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Li W, Bulekova K, Gregor B, White LF, Kolaczyk ED. Estimation of local time-varying reproduction numbers in noisy surveillance data. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210303. [PMID: 35965456 PMCID: PMC9376722 DOI: 10.1098/rsta.2021.0303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Accepted: 04/11/2022] [Indexed: 05/04/2023]
Abstract
A valuable metric in understanding local infectious disease dynamics is the local time-varying reproduction number, i.e. the expected number of secondary local cases caused by each infected individual. Accurate estimation of this quantity requires distinguishing cases arising from local transmission from those imported from elsewhere. Realistically, we can expect identification of cases as local or imported to be imperfect. We study the propagation of such errors in estimation of the local time-varying reproduction number. In addition, we propose a Bayesian framework for estimation of the true local time-varying reproduction number when identification errors exist. And we illustrate the practical performance of our estimator through simulation studies and with outbreaks of COVID-19 in Hong Kong and Victoria, Australia. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.
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Affiliation(s)
- Wenrui Li
- Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA
| | - Katia Bulekova
- Research Computing Services, Information Services and Technology Boston University, Boston, MA 02215, USA
| | - Brian Gregor
- Research Computing Services, Information Services and Technology Boston University, Boston, MA 02215, USA
| | - Laura F. White
- Department of Biostatistics, Boston University, Boston, MA 02215, USA
| | - Eric D. Kolaczyk
- Department of Mathematics and Statistics, Boston University, Boston, MA 02215, USA
- Hariri Institute for Computing, Boston University, Boston,MA 02215, USA
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Zhang XS, Xiong H, Chen Z, Liu W. Importation, Local Transmission, and Model Selection in Estimating the Transmissibility of COVID-19: The Outbreak in Shaanxi Province of China as a Case Study. Trop Med Infect Dis 2022; 7:tropicalmed7090227. [PMID: 36136638 PMCID: PMC9502723 DOI: 10.3390/tropicalmed7090227] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2022] [Revised: 08/30/2022] [Accepted: 08/31/2022] [Indexed: 01/27/2023] Open
Abstract
Background: Since the emergence of the COVID-19 pandemic, many models have been applied to understand its epidemiological characteristics. However, the ways in which outbreak data were used in some models are problematic, for example, importation was mixed up with local transmission. Methods: In this study, five models were proposed for the early Shaanxi outbreak in China. We demonstrated how to select a reasonable model and correctly use the outbreak data. Bayesian inference was used to obtain parameter estimates. Results: Model comparison showed that the renewal equation model generates the best model fitting and the Susceptible-Exposed-Diseased-Asymptomatic-Recovered (SEDAR) model is the worst; the performance of the SEEDAR model, which divides the exposure into two stages and includes the pre-symptomatic transmission, and SEEDDAAR model, which further divides infectious classes into two equally, lies in between. The Richards growth model is invalidated by its continuously increasing prediction. By separating continuous importation from local transmission, the basic reproduction number of COVID-19 in Shaanxi province ranges from 0.45 to 0.61, well below the unit, implying that timely interventions greatly limited contact between people and effectively contained the spread of COVID-19 in Shaanxi. Conclusions: The renewal equation model provides the best modelling; mixing continuous importation with local transmission significantly increases the estimate of transmissibility.
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Affiliation(s)
- Xu-Sheng Zhang
- Statistics, Modelling and Economics, Data, Analytics & Surveillance, UK Health Security Agency, London NW9 5EQ, UK
- Correspondence:
| | - Huan Xiong
- School of Public Health, Kunming Medical University, Kunming 650500, China
| | - Zhengji Chen
- School of Public Health, Kunming Medical University, Kunming 650500, China
| | - Wei Liu
- School of Public Health, Kunming Medical University, Kunming 650500, China
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Li W, Bulekova K, Gregor B, White LF, Kolaczyk ED. Estimation of local time-varying reproduction numbers in noisy surveillance data. MEDRXIV : THE PREPRINT SERVER FOR HEALTH SCIENCES 2022:2021.04.23.21255958. [PMID: 33948612 PMCID: PMC8095231 DOI: 10.1101/2021.04.23.21255958] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
A valuable metric in understanding local infectious disease dynamics is the local time-varying reproduction number, i.e. the expected number of secondary local cases caused by each infected individual. Accurate estimation of this quantity requires distinguishing cases arising from local transmission from those imported from elsewhere. Realistically, we can expect identification of cases as local or imported to be imperfect. We study the propagation of such errors in estimation of the local time-varying reproduction number. In addition, we propose a Bayesian framework for estimation of the true local time-varying reproduction number when identification errors exist. And we illustrate the practical performance of our estimator through simulation studies and with outbreaks of COVID-19 in Hong Kong and Victoria, Australia.
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Affiliation(s)
- Wenrui Li
- Department of Mathematics and Statistics, Boston University, Boston MA, USA
| | - Katia Bulekova
- Research Computing Services, Information Services and Technology, Boston University, Boston MA, USA
| | - Brian Gregor
- Research Computing Services, Information Services and Technology, Boston University, Boston MA, USA
| | - Laura F. White
- Department of Biostatistics, Boston University, Boston MA, USA
| | - Eric D. Kolaczyk
- Department of Mathematics and Statistics, Boston University, Boston MA, USA
- Hariri Institute for Computing, Boston University, Boston MA, USA
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Zhang X. Household Chaos and Caregivers' and Young Children's Mental Health during the COVID-19 Pandemic: A Mediation Model. JOURNAL OF CHILD AND FAMILY STUDIES 2022; 31:1547-1557. [PMID: 35287306 PMCID: PMC8907899 DOI: 10.1007/s10826-022-02283-4] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/17/2022] [Indexed: 05/26/2023]
Abstract
Based on 764 households with young children in Wuhan, China, where the COVID-19 pandemic started, this study investigated how household chaos during the pandemic was associated with the mental health problems of children and their caregivers. It also examined the familial correlates of household chaos. The results showed that household chaos was associated with caregiver-rated symptoms of anxiety/withdrawal, fearfulness and acting out exhibited by young children and the symptoms of anxiety and depression in their caregivers. Moreover, caregivers' depression and anxiety mediated the relations between household chaos and caregiver-rated child mental health problems. Additionally, caregivers living in families with a single caregiver, a larger family size, poorer physical health, and more significant income loss reported greater levels of household chaos during the pandemic. These findings highlight the importance of reducing household chaos to promote the mental health of young children and their caregivers during the pandemic. They also underscore the need to identify families with high levels of chaos based on key background variables.
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Affiliation(s)
- Xiao Zhang
- Faculty of Education, The University of Hong Kong, Pokfulam Road, Hong Kong
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Tian L, Li X, Qi F, Tang QY, Tang V, Liu J, Li Z, Cheng X, Li X, Shi Y, Liu H, Tang LH. Harnessing peak transmission around symptom onset for non-pharmaceutical intervention and containment of the COVID-19 pandemic. Nat Commun 2021; 12:1147. [PMID: 33608519 PMCID: PMC7895830 DOI: 10.1038/s41467-021-21385-z] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Accepted: 01/20/2021] [Indexed: 12/13/2022] Open
Abstract
Within a short period of time, COVID-19 grew into a world-wide pandemic. Transmission by pre-symptomatic and asymptomatic viral carriers rendered intervention and containment of the disease extremely challenging. Based on reported infection case studies, we construct an epidemiological model that focuses on transmission around the symptom onset. The model is calibrated against incubation period and pairwise transmission statistics during the initial outbreaks of the pandemic outside Wuhan with minimal non-pharmaceutical interventions. Mathematical treatment of the model yields explicit expressions for the size of latent and pre-symptomatic subpopulations during the exponential growth phase, with the local epidemic growth rate as input. We then explore reduction of the basic reproduction number R0 through specific transmission control measures such as contact tracing, testing, social distancing, wearing masks and sheltering in place. When these measures are implemented in combination, their effects on R0 multiply. We also compare our model behaviour to the first wave of the COVID-19 spreading in various affected regions and highlight generic and less generic features of the pandemic development.
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Affiliation(s)
- Liang Tian
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
- Department of Physics and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
| | - Xuefei Li
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
- CAS Key Laboratory of Quantitative Engineering Biology, Shenzhen Institute of Synthetic Biology, Shenzhen Institutes of Advanced Technology, Shenzhen, China
| | - Fei Qi
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
- CAS Key Laboratory of Quantitative Engineering Biology, Shenzhen Institute of Synthetic Biology, Shenzhen Institutes of Advanced Technology, Shenzhen, China
| | - Qian-Yuan Tang
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
- Center for Complex Systems Biology, Universal Biology Institute, University of Tokyo, Tokyo, Japan
| | - Viola Tang
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
- Department of Information Systems, Business Statistics and Operations Management, Hong Kong University of Science and Technology, Hong Kong SAR, China
| | - Jiang Liu
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
| | - Zhiyuan Li
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
- Center for Quantitative Biology, Peking University, Haidian, Beijing, China
| | - Xingye Cheng
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
- Department of Physics and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
| | - Xuanxuan Li
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
- Department of Engineering Physics, Tsinghua University, Haidian, Beijing, China
- Physics Department, Beijing Normal University, Haidian, Beijing, China
| | - Yingchen Shi
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
- Department of Engineering Physics, Tsinghua University, Haidian, Beijing, China
- Complex Systems Division, Beijing Computational Science Research Center, Haidian, Beijing, China
| | - Haiguang Liu
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China
- Complex Systems Division, Beijing Computational Science Research Center, Haidian, Beijing, China
- Physics Department, Beijing Normal University, Haidian, Beijing, China
| | - Lei-Han Tang
- COVID-19 Modelling Group, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China.
- Department of Physics and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon, Hong Kong SAR, China.
- Complex Systems Division, Beijing Computational Science Research Center, Haidian, Beijing, China.
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Cheng Q, Liu Z, Cheng G, Huang J. Heterogeneity and effectiveness analysis of COVID-19 prevention and control in major cities in China through time-varying reproduction number estimation. Sci Rep 2020; 10:21953. [PMID: 33319859 PMCID: PMC7738538 DOI: 10.1038/s41598-020-79063-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2020] [Accepted: 12/03/2020] [Indexed: 12/21/2022] Open
Abstract
Beginning on December 31, 2019, the large-scale novel coronavirus disease 2019 (COVID-19) emerged in China. Tracking and analysing the heterogeneity and effectiveness of cities' prevention and control of the COVID-19 epidemic is essential to design and adjust epidemic prevention and control measures. The number of newly confirmed cases in 25 of China's most-affected cities for the COVID-19 epidemic from January 11 to February 10 was collected. The heterogeneity and effectiveness of these 25 cities' prevention and control measures for COVID-19 were analysed by using an estimated time-varying reproduction number method and a serial correlation method. The results showed that the effective reproduction number (R) in 25 cities showed a downward trend overall, but there was a significant difference in the R change trends among cities, indicating that there was heterogeneity in the spread and control of COVID-19 in cities. Moreover, the COVID-19 control in 21 of 25 cities was effective, and the risk of infection decreased because their R had dropped below 1 by February 10, 2020. In contrast, the cities of Wuhan, Tianmen, Ezhou and Enshi still had difficulty effectively controlling the COVID-19 epidemic in a short period of time because their R was greater than 1.
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Affiliation(s)
- Qing Cheng
- College of Systems Engineering, National University of Defense Technology, Changsha, 410073, People's Republic of China.
- Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, 410073, People's Republic of China.
| | - Zeyi Liu
- College of Systems Engineering, National University of Defense Technology, Changsha, 410073, People's Republic of China
- Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, 410073, People's Republic of China
| | - Guangquan Cheng
- College of Systems Engineering, National University of Defense Technology, Changsha, 410073, People's Republic of China
- Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, 410073, People's Republic of China
| | - Jincai Huang
- College of Systems Engineering, National University of Defense Technology, Changsha, 410073, People's Republic of China
- Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, 410073, People's Republic of China
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