LitCovid-sentences  

PMC:7050133 / 7715-16248 JSONTXT 10 Projects

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Id Subject Object Predicate Lexical cue
T47 0-7 Sentence denotes Methods
T48 9-43 Sentence denotes Daily detected and confirmed cases
T49 44-209 Sentence denotes Data 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.
T50 210-401 Sentence denotes 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].
T51 402-573 Sentence denotes 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.
T52 574-722 Sentence denotes The best fitted model was used to predict the detectable cases and was used in assessing detection rate at different periods for different purposes.
T53 723-953 Sentence denotes Data 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).
T54 954-1272 Sentence denotes 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.
T55 1274-1326 Sentence denotes Understanding of the detected cases on a daily basis
T56 1327-1442 Sentence denotes In theory, the true number of persons with COVID-19 infection can never be known no matter how we try to detect it.
T57 1443-1583 Sentence denotes 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.
T58 1584-1807 Sentence denotes 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.
T59 1808-1958 Sentence denotes 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.
T60 1959-2071 Sentence denotes For example, a detectable person in day one can be postponed to next day when testing services become available.
T61 2072-2210 Sentence denotes This will result in reduction in a detection rate < 100% in the day before the testing day and a detection rate > 100% in the testing day.
T62 2212-2246 Sentence denotes Model daily change in the epidemic
T63 2247-2352 Sentence denotes We started our modeling analysis with data of cumulative number of diagnosed COVID-19 infections per day.
T64 2353-2497 Sentence denotes 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:
T65 2498-2854 Sentence denotes 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ F(x)={\int}_{i=1}^t{x}_i=\sum \limits_{i=1}^t{x}_i. $$\end{document}Fx=∫i=1txi=∑i=1txi.
T66 2855-3028 Sentence denotes Results 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.
T67 3029-3102 Sentence denotes To better monitor the epidemic, the first derivative of F(x) can be used:
T68 3103-3555 Sentence denotes 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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
T69 3556-3682 Sentence denotes Information provided by the first derivative F ′ (x) will be more sensitive than F(x), thus can be used to gauge the epidemic.
T70 3683-3757 Sentence denotes Practically, F ′ (x) is equivalent to the newly diagnosed cases every day.
T71 3758-3966 Sentence denotes 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).
T72 3967-4008 Sentence denotes We thus used the second derivative F″(x):
T73 4009-4409 Sentence denotes 3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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
T74 4410-4513 Sentence denotes Mathematically, F′′(x) measures the acceleration of the epidemic or changes in new infections each day.
T75 4514-4754 Sentence denotes Therefore, F′′(x) ≈ 0 is an early indication of neither acceleration nor deceleration of the epidemic; F′′(x) > 0 presents an early indication of acceleration of the epidemic; while F′′(x) < 0 represents an early indication of deceleration.
T76 4756-4812 Sentence denotes Modeling the epidemic with assumption of no intervention
T77 4813-4962 Sentence denotes With a close population assumption and continuous spread of the virus, the number of detected cases can be described using an exponential model [10].
T78 4963-5114 Sentence denotes We thus estimated the potentially detectable new cases every day for the period by fitting the observed daily cumulative cases to an exponential curve:
T79 5115-5579 Sentence denotes 4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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,
T80 5580-5659 Sentence denotes where, α =number of expected cases at the baseline and β = growth rate per day.
T81 5661-5695 Sentence denotes Estimation of daily detection rate
T82 5696-7059 Sentence denotes To 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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ F^{\prime}\left(\overline{x}\right) $$\end{document}F′x¯, we obtained the detection rate Pi for day i as:
T83 7060-7523 Sentence denotes 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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
T84 7524-7581 Sentence denotes We used these estimated Pi in this study in several ways.
T85 7582-7823 Sentence denotes Before January 20, 2020 when the massive intervention was not in position, an estimated Pi > 1 was used as an indication of detecting more than expected cases, while an estimated Pi < 1 as an indication of detecting less than expected cases.
T86 7824-8035 Sentence denotes During 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.
T87 8036-8262 Sentence denotes During the period 14 days (latent period) after the massive intervention, Pi < 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.
T88 8263-8317 Sentence denotes The modeling analysis was completed using spreadsheet.
T89 8318-8533 Sentence denotes 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 Development.