Jinwook Hong
- Artificial Intelligence and Big-Data Convergence Center, Gil Medical Center, Gachon University College of Medicine, Incheon, South Korea
| | - Joonkyung Yoo
- Department of Economics, Rutgers University--New Brunswick, New Brunswick, New Jersey, USA
| | - Jaehun Jung
- Artificial Intelligence and Big-Data Convergence Center, Gil Medical Center, Gachon University College of Medicine, Incheon, South Korea
- Department of Preventive Medicine, Gachon University College of Medicine, Incheon, South Korea
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McGill E, Coulby C, Dam D, Bellos A, McCormick R, Patterson K. Canadian COVID-19 Outbreak Surveillance System: implementation of national surveillance during a global pandemic. CANADIAN JOURNAL OF PUBLIC HEALTH = REVUE CANADIENNE DE SANTE PUBLIQUE 2023; 114:358-367. [PMID: 37074555 PMCID: PMC10116888 DOI: 10.17269/s41997-023-00766-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 03/14/2023] [Indexed: 04/20/2023]
Abstract
SETTING Early in the SARS-CoV-2 pandemic, the need to develop systematic outbreak surveillance at the national level to monitor trends in SARS-CoV-2 outbreaks was identified as a priority for the Public Health Agency of Canada (PHAC). The Canadian COVID-19 Outbreak Surveillance System (CCOSS) was established to monitor the frequency and severity of SARS-CoV-2 outbreaks across various community settings. INTERVENTION PHAC engaged with provincial/territorial partners in May 2020 to develop goals and key data elements for CCOSS. In January 2021, provincial/territorial partners began submitting cumulative outbreak line lists on a weekly basis. OUTCOMES Eight provincial and territorial partners, representing 93% of the population, submit outbreak data on the number of cases and severity indicators (hospitalizations and deaths) for 24 outbreak settings to CCOSS. Outbreak data can be integrated with national case data to supply information on case demographics, clinical outcomes, vaccination status, and variant lineages. Data aggregated to the national level are used to conduct analyses and report on outbreak trends. Evidence from CCOSS analyses has been useful in supporting provincial/territorial outbreak investigations, informing policy recommendations, and monitoring the impact of public health measures (vaccination, closures) in specific outbreak settings. IMPLICATIONS The development of a SARS-CoV-2 outbreak surveillance system complemented case-based surveillance and furthered the understanding of epidemiological trends. Further efforts are required to better understand SARS-CoV-2 outbreaks for Indigenous populations and other priority populations, as well as create linkages between genomic and epidemiological data. As SARS-CoV-2 outbreak surveillance enhanced case surveillance, outbreak surveillance should be a priority for emerging public health threats.
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Affiliation(s)
- Erin McGill
- Infectious Disease Programs Branch, Public Health Agency of Canada, Ottawa, Ontario, Canada.
| | - Cameron Coulby
- Infectious Disease Programs Branch, Public Health Agency of Canada, Ottawa, Ontario, Canada
| | - Demy Dam
- Infectious Disease Programs Branch, Public Health Agency of Canada, Ottawa, Ontario, Canada
| | - Anna Bellos
- Infectious Disease Programs Branch, Public Health Agency of Canada, Toronto, Ontario, Canada
| | - Rachel McCormick
- Infectious Disease Programs Branch, Public Health Agency of Canada, Guelph, Ontario, Canada
| | - Kaitlin Patterson
- Infectious Disease Programs Branch, Public Health Agency of Canada, Moncton, New Brunswick, Canada
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Martignoni MM, Mohammadi Z, Loredo-Osti JC, Hurford A. Extensive SARS-CoV-2 testing reveals BA.1/BA.2 asymptomatic rates and underreporting in school children. CANADA COMMUNICABLE DISEASE REPORT = RELEVE DES MALADIES TRANSMISSIBLES AU CANADA 2023; 49:155-165. [PMID: 38390394 PMCID: PMC10883462 DOI: 10.14745/ccdr.v49i04a08] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/24/2024]
Abstract
Background Case underreporting during the coronavirus disease 2019 (COVID-19) pandemic has been a major challenge to the planning and evaluation of public health responses. School children were often considered a less vulnerable population and underreporting rates may have been particularly high. In January 2022, the Canadian province of Newfoundland and Labrador (NL) was experiencing an Omicron variant outbreak (BA.1/BA.2 subvariants) and public health officials recommended that all returning students complete two rapid antigen tests (RATs) to be performed three days apart. Methods To estimate the prevalence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), we asked parents and guardians to report the results of the RATs completed by K-12 students (approximately 59,000 students) using an online survey. Results When comparing the survey responses with the number of cases and tests reported by the NL testing system, we found that one out of every 4.3 (95% CI, 3.1-5.3) positive households were captured by provincial case count, with 5.1% positivity estimated from the RAT results and 1.2% positivity reported by the provincial testing system. Of positive test results, 62.9% (95% CI, 44.3-83.0) were reported for elementary school students, and the remaining 37.1% (95% CI, 22.7-52.9) were reported for junior high and high school students. Asymptomatic infections were 59.8% of the positive cases. Given the low survey participation rate (3.5%), our results may suffer from sample selection biases and should be interpreted with caution. Conclusion The underreporting ratio is consistent with ratios calculated from serology data and provides insights into infection prevalence and asymptomatic infections in school children; a currently understudied population.
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Affiliation(s)
- Maria M Martignoni
- Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL
| | - Zahra Mohammadi
- Department of Mathematics and Statistics, University of Guelph, Guelph, ON
| | | | - Amy Hurford
- Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL
- Biology Department, Memorial University of Newfoundland, St. John's, NL
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Chen Y, Song H, Liu S. Evaluations of COVID-19 epidemic models with multiple susceptible compartments using exponential and non-exponential distribution for disease stages. Infect Dis Model 2022; 7:795-810. [PMID: 36439948 PMCID: PMC9681122 DOI: 10.1016/j.idm.2022.11.004] [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: 08/31/2022] [Revised: 11/07/2022] [Accepted: 11/08/2022] [Indexed: 11/16/2022] Open
Abstract
Mathematical models have wide applications in studying COVID-19 epidemic transmission dynamics, however, most mathematical models do not take into account the heterogeneity of susceptible populations and the non-exponential distribution infectious period. This paper attempts to investigate whether non-exponentially distributed infectious period can better characterize the transmission process in heterogeneous susceptible populations and how it impacts the control strategies. For this purpose, we establish two COVID-19 epidemic models with heterogeneous susceptible populations based on different assumptions for infectious period: the first one is an exponential distribution model (EDM), and the other one is a gamma distribution model (GDM); explicit formula of peak time of the EDM is presented via our analytical approach. By data fitting with the COVID-19 (Omicron) epidemic in Spain and Norway, it seems that Spain is more suitable for EDM while Norway is more suitable for GDM. Finally, we use EDM and GDM to evaluate the impaction of control strategies such as reduction of transmission rates, and increase of primary course rate (PCR) and booster dose rate (BDR).
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Affiliation(s)
- Yan Chen
- School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China
| | - Haitao Song
- Complex Systems Research Center, Shanxi University, Taiyuan, 030006, China
| | - Shengqiang Liu
- School of Mathematical Sciences, Tiangong University, Tianjin, 300387, China
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Yuan P, Tan Y, Yang L, Aruffo E, Ogden NH, Bélair J, Arino J, Heffernan J, Watmough J, Carabin H, Zhu H. Modeling vaccination and control strategies for outbreaks of monkeypox at gatherings. Front Public Health 2022; 10:1026489. [PMID: 36504958 PMCID: PMC9732364 DOI: 10.3389/fpubh.2022.1026489] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2022] [Accepted: 10/31/2022] [Indexed: 11/27/2022] Open
Abstract
Background The monkeypox outbreak in non-endemic countries in recent months has led the World Health Organization (WHO) to declare a public health emergency of international concern (PHEIC). It is thought that festivals, parties, and other gatherings may have contributed to the outbreak. Methods We considered a hypothetical metropolitan city and modeled the transmission of the monkeypox virus in humans in a high-risk group (HRG) and a low-risk group (LRG) using a Susceptible-Exposed-Infectious-Recovered (SEIR) model and incorporated gathering events. Model simulations assessed how the vaccination strategies combined with other public health measures can contribute to mitigating or halting outbreaks from mass gathering events. Results The risk of a monkeypox outbreak was high when mass gathering events occurred in the absence of public health control measures. However, the outbreaks were controlled by isolating cases and vaccinating their close contacts. Furthermore, contact tracing, vaccinating, and isolating close contacts, if they can be implemented, were more effective for the containment of monkeypox transmission during summer gatherings than a broad vaccination campaign among HRG, when accounting for the low vaccination coverage in the overall population, and the time needed for the development of the immune responses. Reducing the number of attendees and effective contacts during the gathering could also prevent a burgeoning outbreak, as could restricting attendance through vaccination requirements. Conclusion Monkeypox outbreaks following mass gatherings can be made less likely with some restrictions on either the number and density of attendees in the gathering or vaccination requirements. The ring vaccination strategy inoculating close contacts of confirmed cases may not be enough to prevent potential outbreaks; however, mass gatherings can be rendered less risky if that strategy is combined with public health measures, including identifying and isolating cases and contact tracing. Compliance with the community and promotion of awareness are also indispensable to containing the outbreak.
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Affiliation(s)
- Pei Yuan
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, Toronto, ON, Canada,Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, ON, Canada
| | - Yi Tan
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, Toronto, ON, Canada,Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, ON, Canada
| | - Liu Yang
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, Toronto, ON, Canada,Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, ON, Canada,School of Mathematics and Statistics, Northeast Normal University, Changchun, China
| | - Elena Aruffo
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, Toronto, ON, Canada,Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, ON, Canada
| | - Nicholas H. Ogden
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, ON, Canada,Public Health Risk Sciences Division, National Microbiology Laboratory, Public Health Agency of Canada, Saint-Hyacinthe, QC, Canada
| | - Jacques Bélair
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, ON, Canada,Département de Mathématiques et de Statistique, Université de Montréal, Montréal, QC, Canada
| | - Julien Arino
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, ON, Canada,Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada
| | - Jane Heffernan
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, ON, Canada,Department of Mathematics and Statistics, York University, Toronto, ON, Canada
| | - James Watmough
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, ON, Canada,Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, Canada
| | - Hélène Carabin
- Département de Pathologie et Microbiologie, Faculté de médecine vétérinaire, Université de Montréal, Saint-Hyacinthe, QC, Canada,Département de médecine sociale et préventive, École de santé publique de l'Université de Montréal, Montréal, QC, Canada,Centre de Recherche en Santé Publique (CReSP) de l'université de Montréal et du CIUSS du Centre Sud de Montréal, Montréal, QC, Canada,Groupe de Recherche en Épidémiologie des Zoonoses et Santé Publique (GREZOSP), Université de Montréal, Saint-Hyacinthe, QC, Canada
| | - Huaiping Zhu
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, Toronto, ON, Canada,Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, ON, Canada,*Correspondence: Huaiping Zhu
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8
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Yuan P, Tan Y, Yang L, Aruffo E, Ogden NH, Yang G, Lu H, Lin Z, Lin W, Ma W, Fan M, Wang K, Shen J, Chen T, Zhu H. Assessing the mechanism of citywide test-trace-isolate Zero-COVID policy and exit strategy of COVID-19 pandemic. Infect Dis Poverty 2022; 11:104. [PMID: 36192815 PMCID: PMC9529335 DOI: 10.1186/s40249-022-01030-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2022] [Accepted: 09/16/2022] [Indexed: 12/24/2022] Open
Abstract
BACKGROUND Countries that aimed for eliminating the cases of COVID-19 with test-trace-isolate policy are found to have lower infections, deaths, and better economic performance, compared with those that opted for other mitigation strategies. However, the continuous evolution of new strains has raised the question of whether COVID-19 eradication is still possible given the limited public health response capacity and fatigue of the epidemic. We aim to investigate the mechanism of the Zero-COVID policy on outbreak containment, and to explore the possibility of eradication of Omicron transmission using the citywide test-trace-isolate (CTTI) strategy. METHODS We develop a compartmental model incorporating the CTTI Zero-COVID policy to understand how it contributes to the SARS-CoV-2 elimination. We employ our model to mimic the Delta outbreak in Fujian Province, China, from September 10 to October 9, 2021, and the Omicron outbreak in Jilin Province, China for the period from March 1 to April 1, 2022. Projections and sensitivity analyses were conducted using dynamical system and Latin Hypercube Sampling/ Partial Rank Correlation Coefficient (PRCC). RESULTS Calibration results of the model estimate the Fujian Delta outbreak can end in 30 (95% confidence interval CI: 28-33) days, after 10 (95% CI: 9-11) rounds of citywide testing. The emerging Jilin Omicron outbreak may achieve zero COVID cases in 50 (95% CI: 41-57) days if supported with sufficient public health resources and population compliance, which shows the effectiveness of the CTTI Zero-COVID policy. CONCLUSIONS The CTTI policy shows the capacity for the eradication of the Delta outbreaks and also the Omicron outbreaks. Nonetheless, the implementation of radical CTTI is challenging, which requires routine monitoring for early detection, adequate testing capacity, efficient contact tracing, and high isolation compliance, which constrain its benefits in regions with limited resources. Moreover, these challenges become even more acute in the face of more contagious variants with a high proportion of asymptomatic cases. Hence, in regions where CTTI is not possible, personal protection, public health control measures, and vaccination are indispensable for mitigating and exiting the COVID-19 pandemic.
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Affiliation(s)
- Pei Yuan
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J1P3, Canada
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, Canada
| | - Yi Tan
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J1P3, Canada
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, Canada
| | - Liu Yang
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J1P3, Canada
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, Canada
- School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China
| | - Elena Aruffo
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J1P3, Canada
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, Canada
| | - Nicholas H Ogden
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, Canada
- Public Health Risk Sciences Division, National Microbiology Laboratory, Public Health Agency of Canada, Saint-Hyacinthe, Canada
| | - Guojing Yang
- Key Laboratory of Tropical Translational Medicine of Ministry of Education and School of Tropical Medicine and Laboratory Medicine, The First Affiliated Hospital of Hainan Medical University, Hainan Medical University, Haikou, Hainan, China.
| | - Haixia Lu
- School of Arts and Science, Suqian University, Suqian, Jiangsu, China
| | - Zhigui Lin
- School of Mathematical Science, Yangzhou University, Yangzhou, Jiangsu, China
| | - Weichuan Lin
- School of Mathematics and Statistics, Fujian Normal University, Fuzhou, Fujian, China
| | - Wenjun Ma
- Department of Public Health and Preventive Medicine, School of Medicine, Jinan University, Guangzhou, Guangdong, China
- Disease Control and Prevention Institute, Jinan University, Guangzhou, Guangdong, China
| | - Meng Fan
- School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China
| | - Kaifa Wang
- School of Mathematics and Statistics, Southwest University, Chongqing, China
| | - Jianhe Shen
- School of Mathematics and Statistics, Fujian Normal University, Fuzhou, Fujian, China
| | - Tianmu Chen
- School of Public Health and State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, Xiamen University, Xiamen, Fujian, China
| | - Huaiping Zhu
- Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J1P3, Canada.
- Canadian Centre for Diseases Modeling (CCDM), York University, Toronto, Canada.
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