PMC:7050133 / 7715-16248 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/7050133","sourcedb":"PMC","sourceid":"7050133","source_url":"https://www.ncbi.nlm.nih.gov/pmc/7050133","text":"Methods\n\nDaily detected and confirmed cases\nData for this study were daily cumulative cases with COVID-19 infection for the first two months (63 days) of the epidemic from December 8, 2019 to February 8, 2020. These data were derived from two sources: (1) Data for the first 44 days from December 8, 2019 to January 20, 2020 were derived from published studies that were determined scientifically [1]. Since no massive control measures were in place during this period, these data were used as the basis to predict the underlying epidemic, considering the overall epidemic. The best fitted model was used to predict the detectable cases and was used in assessing detection rate at different periods for different purposes.\nData for the remaining 19 days from January 21 to February 8, 2020 were taken from the daily official reports of the National Health Commission of the People’s Republic of China (http://www.nhc.gov.cn/xcs/yqfkdt/gzbd_index.shtml). These data were used together with the data from the first source to monitor the dynamic of COVID-19 on a daily basis to 1) assess whether the COVID-19 epidemic was nonlinear and chaotic, 2) evaluate the responsiveness of the epidemic to the massive measures against it, and 3) inform the future trend of the epidemic.\n\nUnderstanding of the detected cases on a daily basis\nIn theory, the true number of persons with COVID-19 infection can never be known no matter how we try to detect it. In practice, of all the infected cases in a day, there are some who have passed the latent period when the virus reaches a detectable level. These patients can then be detected if: a) detection services are available to them, b) all the potentially infected are accessible to the services and are tested, and c) the testing method is sensitive, valid and reliable. When reading the daily data, we must be aware that the detected and diagnosed cases in any day can be great, equal, or below the number of detectable. For example, a detectable person in day one can be postponed to next day when testing services become available. This will result in reduction in a detection rate \u003c 100% in the day before the testing day and a detection rate \u003e 100% in the testing day.\n\nModel daily change in the epidemic\nWe started our modeling analysis with data of cumulative number of diagnosed COVID-19 infections per day. Let xi =diagnosed new cases at day i, i =(1, 2, …t), the cumulative number of diagnosed new cases F(x) can be mathematically described as below: 1 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$ F(x)={\\int}_{i=1}^t{x}_i=\\sum \\limits_{i=1}^t{x}_i. $$\\end{document}Fx=∫i=1txi=∑i=1txi.\nResults of F(x) provide information most useful for resource allocation to support the prevention and treatment; however F(x) is very insensitive to changes in the epidemic. To better monitor the epidemic, the first derivative of F(x) can be used: 2 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$ F^{\\prime }(x)={\\int}_{i=1}^{\\left(t+1\\right)}{x}_i-{\\int}_{i=1}^t{x}_i=\\sum \\limits_{i=1}^{t+1}{x}_i-\\sum \\limits_{i=1}^t{x}_i $$\\end{document}F′x=∫i=1t+1xi−∫i=1txi=∑i=1t+1xi−∑i=1txi\nInformation provided by the first derivative F ′ (x) will be more sensitive than F(x), thus can be used to gauge the epidemic. Practically, F ′ (x) is equivalent to the newly diagnosed cases every day. A further analysis indicates that F ′ (x), although measuring the transmission speed of the epidemic, provides no information about the acceleration of the epidemic, which will be more sensitive than F ′ (x). We thus used the second derivative F″(x): 3 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$ {F}^{{\\prime\\prime} }(x)={F}^{\\prime}\\left({x}_{\\mathrm{i}+1}\\right)-{F}^{\\prime}\\left({x}_i\\right) $$\\end{document}F″x=F′xi+1−F′xi\nMathematically, F′′(x) measures the acceleration of the epidemic or changes in new infections each day. Therefore, F′′(x) ≈ 0 is an early indication of neither acceleration nor deceleration of the epidemic; F′′(x) \u003e 0 presents an early indication of acceleration of the epidemic; while F′′(x) \u003c 0 represents an early indication of deceleration.\n\nModeling the epidemic with assumption of no intervention\nWith a close population assumption and continuous spread of the virus, the number of detected cases can be described using an exponential model [10]. We thus estimated the potentially detectable new cases every day for the period by fitting the observed daily cumulative cases to an exponential curve: 4 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$ F\\left(\\overline{x}\\right)=\\left(\\alpha \\right){\\mathit{\\exp}}^{\\beta (t)},\\mathrm{t}=\\left(12/8/2019,12/9/2019,\\dots, 1/20/2020\\right), $$\\end{document}Fx¯=αexpβt,t=12/8/201912/9/2019…1/20/2020,\nwhere, α =number of expected cases at the baseline and β = growth rate per day.\n\nEstimation of daily detection rate\nTo assess the completeness of the diagnosed new cases on a daily basis, we used Eq (4) first to obtain a time series of \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$ F\\left(\\overline{x}\\right) $$\\end{document}Fx¯ to represent the estimates of cumulative number of potentially detectable cases; we then used the first derivative \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$ F^{\\prime}\\left(\\overline{x}\\right) $$\\end{document}F′x¯ to obtain another time series of observed new cases each day; finally, with the observed F ′ (xi) and model predicted \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$ F^{\\prime}\\left(\\overline{x}\\right) $$\\end{document}F′x¯, we obtained the detection rate Pi for day i as: 5 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$ {P}_i=F^{\\prime}\\left({x}_i\\right)/{F}^{\\prime}\\left({\\overline{x}}_i\\right),\\mathrm{i}=\\left(12/8/2019,12/9,2019\\dots, 2/8/2020\\right) $$\\end{document}Pi=F′xi/F′x¯i,i=12/8/201912/92019…2/8/2020\nWe used these estimated Pi in this study in several ways. Before January 20, 2020 when the massive intervention was not in position, an estimated Pi \u003e 1 was used as an indication of detecting more than expected cases, while an estimated Pi \u003c 1 as an indication of detecting less than expected cases.\nDuring the early period of massive intervention, an increase trend in Pi over time was used as evidence supporting the effectiveness of the massive intervention in detecting and quarantining more infected cases.\nDuring the period 14 days (latent period) after the massive intervention, Pi \u003c 1 was used as evidence indicating declines in new cases rather than under-detection; thus, it was used as a sign of early declines in the epidemic.\nThe modeling analysis was completed using spreadsheet. As a reference to assess the level of severity of the COVID-19 epidemic, the natural mortality rate of Wuhan population was obtained from the 2018 Statistical Report of Wuhan National Economy and Social 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