PubAnnotation

Id	Subject	Object	Predicate	Lexical cue
T1	0-147	Sentence	denotes	First two months of the 2019 Coronavirus Disease (COVID-19) epidemic in China: real-time surveillance and evaluation with a second derivative model
T2	149-157	Sentence	denotes	Abstract
T3	158-168	Sentence	denotes	Background
T4	169-459	Sentence	denotes	Similar to outbreaks of many other infectious diseases, success in controlling the novel 2019 coronavirus infection requires a timely and accurate monitoring of the epidemic, particularly during its early period with rather limited data while the need for information increases explosively.
T5	461-468	Sentence	denotes	Methods
T6	469-628	Sentence	denotes	In this study, we used a second derivative model to characterize the coronavirus epidemic in China with cumulatively diagnosed cases during the first 2 months.
T7	629-722	Sentence	denotes	The analysis was further enhanced by an exponential model with a close-population assumption.
T8	723-908	Sentence	denotes	This model was built with the data and used to assess the detection rate during the study period, considering the differences between the true infections, detectable and detected cases.
T9	910-917	Sentence	denotes	Results
T10	918-1030	Sentence	denotes	Results from the second derivative modeling suggest the coronavirus epidemic as nonlinear and chaotic in nature.
T11	1031-1239	Sentence	denotes	Although it emerged gradually, the epidemic was highly responsive to massive interventions initiated on January 21, 2020, as indicated by results from both second derivative and exponential modeling analyses.
T12	1240-1313	Sentence	denotes	The epidemic started to decelerate immediately after the massive actions.
T13	1314-1447	Sentence	denotes	The results derived from our analysis signaled the decline of the epidemic 14 days before it eventually occurred on February 4, 2020.
T14	1448-1560	Sentence	denotes	Study findings further signaled an accelerated decline in the epidemic starting in 14 days on February 18, 2020.
T15	1562-1573	Sentence	denotes	Conclusions
T16	1574-1683	Sentence	denotes	The coronavirus epidemic appeared to be nonlinear and chaotic, and was responsive to effective interventions.
T17	1684-1921	Sentence	denotes	The methods used in this study can be applied in surveillance to inform and encourage the general public, public health professionals, clinicians and decision-makers to take coordinative and collaborative efforts to control the epidemic.
T18	1923-1935	Sentence	denotes	Introduction
T19	1936-2019	Sentence	denotes	The epidemic of COVID-19 is caused by a novel virus first detected in Wuhan, China.
T20	2020-2122	Sentence	denotes	This virus was previously named as 2019-nCoV and it is a positive, enveloped, single-strand RNA virus.
T21	2123-2287	Sentence	denotes	It also shares a lot of similarities with two other coronaviruses, the MERS-CoV (Middle East Respiratory Syndrome) and SARS-CoV (Severe Acute Respiratory Syndrome).
T22	2288-2392	Sentence	denotes	Outbreak of the COVID-19 started with the report of a first suspected case on December 8, 2019 in Wuhan.
T23	2393-2622	Sentence	denotes	The first two months of the epidemic covered three significant holidays, including the New Year of 2020, the Chinese New Year’s Day with vacations from January 24 to February 2, 2020, and the Lantern Festival on February 8, 2020.
T24	2623-2870	Sentence	denotes	During this period, one study by the Chinese Center for Disease Prevention and Control (CDC) and Hubei Provincial CDC with data collected by Wuhan CDC documented the details of the epidemic day by day from December 8, 2019 to January 21, 2020 [1].
T25	2871-3082	Sentence	denotes	Data in this study showed that detected and confirmed cases with COVID-19 infection declined from the peak of 44 on January 8 to only 2 on January 19, 2020, suggesting that the epidemic was likely under control.
T26	3083-3284	Sentence	denotes	China officially declared the epidemic as an outbreak on January 20 when obvious human-to-human transmissions were ascertained with reagent probes and primers distributed to local agencies on that day.
T27	3285-3530	Sentence	denotes	Immediately following the declaration, massive actions were taken the next day to curb the epidemic at Wuhan, and soon spread to the whole country from central to local government, including all sectors from business to factories and to schools.
T28	3531-3645	Sentence	denotes	On February 23, 2020, Wuhan City and other cities along with the main traffic lines around Wuhan were locked down.
T29	3646-4006	Sentence	denotes	Rigorous efforts were devoted to 1) identify the infected and bring them to treatment in hospitals for infectious diseases, 2) locate and quarantine all those who had contact with the infected, 3) sterilize environmental pathogens, 4) promote mask use, and 5) release to the public of number of infected, suspected, under treatment and deaths on a daily basis.
T30	4007-4232	Sentence	denotes	On January 24, 2020, the New Year’s Eve and 25, the Chinese New Year’s Day, President Xi Jinping held a special meeting at the Central Chinese Government and decided to implement massive national efforts to curb the epidemic.
T31	4233-4339	Sentence	denotes	An Anti- COVID-19 Group headed by Premier Li Keqiang was established to lead the massive national efforts.
T32	4340-4428	Sentence	denotes	Vice Premier Sun Chunlan was sent to Hubei and Wuhan to directly lead the local efforts.
T33	4429-4554	Sentence	denotes	A massive number of detection kits were made available to all locations to test all susceptible patients for final diagnosis.
T34	4555-4701	Sentence	denotes	People in other cities and provinces who either traveled to or out of Wuhan were quarantined, with suspected patients being diagnosed and treated.
T35	4702-4876	Sentence	denotes	The sudden escalation of the control and the spread of the number of infected and deaths, however, ignited strong emotional responses of fear and panic among people in Wuhan.
T36	4877-5048	Sentence	denotes	The negative emotional responses soon spread from Wuhan to other parts of China, and further to the world via almost all communication channels, particularly social media.
T37	5049-5567	Sentence	denotes	The highly emotional responses of the public were fueled by (1) sudden increases in the number of detected new cases after the massive intervention measures to identify the infected; (2) massive growing needs for masks; (3) a large number of suspected patients waiting to confirm their diagnose; (4) a large number of diagnosed COVID-19 patients for treatment; and (5) a growing number of deaths, despite national efforts to improve therapy, including the decision to build two large hospitals within a period of days.
T38	5568-5770	Sentence	denotes	The emotional responses, mostly stimulated by the daily release of data have created a big barrier for effective control of the epidemic as has been observed in other epidemics of similar nature [2, 3].
T39	5771-5947	Sentence	denotes	It is a paradox that during the early period of an epidemic, little is known or available about the new infections; while the need for such information is at the highest level.
T40	5948-5991	Sentence	denotes	This is particularly true for the COVID-19.
T41	5992-6330	Sentence	denotes	The occurrence of this epidemic may follow a nonlinear, chaotic and catastrophic process, rather similar to the epidemic of SARS that occurred in Hong Kong in 2003 [2], the Ebola epidemic in West Africa during 2013–16 [4, 5], the pandemic of 2009 H1N1 epidemic started [6–8] and the recent measles outbreaks in the United States (US) [9].
T42	6331-6575	Sentence	denotes	Similar to an eruption of a volcano or occurrence of an earthquake, no matter how closely it is monitored, how much research we have done, how much we know about it, no one knows for sure if and when the virus infection will become an outbreak.
T43	6576-6732	Sentence	denotes	Therefore, there is no so-called rational responses, no standard-operating-procedure (SOP) to follow, no measures to take without negative consequences [2].
T44	6733-6883	Sentence	denotes	However, defining the COVID-19 as nonlinear and chaotic does not mean that we cannot do anything after we knew it was an outbreak, but simply waiting.
T45	6884-7486	Sentence	denotes	On the contrary, defining it as nonlinear and chaotic will better inform us to make right decisions and to take appropriate actions. (1) During the early stage of an infection, which we cannot tell whether it will be growing into an outbreak, we must closely monitor it using limited data and to find the early signs of change and to predict if and when it will become an outbreak; (2) After it is declared as an outbreak, it is better to take actions as soon as possible since infectious diseases can be controlled even without knowledge of the biology [10]; and evaluate if the control measures work.
T46	7487-7713	Sentence	denotes	The ultimate goal of this study is to attempt to provide some solutions to this paradox by providing early messages to inform control measures, to be optimistic and not panic, to ask right questions, and to take right actions.
T47	7715-7722	Sentence	denotes	Methods
T48	7724-7758	Sentence	denotes	Daily detected and confirmed cases
T49	7759-7924	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	7925-8116	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	8117-8288	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	8289-8437	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	8438-8668	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	8669-8987	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	8989-9041	Sentence	denotes	Understanding of the detected cases on a daily basis
T56	9042-9157	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	9158-9298	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	9299-9522	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	9523-9673	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	9674-9786	Sentence	denotes	For example, a detectable person in day one can be postponed to next day when testing services become available.
T61	9787-9925	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	9927-9961	Sentence	denotes	Model daily change in the epidemic
T63	9962-10067	Sentence	denotes	We started our modeling analysis with data of cumulative number of diagnosed COVID-19 infections per day.
T64	10068-10212	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	10213-10569	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	10570-10743	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	10744-10817	Sentence	denotes	To better monitor the epidemic, the first derivative of F(x) can be used:
T68	10818-11270	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	11271-11397	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	11398-11472	Sentence	denotes	Practically, F ′ (x) is equivalent to the newly diagnosed cases every day.
T71	11473-11681	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	11682-11723	Sentence	denotes	We thus used the second derivative F″(x):
T73	11724-12124	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	12125-12228	Sentence	denotes	Mathematically, F′′(x) measures the acceleration of the epidemic or changes in new infections each day.
T75	12229-12469	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	12471-12527	Sentence	denotes	Modeling the epidemic with assumption of no intervention
T77	12528-12677	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	12678-12829	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	12830-13294	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	13295-13374	Sentence	denotes	where, α =number of expected cases at the baseline and β = growth rate per day.
T81	13376-13410	Sentence	denotes	Estimation of daily detection rate
T82	13411-14774	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	14775-15238	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	15239-15296	Sentence	denotes	We used these estimated Pi in this study in several ways.
T85	15297-15538	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	15539-15750	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	15751-15977	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	15978-16032	Sentence	denotes	The modeling analysis was completed using spreadsheet.
T89	16033-16248	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.
T90	16250-16257	Sentence	denotes	Results
T91	16259-16308	Sentence	denotes	Cumulative number of detected and diagnosed cases
T92	16309-16477	Sentence	denotes	The COVID-19 epidemic was initiated in Wuhan, the Provincial Capital of Hubei Province with a total population of 14.2 million, including 5.1 million mobile population.
T93	16478-16563	Sentence	denotes	The mortality rate was 5.5/1000 for Wuhan residents with most available data in 2018.
T94	16564-16754	Sentence	denotes	Assuming all diagnosed cases in China were infected in Wuhan (an exaggerated scenarios for illustration purpose), the two-month incidence rate of COVID-19 was 2.6/1000 among Wuhan residents.
T95	16755-16899	Sentence	denotes	Based on reported case mortality of 2.3%, the population-based mortality of COVID-19 was 0.6/1000, or 1/9th of the mortality of Wuhan residents.
T96	16900-17037	Sentence	denotes	Figure 1 presents the cumulative diagnosed cases F(x) and major events during the study period from December 8, 2019 to February 8, 2020.
T97	17038-17109	Sentence	denotes	During the period, a total of 37,198 cases were diagnosed and reported.
T98	17110-17274	Sentence	denotes	The daily cases varied from 0 to 3886 with the median cases of 199 (January 8, 2020), and inter-quarter range (IQR) of 24 (December 23), and 830 (January 23, 2020).
T99	17275-17462	Sentence	denotes	Fig. 1 Cumulative number of diagnosed COVID-19(2019-nCoV) infection F(x) and key events before, during and after declaration of the outbreak in the first 2 months of the Epidemic in China
T100	17464-17526	Sentence	denotes	Dynamics of the epidemic and response to massive interventions
T101	17527-17751	Sentence	denotes	The dynamic changes based on the observed F(x) in Fig. 1 were presented in Fig. 2 using the first derivatives F ′ (x) (top panel of the figure) and the second derivative F ′ ′ (x) (bottom panel of the figure), respectively.
T102	17752-17927	Sentence	denotes	Before the declaration of outbreak, information provided by the two dynamic measured was similar: not much variations were revealed relative to the changes after the outbreak.
T103	17928-18012	Sentence	denotes	These findings suggest the nonlinear and chaotic character of the COVID-19 outbreak.
T104	18013-18203	Sentence	denotes	Fig. 2 The first F′(x) and second derivative F″(x) of diagnosed COVID-19 (formally 2019-nCoV infection) F(x) before, during and after declaring the outbreak in first 2 months of the Epidemic
T105	18204-18310	Sentence	denotes	After declaring the outbreak on January 20, information revealed by F ′ ′ (x) differed much from F ′ (x).
T106	18311-18486	Sentence	denotes	Based on information from F ′ (x), the newly diagnosed F ′ (x) cases increased progressively with some fluctuation, then peaked on February 4, 2020, and followed by a decline.
T107	18487-18652	Sentence	denotes	The increases in the diagnosed cases could be either due to the natural growth of the epidemic in itself, or due to the interventions to detect the infected or both.
T108	18653-18734	Sentence	denotes	Furthermore, F ′ (x) provided no sign of epidemic decline until February 4, 2020.
T109	18735-18879	Sentence	denotes	In other words, we have to wait for at least 14 days after the massive anti-COVID-19 epidemic without using information derived from F ′ ′ (x).
T110	18880-19013	Sentence	denotes	Quite different from F ′ (x), F ′′ (x) removed the time trend of F ′ (x) to show the acceleration/deceleration of diagnosed COVID-19.
T111	19014-19172	Sentence	denotes	Consequently, F ′ ′ (x) was much more sensitive than F ′ (x) to gauge the intrinsic dynamics of the epidemic in response to the massive anti-COVID-19 action.
T112	19173-19342	Sentence	denotes	Since January 21, 2020 after the massive anti-COVID actions, the F ′ ′ (x) suddenly became very active, as indicated by the alternative accelerations and decelerations.
T113	19343-19644	Sentence	denotes	F ′ ′ (x) reached the peak on January 27 after the distribution of large number of test kits on January 26, which was an action based on the decision at the central government level in a meeting held by Chinese President Xi Jinping on January 24 and 25, the Chinese New Year’s Eve and New Year’s Day.
T114	19645-19997	Sentence	denotes	In addition, the estimated F ′′ (x) captured three significant decelerations on January 28, February 5 and 6 (two days in a row), and 8, 2020 respectively; corresponding to the intensified massive actions in locating and treating the infected, locking down more communities, plus mask use and massive pathogen sterilization in neighborhood environment.
T115	19998-20236	Sentence	denotes	In addition to informing whether the epidemic was responsive to the massive interventions, information from F ′′ (x) signaled an overall downturn of the epidemic since the beginning of the massive anti-COVID-19 action on January 21, 2020.
T116	20237-20323	Sentence	denotes	This was further pronounced by the band region between the two dotted lines in Fig. 2.
T117	20324-20461	Sentence	denotes	Despite zigzags, an overall downward trend in F ′′ (x) was clearly revealed by the downward and progressively narrowing down band region.
T118	20462-20586	Sentence	denotes	This trend strongly indicates that the epidemic could be brought under control soon with the current interventions in place.
T119	20588-20625	Sentence	denotes	Exponential growth and detection rate
T120	20626-20701	Sentence	denotes	The observed F(x) fit the exponential model of Eq. 4 well with R2 = 0.9778.
T121	20702-20799	Sentence	denotes	The estimated α =1.1070, representing the first person who was infected and ignited the epidemic.
T122	20800-20854	Sentence	denotes	The estimated β =0.1716, representing the growth rate.
T123	20855-20947	Sentence	denotes	Using this estimated growth rate, it takes only 4 days for the diagnosed COVID-19 to double.
T124	20948-21102	Sentence	denotes	Figure 3 presents the daily detection rates, estimated with the fitted exponential model from day one of the epidemic to the last day of the study period.
T125	21103-21259	Sentence	denotes	Based on findings in this figure and data from Figs. 1 and 2, we divided the COVID-19 epidemic during the first two months of the epidemic into five phases.
T126	21260-21432	Sentence	denotes	Fig. 3 Estimated daily detection rate Pi of COVID-19 (2019-nCoV) infection before, during and after declaration of the outbreak, the first 2 months of the Epidemic in China
T127	21433-21473	Sentence	denotes	Phase 1 was from December 8 to 25, 2019.
T128	21474-21574	Sentence	denotes	During this period, the detection rate Pi was high overall, with fluctuations around and above 100%.
T129	21575-21678	Sentence	denotes	This was corresponding to the early period after the first suspected case was identified and diagnosed.
T130	21679-21762	Sentence	denotes	Phase 2 was from December 26, 2019 to January 8, 2020, covering the New Year’s Day.
T131	21763-21891	Sentence	denotes	The detection rate Pi fluctuated at around 50% with the lowest of 17% on December 31, 2019 and the highest of 108% on January 8.
T132	21892-22054	Sentence	denotes	Phase 3 was from January 8 to 20, 2020, and it was featured with a progressive decline in the estimated Pi from 105% on January 8, 2020 to 1% on January 20, 2020.
T133	22055-22218	Sentence	denotes	This progressive declining period was the time for the Chinese to prepare for the traditional Chinese New Year’s with the longest and highest level of celebration.
T134	22219-22306	Sentence	denotes	Unfortunately, the COVID-19 as an outbreak was silently stepping in during this period.
T135	22307-22473	Sentence	denotes	Phase 4 was from January 20 to 27, 2020 with the estimated Pi increased from 1% on January 20, 2020 to surpass 100%, and reached the peak of 170% on January 27, 2020.
T136	22474-22640	Sentence	denotes	This period was corresponding to the initiation and progressive intensifying of the massive intervention organized and coordinated by the Central Government of China.
T137	22641-22791	Sentence	denotes	Phase 5 started from January 27, 2020 to the end of the study period, corresponding to the sustained massive national efforts, plus frequent emphases.
T138	22792-23028	Sentence	denotes	Different from the previous four phases, reductions in the estimated Pi during this phase were not an indication of under-detection but an indication of declines in the epidemic reflected by the detected and confirmed cases of COVID-19.
T139	23029-23138	Sentence	denotes	This is because the model predicted Pi did not consider any interventions but natural growth of the epidemic.
T140	23139-23153	Sentence	denotes	Based on Figs.
T141	23154-23698	Sentence	denotes	2 and 3 (Phase 4 and 5), three pieces of information can be derived: (1) The epidemic was highly sensitive to external interventions, supporting the nonlinear and chaotic characters revealed by the long latent period in the first three phases; (2) the massive national efforts were highly effective in detecting the detectable COVID-19; (3) signal for the COVID-19 in China to decline appeared on January 21 in 2020, 14 days before the start of eventual declines on February 4, as indicated by F ′ ′ (x) and F ′ (x) in Fig. 2 and Pi in Fig. 3.
T142	23700-23711	Sentence	denotes	Disscussion
T143	23712-23843	Sentence	denotes	In this study, we used a novel approach to distill information from the cumulative number of diagnosed cases of COVID-19 infection.
T144	23844-24003	Sentence	denotes	Among various types of surveillance data, this data often reported the earliest and on a continuous basis with high completeness and are most widely available.
T145	24004-24115	Sentence	denotes	In addition, patients with a diagnosed infection are those with high likelihoods to spread the virus to others.
T146	24116-24256	Sentence	denotes	Findings from this study provided useful information in a real time manner to monitor, evaluate and forecast the COVID-19 epidemic in China.
T147	24257-24489	Sentence	denotes	The methods used in this study although somewhat mathematical, are easy to follow while information extracted from the commonly used data with the methods are highly useful and more sensitive than the daily new and cumulative cases.
T148	24491-24544	Sentence	denotes	Nonlinear and chaotic nature of the COVID-19 outbreak
T149	24545-24798	Sentence	denotes	Although an analytical demonstration of the COVID-19 outbreak as nonlinear, chaotic and catastrophic requires more time to wait till the epidemic ends, evidence in the first 2 months suggests that the COVID-19 outbreak in China is nonlinear and chaotic.
T150	24799-24959	Sentence	denotes	The epidemic emerged suddenly after a long latent period without dramatic changes as revealed from the cumulative cases, and their first and second derivatives.
T151	24960-25161	Sentence	denotes	The high responsiveness of the epidemic to interventions adds additional evidence supporting the chaotic and catastrophic nature, and demonstrating the selection of a good timing to start intervention.
T152	25162-25436	Sentence	denotes	Many of these characters are similar to those observed in the 2003 SARS epidemic started in Hong Kong [2], the 2013–16 Ebola spread in the West Africa [4, 5], the 2009 pandemic of H1N1 started in the US [6–8], and the measles outbreaks over 80 cities in the US recently [9].
T153	25437-25521	Sentence	denotes	Even the seasonal common flu has been proved to have a nonlinear component [11, 12].
T154	25522-25737	Sentence	denotes	The significance of nonlinear and chaotic nature of COVID-19 means that no methods are available to predict exactly at what point in time the epidemic will emerge as an outbreak, just like volcanoes and earthquakes.
T155	25738-25835	Sentence	denotes	Therefore, practically there is no so-called a best time or missed the best time to take actions.
T156	25836-25906	Sentence	denotes	There will also no so-called rational analysis and rational responses.
T157	25907-26064	Sentence	denotes	There is no silver bullet to use, no standard-operating-procedure (SOP) to follow, and no measures without negative consequences to control the epidemic [2].
T158	26065-26193	Sentence	denotes	For example, it took more than 6 months for both the US and the WHO to determine the 2009 H1N1 pandemic as an outbreak [13, 14].
T159	26194-26471	Sentence	denotes	Therefore, knowing the nonlinear and chaotic nature of an epidemic outbreak, like COVID-19, for all stockholders will be essential to the mobilization of resources, working together, taking all actions possible to control the epidemic, and minimizing the negative consequences.
T160	26472-27063	Sentence	denotes	Specifically, what we can do to deal with an outbreak like COVID-19 would be to (1) collect information as early as possible, (2) monitor the epidemic as close as possible just like we do for an earthquake and make preparations for a hurricane and (3) communicate with the society and use confirmed data appropriately reframed not causing or exacerbating fear and panic in the public, stress and distress among medical and public health professionals, as well as administrators to make right decisions and take the right strategies at the right time in the right places for the right people.
T161	27064-27209	Sentence	denotes	Knowing the nonlinear and chaotic nature is also essential for taking actions to control the outbreak of an epidemic like the COVID-19 infection.
T162	27210-27603	Sentence	denotes	As soon as an outbreak is confirmed, the follow measures should be in position immediately 1) closely and carefully monitor the epidemic; 2) take evidence-based interventions to control the epidemic, 3) actively assess responses of the epidemic to the interventions; 4) allow errors in the intervention, particularly during the early period of the epidemic, 5) always prepare for alternatives.
T163	27604-27676	Sentence	denotes	Another confusion is, when an epidemic starts, everyone asks what it is?
T164	27677-27696	Sentence	denotes	How does it happen?
T165	27697-27732	Sentence	denotes	How should I do to avoid infection?
T166	27733-27766	Sentence	denotes	Is there any effective treatment?
T167	27767-27894	Sentence	denotes	Answering these questions takes time, but there is no need to wait till all these questions are resolved before taking actions.
T168	27895-27992	Sentence	denotes	We can take actions to prevent COVID-19 immediately while waiting for answers to these questions.
T169	27993-28145	Sentence	denotes	This is because we have the evidence-based strategy for control and prevention of any infectious disease without complete understanding of an infection.
T170	28146-28334	Sentence	denotes	That is so-called Tri-Component Strategy: locating and controlling the sources of infection, identifying and blocking the transmission paths, and protecting those who are susceptible [10].
T171	28335-28414	Sentence	denotes	This was just what China has done, is doing, and will continue to do this time.
T172	28415-28677	Sentence	denotes	Typical examples of control and prevention measures include locking down of cities, communities, and villages with potential of large scale transmission, massive environment sterilization, promotion of mask use, efforts to locate, isolate and treat the infected.
T173	28678-28864	Sentence	denotes	More importantly, most of these actions are initiated, mobilized, coordinated and supported by the government from central to local, and enhanced by volunteers and international support.
T174	28866-28905	Sentence	denotes	Highly effective of the national effort
T175	28906-29085	Sentence	denotes	Another important piece of findings is that we detected the effect of the national efforts taken by China from the beginning when they were in position till the end of this study.
T176	29086-29277	Sentence	denotes	For example, from the second derivative, we observed increases in the infected through the action on January 22, 2020, the next day after the massive intervention started on January 21, 2020.
T177	29278-29337	Sentence	denotes	This result was also picked up by the exponential modeling.
T178	29338-29483	Sentence	denotes	From day one on January 21, 2020 when the massive intervention measures activated to February 4, 2020 is the latent period of COVID-19 infection.
T179	29484-29715	Sentence	denotes	The second derivative precisely recorded the change in newly diagnosed cases in response to the massive measures, reflected as the rapid increase in detection rate, consistent with the result from the exponential modeling analysis.
T180	29716-29964	Sentence	denotes	The detected responsiveness of the epidemic to the intervention provided data to predict the occurrence of deceleration of the epidemic on February 4, 2020 if the same measures persist, which was exactly what we observed from the second derivative.
T181	29965-30044	Sentence	denotes	Based on the findings from our analysis, the COVID-19 in China may end up soon.
T182	30045-30266	Sentence	denotes	Despite a delay of 43 days from the first confirmed cases on December 8, 2019 to January 20, 2020, the COVID-19 epidemic was highly responsive to massive interventions, supporting the effectiveness of these interventions.
T183	30267-30654	Sentence	denotes	It is our prediction that the outbreak of the COVID-19 infection will be brought under control by the end of February 2020, given the effective control measures known to everyone, increases in immune level in the total population due to latent infections, and most widely spread of knowledge and skills for infectious disease control and prevention among the 1.4 billion people in China.
T184	30656-30690	Sentence	denotes	Effective methods for surveillance
T185	30691-30771	Sentence	denotes	There are a number of advantages of methods we developed and used in this study.
T186	30772-31091	Sentence	denotes	First, framing the diagnosed cases as the cumulative, the first and the second derivative constructs a system to gauge the epidemic, with the cumulative cases showing the overall level of the epidemic, the first derivative to reflect the change of the epidemic, and the second derivative to monitor the speed of change.
T187	31092-31383	Sentence	denotes	By inclusion of the mortality rate as a reference, results from our approach will be (1) comprehensive to inform the public to be prepared, not scared and not to blame others; (2) useful for administrators to make decisions; (3) valuable for medical and health professionals to take actions.
T188	31384-31697	Sentence	denotes	Second, we conceptually separated (1) the true number of infections, which will never be practically detected, from (2) the infections that are practically detectable if services are available and accessible and detection technologies are sensitive and reliable, and (3) the actually detected cases of infections.
T189	31698-31936	Sentence	denotes	This classification greatly improved our understanding of the observed data as well as findings from the two derivatives, and aided us in assessing the responsiveness to the massive interventions, and predicting of the epidemic over time.
T190	31937-32152	Sentence	denotes	The clarification also enhanced our analytical approach by adding an exponential model to evaluate the detection rate and to bring more data assessing the responsiveness of the epidemic to the massive interventions.
T191	32153-32283	Sentence	denotes	We highly recommend the inclusion of the methods as a part of routine surveillance in disease control and prevention institutions.
T192	32285-32312	Sentence	denotes	Limitations and future plan
T193	32313-32335	Sentence	denotes	There are limitations.
T194	32336-32402	Sentence	denotes	First, this study covered only the first 2 months of the epidemic.
T195	32403-32504	Sentence	denotes	We will continue to evaluate the utility of this method as we follow the development of the epidemic.
T196	32505-32576	Sentence	denotes	Second, the methods used in this study was based on a close population.
T197	32577-32717	Sentence	denotes	This hypothesis may not be true because of a large number of people with potential history of exposure in China traveled to other countries.
T198	32718-32900	Sentence	denotes	Up to February 8, 2020, the total cases diagnosed were 37,552 worldwide (Worldometer on Coronavirus) with 37,198 in China, which accounted for 99.1% of the total number of the world.
T199	32901-32978	Sentence	denotes	Therefore, the impact of close-population assumption would be rather limited.
T200	32979-33058	Sentence	denotes	Third, there was a lack of individual patient-level data for detailed analysis.
T201	33059-33232	Sentence	denotes	Fourth, our model can be further improved with other data, such as cases by severity, number of the suspected, number of those who received treatments and treatment results.
T202	33233-33347	Sentence	denotes	We will follow the epidemic closely and prepare for further research on the topic when more data become available.
T203	33348-33706	Sentence	denotes	Despite the limitations, this study provided new data to encourage those who are infected to better fight against the infections; to inform and encourage the general public, the medical and health professionals and the government to continue their current measures and to think of more measures that are innovative and effective to end the COVID-19 epidemic.
T204	33707-34088	Sentence	denotes	One of the greatest motivations for this study is to attempt to provide right information at the population level in a real manner to complement the data from micro-organism centered and laboratory-based biological, molecular, pharmacological and clinical information in both the academic and the mass media that often scare rather than encourage people, even health professionals.
T205	34089-34147	Sentence	denotes	Of the diagnosed COVID-19 cases, less than 20% are severe.
T206	34148-34260	Sentence	denotes	Findings from our study indicated that there is no need to be panic from a public health population perspective.
T207	34261-34413	Sentence	denotes	Although the total cases COVID-19 reached to big numbers, but the 2-month incidence rate was about a half of the natural death rate for Wuhan residents.
T208	34415-34552	Sentence	denotes	Qiqing Mo, a visiting graduate student at University of Florida, coming from Guangxi Medical University, participated in data collection.
T209	34553-34622	Sentence	denotes	This study would take longer time to complete without her assistance.
T210	34624-34646	Sentence	denotes	Authors’ contributions
T211	34647-34769	Sentence	denotes	Chen X and Yu B conceived the topic together and joined conducted the analysis and participated in manuscript development.
T212	34770-34884	Sentence	denotes	Yu B spent time to collect data, verify results and review and comments on the manuscript first drafted by Chen X.
T213	34885-34938	Sentence	denotes	The author(s) read and approved the final manuscript.
T214	34940-34947	Sentence	denotes	Funding
T215	34948-34953	Sentence	denotes	None.
T216	34955-34997	Sentence	denotes	Ethics approval and consent to participate
T217	34998-35013	Sentence	denotes	Not applicable.
T218	35015-35038	Sentence	denotes	Consent for publication
T219	35039-35054	Sentence	denotes	Not applicable.
T220	35056-35075	Sentence	denotes	Competing interests
T221	35076-35134	Sentence	denotes	The authors declare that they have no competing interests.

T1

Sentence

denotes

First two months of the 2019 Coronavirus Disease (COVID-19) epidemic in China: real-time surveillance and evaluation with a second derivative model

T2

149-157

Sentence

denotes

Abstract

T3

158-168

Sentence

denotes

Background

T4

169-459

Sentence

denotes

Similar to outbreaks of many other infectious diseases, success in controlling the novel 2019 coronavirus infection requires a timely and accurate monitoring of the epidemic, particularly during its early period with rather limited data while the need for information increases explosively.

T5

461-468

Sentence

denotes

Methods

T6

469-628

Sentence

denotes

In this study, we used a second derivative model to characterize the coronavirus epidemic in China with cumulatively diagnosed cases during the first 2 months.

T7

629-722

Sentence

denotes

The analysis was further enhanced by an exponential model with a close-population assumption.

T8

723-908

Sentence

denotes

This model was built with the data and used to assess the detection rate during the study period, considering the differences between the true infections, detectable and detected cases.

T9

910-917

Sentence

denotes

Results

T10

918-1030

Sentence

denotes

Results from the second derivative modeling suggest the coronavirus epidemic as nonlinear and chaotic in nature.

T11

1031-1239

Sentence

denotes

Although it emerged gradually, the epidemic was highly responsive to massive interventions initiated on January 21, 2020, as indicated by results from both second derivative and exponential modeling analyses.

T12

1240-1313

Sentence

denotes

The epidemic started to decelerate immediately after the massive actions.

T13

1314-1447

Sentence

denotes

The results derived from our analysis signaled the decline of the epidemic 14 days before it eventually occurred on February 4, 2020.

T14

1448-1560

Sentence

denotes

Study findings further signaled an accelerated decline in the epidemic starting in 14 days on February 18, 2020.

T15

1562-1573

Sentence

denotes

Conclusions

T16

1574-1683

Sentence

denotes

The coronavirus epidemic appeared to be nonlinear and chaotic, and was responsive to effective interventions.

T17

1684-1921

Sentence

denotes

The methods used in this study can be applied in surveillance to inform and encourage the general public, public health professionals, clinicians and decision-makers to take coordinative and collaborative efforts to control the epidemic.

T18

1923-1935

Sentence

denotes

Introduction

T19

1936-2019

Sentence

denotes

The epidemic of COVID-19 is caused by a novel virus first detected in Wuhan, China.

T20

2020-2122

Sentence

denotes

This virus was previously named as 2019-nCoV and it is a positive, enveloped, single-strand RNA virus.

T21

2123-2287

Sentence

denotes

It also shares a lot of similarities with two other coronaviruses, the MERS-CoV (Middle East Respiratory Syndrome) and SARS-CoV (Severe Acute Respiratory Syndrome).

T22

2288-2392

Sentence

denotes

Outbreak of the COVID-19 started with the report of a first suspected case on December 8, 2019 in Wuhan.

T23

2393-2622

Sentence

denotes

The first two months of the epidemic covered three significant holidays, including the New Year of 2020, the Chinese New Year’s Day with vacations from January 24 to February 2, 2020, and the Lantern Festival on February 8, 2020.

T24

2623-2870

Sentence

denotes

During this period, one study by the Chinese Center for Disease Prevention and Control (CDC) and Hubei Provincial CDC with data collected by Wuhan CDC documented the details of the epidemic day by day from December 8, 2019 to January 21, 2020 [1].

T25

2871-3082

Sentence

denotes

Data in this study showed that detected and confirmed cases with COVID-19 infection declined from the peak of 44 on January 8 to only 2 on January 19, 2020, suggesting that the epidemic was likely under control.

T26

3083-3284

Sentence

denotes

China officially declared the epidemic as an outbreak on January 20 when obvious human-to-human transmissions were ascertained with reagent probes and primers distributed to local agencies on that day.

T27

3285-3530

Sentence

denotes

Immediately following the declaration, massive actions were taken the next day to curb the epidemic at Wuhan, and soon spread to the whole country from central to local government, including all sectors from business to factories and to schools.

T28

3531-3645

Sentence

denotes

On February 23, 2020, Wuhan City and other cities along with the main traffic lines around Wuhan were locked down.

T29

3646-4006

Sentence

denotes

Rigorous efforts were devoted to 1) identify the infected and bring them to treatment in hospitals for infectious diseases, 2) locate and quarantine all those who had contact with the infected, 3) sterilize environmental pathogens, 4) promote mask use, and 5) release to the public of number of infected, suspected, under treatment and deaths on a daily basis.

T30

4007-4232

Sentence

denotes

On January 24, 2020, the New Year’s Eve and 25, the Chinese New Year’s Day, President Xi Jinping held a special meeting at the Central Chinese Government and decided to implement massive national efforts to curb the epidemic.

T31

4233-4339

Sentence

denotes

An Anti- COVID-19 Group headed by Premier Li Keqiang was established to lead the massive national efforts.

T32

4340-4428

Sentence

denotes

Vice Premier Sun Chunlan was sent to Hubei and Wuhan to directly lead the local efforts.

T33

4429-4554

Sentence

denotes

A massive number of detection kits were made available to all locations to test all susceptible patients for final diagnosis.

T34

4555-4701

Sentence

denotes

People in other cities and provinces who either traveled to or out of Wuhan were quarantined, with suspected patients being diagnosed and treated.

T35

4702-4876

Sentence

denotes

The sudden escalation of the control and the spread of the number of infected and deaths, however, ignited strong emotional responses of fear and panic among people in Wuhan.

T36

4877-5048

Sentence

denotes

The negative emotional responses soon spread from Wuhan to other parts of China, and further to the world via almost all communication channels, particularly social media.

T37

5049-5567

Sentence

denotes

The highly emotional responses of the public were fueled by (1) sudden increases in the number of detected new cases after the massive intervention measures to identify the infected; (2) massive growing needs for masks; (3) a large number of suspected patients waiting to confirm their diagnose; (4) a large number of diagnosed COVID-19 patients for treatment; and (5) a growing number of deaths, despite national efforts to improve therapy, including the decision to build two large hospitals within a period of days.

T38

5568-5770

Sentence

denotes

The emotional responses, mostly stimulated by the daily release of data have created a big barrier for effective control of the epidemic as has been observed in other epidemics of similar nature [2, 3].

T39

5771-5947

Sentence

denotes

It is a paradox that during the early period of an epidemic, little is known or available about the new infections; while the need for such information is at the highest level.

T40

5948-5991

Sentence

denotes

This is particularly true for the COVID-19.

T41

5992-6330

Sentence

denotes

The occurrence of this epidemic may follow a nonlinear, chaotic and catastrophic process, rather similar to the epidemic of SARS that occurred in Hong Kong in 2003 [2], the Ebola epidemic in West Africa during 2013–16 [4, 5], the pandemic of 2009 H1N1 epidemic started [6–8] and the recent measles outbreaks in the United States (US) [9].

T42

6331-6575

Sentence

denotes

Similar to an eruption of a volcano or occurrence of an earthquake, no matter how closely it is monitored, how much research we have done, how much we know about it, no one knows for sure if and when the virus infection will become an outbreak.

T43

6576-6732

Sentence

denotes

Therefore, there is no so-called rational responses, no standard-operating-procedure (SOP) to follow, no measures to take without negative consequences [2].

T44

6733-6883

Sentence

denotes

However, defining the COVID-19 as nonlinear and chaotic does not mean that we cannot do anything after we knew it was an outbreak, but simply waiting.

T45

6884-7486

Sentence

denotes

On the contrary, defining it as nonlinear and chaotic will better inform us to make right decisions and to take appropriate actions. (1) During the early stage of an infection, which we cannot tell whether it will be growing into an outbreak, we must closely monitor it using limited data and to find the early signs of change and to predict if and when it will become an outbreak; (2) After it is declared as an outbreak, it is better to take actions as soon as possible since infectious diseases can be controlled even without knowledge of the biology [10]; and evaluate if the control measures work.

T46

7487-7713

Sentence

denotes

The ultimate goal of this study is to attempt to provide some solutions to this paradox by providing early messages to inform control measures, to be optimistic and not panic, to ask right questions, and to take right actions.

T47

7715-7722

Sentence

denotes

Methods

T48

7724-7758

Sentence

denotes

Daily detected and confirmed cases

T49

7759-7924

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

7925-8116

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

8117-8288

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

8289-8437

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

8438-8668

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

8669-8987

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

8989-9041

Sentence

denotes

Understanding of the detected cases on a daily basis

T56

9042-9157

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

9158-9298

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

9299-9522

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

9523-9673

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

9674-9786

Sentence

denotes

For example, a detectable person in day one can be postponed to next day when testing services become available.

T61

9787-9925

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

9927-9961

Sentence

denotes

Model daily change in the epidemic

T63

9962-10067

Sentence

denotes

We started our modeling analysis with data of cumulative number of diagnosed COVID-19 infections per day.

T64

10068-10212

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

10213-10569

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

10570-10743

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

10744-10817

Sentence

denotes

To better monitor the epidemic, the first derivative of F(x) can be used:

T68

10818-11270

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

11271-11397

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

11398-11472

Sentence

denotes

Practically, F ′ (x) is equivalent to the newly diagnosed cases every day.

T71

11473-11681

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

11682-11723

Sentence

denotes

We thus used the second derivative F″(x):

T73

11724-12124

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

12125-12228

Sentence

denotes

Mathematically, F′′(x) measures the acceleration of the epidemic or changes in new infections each day.

T75

12229-12469

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

12471-12527

Sentence

denotes

Modeling the epidemic with assumption of no intervention

T77

12528-12677

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

12678-12829

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

12830-13294

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

13295-13374

Sentence

denotes

where, α =number of expected cases at the baseline and β = growth rate per day.

T81

13376-13410

Sentence

denotes

Estimation of daily detection rate

T82

13411-14774

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

14775-15238

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

15239-15296

Sentence

denotes

We used these estimated Pi in this study in several ways.

T85

15297-15538

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

15539-15750

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

15751-15977

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

15978-16032

Sentence

denotes

The modeling analysis was completed using spreadsheet.

T89

16033-16248

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.

T90

16250-16257

Sentence

denotes

Results

T91

16259-16308

Sentence

denotes

Cumulative number of detected and diagnosed cases

T92

16309-16477

Sentence

denotes

The COVID-19 epidemic was initiated in Wuhan, the Provincial Capital of Hubei Province with a total population of 14.2 million, including 5.1 million mobile population.

T93

16478-16563

Sentence

denotes

The mortality rate was 5.5/1000 for Wuhan residents with most available data in 2018.

T94

16564-16754

Sentence

denotes

Assuming all diagnosed cases in China were infected in Wuhan (an exaggerated scenarios for illustration purpose), the two-month incidence rate of COVID-19 was 2.6/1000 among Wuhan residents.

T95

16755-16899

Sentence

denotes

Based on reported case mortality of 2.3%, the population-based mortality of COVID-19 was 0.6/1000, or 1/9th of the mortality of Wuhan residents.

T96

16900-17037

Sentence

denotes

Figure 1 presents the cumulative diagnosed cases F(x) and major events during the study period from December 8, 2019 to February 8, 2020.

T97

17038-17109

Sentence

denotes

During the period, a total of 37,198 cases were diagnosed and reported.

T98

17110-17274

Sentence

denotes

The daily cases varied from 0 to 3886 with the median cases of 199 (January 8, 2020), and inter-quarter range (IQR) of 24 (December 23), and 830 (January 23, 2020).

T99

17275-17462

Sentence

denotes

Fig. 1 Cumulative number of diagnosed COVID-19(2019-nCoV) infection F(x) and key events before, during and after declaration of the outbreak in the first 2 months of the Epidemic in China

T100

17464-17526

Sentence

denotes

Dynamics of the epidemic and response to massive interventions

T101

17527-17751

Sentence

denotes

The dynamic changes based on the observed F(x) in Fig. 1 were presented in Fig. 2 using the first derivatives F ′ (x) (top panel of the figure) and the second derivative F ′ ′ (x) (bottom panel of the figure), respectively.

T102

17752-17927

Sentence

denotes

Before the declaration of outbreak, information provided by the two dynamic measured was similar: not much variations were revealed relative to the changes after the outbreak.

T103

17928-18012

Sentence

denotes

These findings suggest the nonlinear and chaotic character of the COVID-19 outbreak.

T104

18013-18203

Sentence

denotes

Fig. 2 The first F′(x) and second derivative F″(x) of diagnosed COVID-19 (formally 2019-nCoV infection) F(x) before, during and after declaring the outbreak in first 2 months of the Epidemic

T105

18204-18310

Sentence

denotes

After declaring the outbreak on January 20, information revealed by F ′ ′ (x) differed much from F ′ (x).

T106

18311-18486

Sentence

denotes

Based on information from F ′ (x), the newly diagnosed F ′ (x) cases increased progressively with some fluctuation, then peaked on February 4, 2020, and followed by a decline.

T107

18487-18652

Sentence

denotes

The increases in the diagnosed cases could be either due to the natural growth of the epidemic in itself, or due to the interventions to detect the infected or both.

T108

18653-18734

Sentence

denotes

Furthermore, F ′ (x) provided no sign of epidemic decline until February 4, 2020.

T109

18735-18879

Sentence

denotes

In other words, we have to wait for at least 14 days after the massive anti-COVID-19 epidemic without using information derived from F ′ ′ (x).

T110

18880-19013

Sentence

denotes

Quite different from F ′ (x), F ′′ (x) removed the time trend of F ′ (x) to show the acceleration/deceleration of diagnosed COVID-19.

T111

19014-19172

Sentence

denotes

Consequently, F ′ ′ (x) was much more sensitive than F ′ (x) to gauge the intrinsic dynamics of the epidemic in response to the massive anti-COVID-19 action.

T112

19173-19342

Sentence

denotes

Since January 21, 2020 after the massive anti-COVID actions, the F ′ ′ (x) suddenly became very active, as indicated by the alternative accelerations and decelerations.

T113

19343-19644

Sentence

denotes

F ′ ′ (x) reached the peak on January 27 after the distribution of large number of test kits on January 26, which was an action based on the decision at the central government level in a meeting held by Chinese President Xi Jinping on January 24 and 25, the Chinese New Year’s Eve and New Year’s Day.

T114

19645-19997

Sentence

denotes

In addition, the estimated F ′′ (x) captured three significant decelerations on January 28, February 5 and 6 (two days in a row), and 8, 2020 respectively; corresponding to the intensified massive actions in locating and treating the infected, locking down more communities, plus mask use and massive pathogen sterilization in neighborhood environment.

T115

19998-20236

Sentence

denotes

In addition to informing whether the epidemic was responsive to the massive interventions, information from F ′′ (x) signaled an overall downturn of the epidemic since the beginning of the massive anti-COVID-19 action on January 21, 2020.

T116

20237-20323

Sentence

denotes

This was further pronounced by the band region between the two dotted lines in Fig. 2.

T117

20324-20461

Sentence

denotes

Despite zigzags, an overall downward trend in F ′′ (x) was clearly revealed by the downward and progressively narrowing down band region.

T118

20462-20586

Sentence

denotes

This trend strongly indicates that the epidemic could be brought under control soon with the current interventions in place.

T119

20588-20625

Sentence

denotes

Exponential growth and detection rate

T120

20626-20701

Sentence

denotes

The observed F(x) fit the exponential model of Eq. 4 well with R2 = 0.9778.

T121

20702-20799

Sentence

denotes

The estimated α =1.1070, representing the first person who was infected and ignited the epidemic.

T122

20800-20854

Sentence

denotes

The estimated β =0.1716, representing the growth rate.

T123

20855-20947

Sentence

denotes

Using this estimated growth rate, it takes only 4 days for the diagnosed COVID-19 to double.

T124

20948-21102

Sentence

denotes

Figure 3 presents the daily detection rates, estimated with the fitted exponential model from day one of the epidemic to the last day of the study period.

T125

21103-21259

Sentence

denotes

Based on findings in this figure and data from Figs. 1 and 2, we divided the COVID-19 epidemic during the first two months of the epidemic into five phases.

T126

21260-21432

Sentence

denotes

Fig. 3 Estimated daily detection rate Pi of COVID-19 (2019-nCoV) infection before, during and after declaration of the outbreak, the first 2 months of the Epidemic in China

T127

21433-21473

Sentence

denotes

Phase 1 was from December 8 to 25, 2019.

T128

21474-21574

Sentence

denotes

During this period, the detection rate Pi was high overall, with fluctuations around and above 100%.

T129

21575-21678

Sentence

denotes

This was corresponding to the early period after the first suspected case was identified and diagnosed.

T130

21679-21762

Sentence

denotes

Phase 2 was from December 26, 2019 to January 8, 2020, covering the New Year’s Day.

T131

21763-21891

Sentence

denotes

The detection rate Pi fluctuated at around 50% with the lowest of 17% on December 31, 2019 and the highest of 108% on January 8.

T132

21892-22054

Sentence

denotes

Phase 3 was from January 8 to 20, 2020, and it was featured with a progressive decline in the estimated Pi from 105% on January 8, 2020 to 1% on January 20, 2020.

T133

22055-22218

Sentence

denotes

This progressive declining period was the time for the Chinese to prepare for the traditional Chinese New Year’s with the longest and highest level of celebration.

T134

22219-22306

Sentence

denotes

Unfortunately, the COVID-19 as an outbreak was silently stepping in during this period.

T135

22307-22473

Sentence

denotes

Phase 4 was from January 20 to 27, 2020 with the estimated Pi increased from 1% on January 20, 2020 to surpass 100%, and reached the peak of 170% on January 27, 2020.

T136

22474-22640

Sentence

denotes

This period was corresponding to the initiation and progressive intensifying of the massive intervention organized and coordinated by the Central Government of China.

T137

22641-22791

Sentence

denotes

Phase 5 started from January 27, 2020 to the end of the study period, corresponding to the sustained massive national efforts, plus frequent emphases.

T138

22792-23028

Sentence

denotes

Different from the previous four phases, reductions in the estimated Pi during this phase were not an indication of under-detection but an indication of declines in the epidemic reflected by the detected and confirmed cases of COVID-19.

T139

23029-23138

Sentence

denotes

This is because the model predicted Pi did not consider any interventions but natural growth of the epidemic.

T140

23139-23153

Sentence

denotes

Based on Figs.

T141

23154-23698

Sentence

denotes

2 and 3 (Phase 4 and 5), three pieces of information can be derived: (1) The epidemic was highly sensitive to external interventions, supporting the nonlinear and chaotic characters revealed by the long latent period in the first three phases; (2) the massive national efforts were highly effective in detecting the detectable COVID-19; (3) signal for the COVID-19 in China to decline appeared on January 21 in 2020, 14 days before the start of eventual declines on February 4, as indicated by F ′ ′ (x) and F ′ (x) in Fig. 2 and Pi in Fig. 3.

T142

23700-23711

Sentence

denotes

Disscussion

T143

23712-23843

Sentence

denotes

In this study, we used a novel approach to distill information from the cumulative number of diagnosed cases of COVID-19 infection.

T144

23844-24003

Sentence

denotes

Among various types of surveillance data, this data often reported the earliest and on a continuous basis with high completeness and are most widely available.

T145

24004-24115

Sentence

denotes

In addition, patients with a diagnosed infection are those with high likelihoods to spread the virus to others.

T146

24116-24256

Sentence

denotes

Findings from this study provided useful information in a real time manner to monitor, evaluate and forecast the COVID-19 epidemic in China.

T147

24257-24489

Sentence

denotes

The methods used in this study although somewhat mathematical, are easy to follow while information extracted from the commonly used data with the methods are highly useful and more sensitive than the daily new and cumulative cases.

T148

24491-24544

Sentence

denotes

Nonlinear and chaotic nature of the COVID-19 outbreak

T149

24545-24798

Sentence

denotes

Although an analytical demonstration of the COVID-19 outbreak as nonlinear, chaotic and catastrophic requires more time to wait till the epidemic ends, evidence in the first 2 months suggests that the COVID-19 outbreak in China is nonlinear and chaotic.

T150

24799-24959

Sentence

denotes

The epidemic emerged suddenly after a long latent period without dramatic changes as revealed from the cumulative cases, and their first and second derivatives.

T151

24960-25161

Sentence

denotes

The high responsiveness of the epidemic to interventions adds additional evidence supporting the chaotic and catastrophic nature, and demonstrating the selection of a good timing to start intervention.

T152

25162-25436

Sentence

denotes

Many of these characters are similar to those observed in the 2003 SARS epidemic started in Hong Kong [2], the 2013–16 Ebola spread in the West Africa [4, 5], the 2009 pandemic of H1N1 started in the US [6–8], and the measles outbreaks over 80 cities in the US recently [9].

T153

25437-25521

Sentence

denotes

Even the seasonal common flu has been proved to have a nonlinear component [11, 12].

T154

25522-25737

Sentence

denotes

The significance of nonlinear and chaotic nature of COVID-19 means that no methods are available to predict exactly at what point in time the epidemic will emerge as an outbreak, just like volcanoes and earthquakes.

T155

25738-25835

Sentence

denotes

Therefore, practically there is no so-called a best time or missed the best time to take actions.

T156

25836-25906

Sentence

denotes

There will also no so-called rational analysis and rational responses.

T157

25907-26064

Sentence

denotes

There is no silver bullet to use, no standard-operating-procedure (SOP) to follow, and no measures without negative consequences to control the epidemic [2].

T158

26065-26193

Sentence

denotes

For example, it took more than 6 months for both the US and the WHO to determine the 2009 H1N1 pandemic as an outbreak [13, 14].

T159

26194-26471

Sentence

denotes

Therefore, knowing the nonlinear and chaotic nature of an epidemic outbreak, like COVID-19, for all stockholders will be essential to the mobilization of resources, working together, taking all actions possible to control the epidemic, and minimizing the negative consequences.

T160

26472-27063

Sentence

denotes

Specifically, what we can do to deal with an outbreak like COVID-19 would be to (1) collect information as early as possible, (2) monitor the epidemic as close as possible just like we do for an earthquake and make preparations for a hurricane and (3) communicate with the society and use confirmed data appropriately reframed not causing or exacerbating fear and panic in the public, stress and distress among medical and public health professionals, as well as administrators to make right decisions and take the right strategies at the right time in the right places for the right people.

T161

27064-27209

Sentence

denotes

Knowing the nonlinear and chaotic nature is also essential for taking actions to control the outbreak of an epidemic like the COVID-19 infection.

T162

27210-27603

Sentence

denotes

As soon as an outbreak is confirmed, the follow measures should be in position immediately 1) closely and carefully monitor the epidemic; 2) take evidence-based interventions to control the epidemic, 3) actively assess responses of the epidemic to the interventions; 4) allow errors in the intervention, particularly during the early period of the epidemic, 5) always prepare for alternatives.

T163

27604-27676

Sentence

denotes

Another confusion is, when an epidemic starts, everyone asks what it is?

T164

27677-27696

Sentence

denotes

How does it happen?

T165

27697-27732

Sentence

denotes

How should I do to avoid infection?

T166

27733-27766

Sentence

denotes

Is there any effective treatment?

T167

27767-27894

Sentence

denotes

Answering these questions takes time, but there is no need to wait till all these questions are resolved before taking actions.

T168

27895-27992

Sentence

denotes

We can take actions to prevent COVID-19 immediately while waiting for answers to these questions.

T169

27993-28145

Sentence

denotes

This is because we have the evidence-based strategy for control and prevention of any infectious disease without complete understanding of an infection.

T170

28146-28334

Sentence

denotes

That is so-called Tri-Component Strategy: locating and controlling the sources of infection, identifying and blocking the transmission paths, and protecting those who are susceptible [10].

T171

28335-28414

Sentence

denotes

This was just what China has done, is doing, and will continue to do this time.

T172

28415-28677

Sentence

denotes

Typical examples of control and prevention measures include locking down of cities, communities, and villages with potential of large scale transmission, massive environment sterilization, promotion of mask use, efforts to locate, isolate and treat the infected.

T173

28678-28864

Sentence

denotes

More importantly, most of these actions are initiated, mobilized, coordinated and supported by the government from central to local, and enhanced by volunteers and international support.

T174

28866-28905

Sentence

denotes

Highly effective of the national effort

T175

28906-29085

Sentence

denotes

Another important piece of findings is that we detected the effect of the national efforts taken by China from the beginning when they were in position till the end of this study.

T176

29086-29277

Sentence

denotes

For example, from the second derivative, we observed increases in the infected through the action on January 22, 2020, the next day after the massive intervention started on January 21, 2020.

T177

29278-29337

Sentence

denotes

This result was also picked up by the exponential modeling.

T178

29338-29483

Sentence

denotes

From day one on January 21, 2020 when the massive intervention measures activated to February 4, 2020 is the latent period of COVID-19 infection.

T179

29484-29715

Sentence

denotes

The second derivative precisely recorded the change in newly diagnosed cases in response to the massive measures, reflected as the rapid increase in detection rate, consistent with the result from the exponential modeling analysis.

T180

29716-29964

Sentence

denotes

The detected responsiveness of the epidemic to the intervention provided data to predict the occurrence of deceleration of the epidemic on February 4, 2020 if the same measures persist, which was exactly what we observed from the second derivative.

T181

29965-30044

Sentence

denotes

Based on the findings from our analysis, the COVID-19 in China may end up soon.

T182

30045-30266

Sentence

denotes

Despite a delay of 43 days from the first confirmed cases on December 8, 2019 to January 20, 2020, the COVID-19 epidemic was highly responsive to massive interventions, supporting the effectiveness of these interventions.

T183

30267-30654

Sentence

denotes

It is our prediction that the outbreak of the COVID-19 infection will be brought under control by the end of February 2020, given the effective control measures known to everyone, increases in immune level in the total population due to latent infections, and most widely spread of knowledge and skills for infectious disease control and prevention among the 1.4 billion people in China.

T184

30656-30690

Sentence

denotes

Effective methods for surveillance

T185

30691-30771

Sentence

denotes

There are a number of advantages of methods we developed and used in this study.

T186

30772-31091

Sentence

denotes

First, framing the diagnosed cases as the cumulative, the first and the second derivative constructs a system to gauge the epidemic, with the cumulative cases showing the overall level of the epidemic, the first derivative to reflect the change of the epidemic, and the second derivative to monitor the speed of change.

T187

31092-31383

Sentence

denotes

By inclusion of the mortality rate as a reference, results from our approach will be (1) comprehensive to inform the public to be prepared, not scared and not to blame others; (2) useful for administrators to make decisions; (3) valuable for medical and health professionals to take actions.

T188

31384-31697

Sentence

denotes

Second, we conceptually separated (1) the true number of infections, which will never be practically detected, from (2) the infections that are practically detectable if services are available and accessible and detection technologies are sensitive and reliable, and (3) the actually detected cases of infections.

T189

31698-31936

Sentence

denotes

This classification greatly improved our understanding of the observed data as well as findings from the two derivatives, and aided us in assessing the responsiveness to the massive interventions, and predicting of the epidemic over time.

T190

31937-32152

Sentence

denotes

The clarification also enhanced our analytical approach by adding an exponential model to evaluate the detection rate and to bring more data assessing the responsiveness of the epidemic to the massive interventions.

T191

32153-32283

Sentence

denotes

We highly recommend the inclusion of the methods as a part of routine surveillance in disease control and prevention institutions.

T192

32285-32312

Sentence

denotes

Limitations and future plan

T193

32313-32335

Sentence

denotes

There are limitations.

T194

32336-32402

Sentence

denotes

First, this study covered only the first 2 months of the epidemic.

T195

32403-32504

Sentence

denotes

We will continue to evaluate the utility of this method as we follow the development of the epidemic.

T196

32505-32576

Sentence

denotes

Second, the methods used in this study was based on a close population.

T197

32577-32717

Sentence

denotes

This hypothesis may not be true because of a large number of people with potential history of exposure in China traveled to other countries.

T198

32718-32900

Sentence

denotes

Up to February 8, 2020, the total cases diagnosed were 37,552 worldwide (Worldometer on Coronavirus) with 37,198 in China, which accounted for 99.1% of the total number of the world.

T199

32901-32978

Sentence

denotes

Therefore, the impact of close-population assumption would be rather limited.

T200

32979-33058

Sentence

denotes

Third, there was a lack of individual patient-level data for detailed analysis.

T201

33059-33232

Sentence

denotes

Fourth, our model can be further improved with other data, such as cases by severity, number of the suspected, number of those who received treatments and treatment results.

T202

33233-33347

Sentence

denotes

We will follow the epidemic closely and prepare for further research on the topic when more data become available.

T203

33348-33706

Sentence

denotes

Despite the limitations, this study provided new data to encourage those who are infected to better fight against the infections; to inform and encourage the general public, the medical and health professionals and the government to continue their current measures and to think of more measures that are innovative and effective to end the COVID-19 epidemic.

T204

33707-34088

Sentence

denotes

One of the greatest motivations for this study is to attempt to provide right information at the population level in a real manner to complement the data from micro-organism centered and laboratory-based biological, molecular, pharmacological and clinical information in both the academic and the mass media that often scare rather than encourage people, even health professionals.

T205

34089-34147

Sentence

denotes

Of the diagnosed COVID-19 cases, less than 20% are severe.

T206

34148-34260

Sentence

denotes

Findings from our study indicated that there is no need to be panic from a public health population perspective.

T207

34261-34413

Sentence

denotes

Although the total cases COVID-19 reached to big numbers, but the 2-month incidence rate was about a half of the natural death rate for Wuhan residents.

T208

34415-34552

Sentence

denotes

Qiqing Mo, a visiting graduate student at University of Florida, coming from Guangxi Medical University, participated in data collection.

T209

34553-34622

Sentence

denotes

This study would take longer time to complete without her assistance.

T210

34624-34646

Sentence

denotes

Authors’ contributions

T211

34647-34769

Sentence

denotes

Chen X and Yu B conceived the topic together and joined conducted the analysis and participated in manuscript development.

T212

34770-34884

Sentence

denotes

Yu B spent time to collect data, verify results and review and comments on the manuscript first drafted by Chen X.

T213

34885-34938

Sentence

denotes

The author(s) read and approved the final manuscript.

T214

34940-34947

Sentence

denotes

Funding

T215

34948-34953

Sentence

denotes

None.

T216

34955-34997

Sentence

denotes

Ethics approval and consent to participate

T217

34998-35013

Sentence

denotes

Not applicable.

T218

35015-35038

Sentence

denotes

Consent for publication

T219

35039-35054

Sentence

denotes

Not applicable.

T220

35056-35075

Sentence

denotes

Competing interests

T221

35076-35134

Sentence

denotes

The authors declare that they have no competing interests.

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