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T1 0-89 Sentence denotes Phase-adjusted estimation of the number of Coronavirus Disease 2019 cases in Wuhan, China
T2 91-99 Sentence denotes Abstract
T3 100-253 Sentence denotes An outbreak of clusters of viral pneumonia due to a novel coronavirus (2019-nCoV/SARS-CoV-2) happened in Wuhan, Hubei Province in China in December 2019.
T4 254-421 Sentence denotes Since the outbreak, several groups reported estimated R0 of Coronavirus Disease 2019 (COVID-19) and generated valuable prediction for the early phase of this outbreak.
T5 422-520 Sentence denotes After implementation of strict prevention and control measures in China, new estimation is needed.
T6 521-698 Sentence denotes An infectious disease dynamics SEIR (Susceptible, Exposed, Infectious, and Removed) model was applied to estimate the epidemic trend in Wuhan, China under two assumptions of Rt.
T7 699-758 Sentence denotes In the first assumption, Rt was assumed to maintain over 1.
T8 759-903 Sentence denotes The estimated number of infections would continue to increase throughout February without any indication of dropping with Rt = 1.9, 2.6, or 3.1.
T9 904-1004 Sentence denotes The number of infections would reach 11,044, 70,258, and 227,989, respectively, by 29 February 2020.
T10 1005-1235 Sentence denotes In the second assumption, Rt was assumed to gradually decrease at different phases from high level of transmission (Rt = 3.1, 2.6, and 1.9) to below 1 (Rt = 0.9 or 0.5) owing to increasingly implemented public health intervention.
T11 1236-1362 Sentence denotes Several phases were divided by the dates when various levels of prevention and control measures were taken in effect in Wuhan.
T12 1363-1477 Sentence denotes The estimated number of infections would reach the peak in late February, which is 58,077–84,520 or 55,869–81,393.
T13 1478-1655 Sentence denotes Whether or not the peak of the number of infections would occur in February 2020 may be an important index for evaluating the sufficiency of the current measures taken in China.
T14 1656-1964 Sentence denotes Regardless of the occurrence of the peak, the currently strict measures in Wuhan should be continuously implemented and necessary strict public health measures should be applied in other locations in China with high number of COVID-19 cases, in order to reduce Rt to an ideal level and control the infection.
T15 1966-1978 Sentence denotes Introduction
T16 1979-2113 Sentence denotes 2019 Novel coronavirus (2019-nCoV/SARS-CoV-2) has given rise to an outbreak of viral pneumonia in Wuhan, China since December 20191,2.
T17 2114-2209 Sentence denotes World Health Organization (WHO) now has named the disease Coronavirus Disease 2019 (COVID-19)3.
T18 2210-2314 Sentence denotes Most cases from the initial cluster had an epidemiological link to the Huanan Seafood Wholesale Market4.
T19 2315-2508 Sentence denotes Patients have clinical manifestations, including fever, cough, shortness of breath, muscle ache, confusion, headache, sore throat, rhinorrhoea, chest pain, diarrhea, and nausea and vomiting5,6.
T20 2509-2830 Sentence denotes As of 17 February 2020, a cumulative total of 72,436 confirmed cases (including 11,741 currently severe cases), 6242 currently suspect cases, a cumulative total of 1868 deaths and 12,552 cases discharged from hospital were reported by National Health Commission of the People’s Republic of China (NHC) in mainland China7.
T21 2831-3051 Sentence denotes The significant increases in the number of confirmed cases in China and abroad led to the announcement made by WHO on 30 January that the event has already constituted a Public Health Emergency of International Concern8.
T22 3052-3409 Sentence denotes The reproduction number, R, measures the transmissibility of a virus, representing the average number of new infections generated by each infected person, the initial constant of which is called the basic reproduction number, R09, and the actual average number of secondary cases per infected case at time t is called effective reproduction number, Rt10–12.
T23 3410-3488 Sentence denotes Rt shows time-dependent variation with the implementation of control measures.
T24 3489-3705 Sentence denotes R > 1 indicates that the outbreak is self-sustaining unless effective control measures are implemented, while R < 1 indicates that the number of new cases decreases over time and, eventually, the outbreak will stop9.
T25 3706-3847 Sentence denotes Over the past month, several groups reported estimated R0 of COVID-19 and generated valuable prediction for the early phase of this outbreak.
T26 3848-4003 Sentence denotes In particular, Imai et al.9 provided the first estimation, using R0 of 2.6 and based on the number of cases in China and those detected in other countries.
T27 4004-4070 Sentence denotes Other authors estimated R0 to be 3.813, 6.4714, 2.215, and 2.6816.
T28 4071-4203 Sentence denotes These predictions were very alerting and suggestions have been made for very strict public health measures to contain the epidemics.
T29 4204-4303 Sentence denotes In response to the outbreak of COVID-19, a series of prompt public health measures have been taken.
T30 4304-4422 Sentence denotes On 1 January, the Huanan Seafood Wholesale Market was closed in the hope of eliminating zoonotic source of the virus5.
T31 4423-4693 Sentence denotes On 11 January, upon isolation of the viral strain for COVID-19 and establishment of its whole-genome sequences17, reverse transcription-polymerase chain reaction (RT-PCR) reagents were developed and provided to Wuhan, which ensured the fast ascertainment of infection15.
T32 4694-4810 Sentence denotes On 21 January, Emergency Response System was activated to better provide ongoing support to the COVID-19 response18.
T33 4811-4954 Sentence denotes Ever since the outbreak, the work of intensive surveillance, epidemiological investigations, and isolation of suspect cases gradually improved.
T34 4955-5074 Sentence denotes Those having had close contacts with infections were asked to receive medical observation and quarantine for 14 days19.
T35 5075-5204 Sentence denotes Travel from and to Wuhan City as well as other medium-sized cities in Hubei Province has been restricted since 23 January 202020.
T36 5205-5296 Sentence denotes The 2019-nCoV/SARS-CoV-2 has at least 79.5% similarity in genetic sequence to SARS-CoV5,17.
T37 5297-5445 Sentence denotes Riley21 estimated that 2.7 secondary infections were generated per case on average (R0 = 2.7) at the start of the SARS epidemic without controlling.
T38 5446-5568 Sentence denotes After isolating the patients and controlling the infection by the authority, the value of Rt for SARS decreased to 0.2522.
T39 5569-5716 Sentence denotes As Li et al.15 mentioned, it is possible that subsequent control measures in Wuhan, and elsewhere in mainland China, have reduced transmissibility.
T40 5717-5913 Sentence denotes A new estimation of the epidemic dynamics taking the unprecedentedly strict prevention and control measures in China into consideration is required to better guide the future prevention decisions.
T41 5914-6149 Sentence denotes In this article, we intended to make phase-adjusted estimation of the epidemic trend for the 2019-nCoV / SARS-CoV-2 infection transmission in Wuhan, China under two assumptions of Rt (maintaining high >1 or gradually decreasing to <1).
T42 6150-6398 Sentence denotes We hope to depict two types of epidemic dynamics to provide potential evaluation standard for the effects of current prevention and control measures, and to provide theoretical basis for future prevention decisions of the current epidemic in China.
T43 6400-6407 Sentence denotes Results
T44 6409-6524 Sentence denotes Estimation of the epidemic trend assuming that the prevention and control measures are insufficient in Wuhan, China
T45 6525-6675 Sentence denotes Assuming the epidemic continues to develop with R0 = 1.9, 2.6, and 3.19 from 1 December 2019, the number of infections will continue to rise (Fig. 1).
T46 6676-6815 Sentence denotes By the end of February 2020, COVID-19 cases would be 11,044, 70,258, and 227,989 in Wuhan, China with R0 = 1.9, 2.6, and 3.1, respectively.
T47 6816-6894 Sentence denotes Detailed calculation process is included in the Materials and methods section.
T48 6895-7015 Sentence denotes Fig. 1 Estimation of the number of COVID-19 cases in Wuhan, China (December 2019–February 2020, R0 = 1.9, 2.6, and 3.1).
T49 7016-7188 Sentence denotes In all, 11,044, 70,258, and 227,989 represent the estimated number of COVID-19 cases by the end of February 2020 in Wuhan, China, with R0 = 1.9, 2.6, and 3.1, respectively.
T50 7190-7303 Sentence denotes Estimation of the epidemic trend assuming that the prevention and control measures are sufficient in Wuhan, China
T51 7304-7354 Sentence denotes The first phase (1 December 2019–23 January 2020):
T52 7355-7454 Sentence denotes It was the early phase of the epidemic when a few prevention and control measures were implemented.
T53 7455-7558 Sentence denotes The number of infections in Wuhan, China reached 17,656–25,875 by the end of this phase with R0 as 3.1.
T54 7559-7610 Sentence denotes The second phase (24 January 2020–2 February 2020):
T55 7611-7737 Sentence denotes From 23 January 2020 on, public transportations to and from Wuhan, as well as public transportation within Wuhan were stopped.
T56 7738-7847 Sentence denotes While gathering events inside Wuhan was banned, quarantine and isolation were gradually established in Wuhan.
T57 7848-7939 Sentence denotes The number of infections was 32,061–46,905 by the end of this phase as Rt decreased to 2.6.
T58 7940-7991 Sentence denotes The third phase (3 February 2020–15 February 2020):
T59 7992-8169 Sentence denotes New infectious disease hospitals and mobile cabin hospitals came into service and many medical and public health teams from other provinces and cities in China arrived in Wuhan.
T60 8170-8244 Sentence denotes The quarantine and isolation at the community level were further enhanced.
T61 8245-8339 Sentence denotes The number of infections would reach 53,070–77,390 if Rt could be reduced sequentially to 1.9.
T62 8340-8384 Sentence denotes The fourth phase (from 15 February 2020 on):
T63 8385-8485 Sentence denotes All of the most restrict public health measures may need a longest incubation period to take effect.
T64 8486-8653 Sentence denotes If Rt could be gradually reduced to 0.9 or 0.5 in the fourth phase, the epidemic peaks and inflection points might occur in Wuhan, China on 23 February or 19 February.
T65 8654-8760 Sentence denotes The number of infections would be 58,077–84,520 or 55,869–81,393 with Rt = 0.9 or 0.5, respectively (Figs.
T66 8761-8770 Sentence denotes 2 and 3).
T67 8771-8893 Sentence denotes Fig. 2 Phase-adjusted estimation of the number of COVID-19 cases in Wuhan, China (1 December 2019–30 April 2020, E = 20I).
T68 8894-9233 Sentence denotes In all, 55,869 represents the estimated peak number of COVID-19 cases on 19 February 2020 in Wuhan, China with R0 = 0.5; 58,077 represents the estimated peak number of COVID-19 cases on 23 February 2020 in Wuhan, China with R0 = 0.9; E: number of exposed cases; I: number of infectious cases; E was assumed to be 20 times of I at baseline.
T69 9234-9356 Sentence denotes Fig. 3 Phase-adjusted estimation of the number of COVID-19 cases in Wuhan, China (1 December 2019–30 April 2020, E = 30I).
T70 9357-9696 Sentence denotes In all, 81,393 represents the estimated peak number of COVID-19 cases on 19 February 2020 in Wuhan, China with R0 = 0.5; 84,520 represents the estimated peak number of COVID-19 cases on 23 February 2020 in Wuhan, China with R0 = 0.9; E: number of exposed cases; I: number of infectious cases; E was assumed to be 30 times of I at baseline.
T71 9697-9872 Sentence denotes Our model predicted 2323–3381 deaths in Wuhan, China when we assumed Rt as 0.9 and the percent of deaths as 4%; 2235–3256 deaths when we assumed Rt as 0.5 at the fourth phase.
T72 9873-9934 Sentence denotes An average of 2279–3318 deaths were also estimated (Table 1).
T73 9935-10027 Sentence denotes Table 1 Estimating the number of deaths of COVID-19 cases in Wuhan, China (Rt = 0.9 or 0.5).
T74 10028-10053 Sentence denotes Rt = 0.9 Rt = 0.5 Average
T75 10054-10107 Sentence denotes Total cases 58,077–84,520 55,869–81,393 56,973–82,957
T76 10108-10149 Sentence denotes Deaths (4%) 2323–3381 2235–3256 2279–3318
T77 10150-10192 Sentence denotes Deaths (10%) 5808–8452 5587–8139 5697–8296
T78 10193-10244 Sentence denotes The estimated percent of deaths is about 4–10%6,24.
T79 10245-10500 Sentence denotes When we assumed Rt as 0.9 and the percent of deaths 10% based on calculation of case fatality rate (CFR) at early stage of the epidemic6, our model predicted 5808–8452 deaths in Wuhan, China; 5587–8139 deaths when we assumed Rt as 0.5 at the fourth phase.
T80 10501-10552 Sentence denotes An average of 5697–8296 deaths were also estimated.
T81 10554-10564 Sentence denotes Discussion
T82 10565-10871 Sentence denotes Estimations of the transmission risk and the epidemic trend of COVID-19 are of great importance because these can arouse the vigilance of the policy makers, health professionals, and the whole society so that enough resources would be mobilized in a speedy and efficient way for both control and treatment.
T83 10872-11151 Sentence denotes We estimated the number of infections using SEIR (Susceptible, Exposed, Infectious, and Removed) model under two assumptions of Rt (Rt maintaining to be >1 or Rt gradually decreasing to <1) in the purpose of depicting various possible epidemic trends of COVID-19 in Wuhan, China.
T84 11152-11353 Sentence denotes Two estimations provide an approach for evaluating the sufficiency of the current measures taken in China, depending on whether or not the peak of the number of infections would occur in February 2020.
T85 11354-11524 Sentence denotes Assuming the current control measures were ineffective and insufficient, the estimated number of infections would continue to increase throughout February without a peak.
T86 11525-11691 Sentence denotes On the other hand, assuming the current control measures were effective and sufficient, the estimated number of infections would reach the peak in late February 2020.
T87 11692-11807 Sentence denotes According to Read’s research13, R0 for COVID-19 outbreak is much higher compared with other emergent coronaviruses.
T88 11808-11885 Sentence denotes It might be very difficult to contain or control the spreading of this virus.
T89 11886-12152 Sentence denotes If the prevention and control measures were not sufficient or some new factors occurred (e.g., a large proportion of cases with mild or none symptoms existed in the community; there were more zoonotic sources), the epidemic might continue to develop at a high speed.
T90 12153-12398 Sentence denotes Therefore, we depicted first the epidemic dynamics of the relatively unsatisfying circumstance based on the R0 estimated before the unprecedented efforts of China in the containment of the epidemics occurred and the newest documented parameters.
T91 12399-12594 Sentence denotes The curve continued to go up throughout February without any indication of dropping, indicating the need for further enhancement of public health measures for containment of the current outbreak.
T92 12595-13225 Sentence denotes However, as mentioned by WHO in the statement on 30 January, “it is still possible to interrupt virus spread, provided that countries put in place strong measures to detect disease early, isolate and treat cases, trace contacts, and promote social-distancing measures commensurate with the risk.”8 Responding to the outbreak, China has taken a series of unprecedentedly strict measures regardless of economic losses, including daily contact with WHO and comprehensive multi-sectoral approaches to fight against the virus and prevent further spread, showing the sense of responsibility of China to its citizens and the whole world.
T93 13226-13337 Sentence denotes Epidemic information has been released in an open, transparent, responsible, and timely manner home and abroad.
T94 13338-13424 Sentence denotes Cooperation has been established with other countries and international organizations.
T95 13425-13512 Sentence denotes These measures have won full recognition of the international community, including WHO.
T96 13513-13664 Sentence denotes Specifically in Wuhan, in the early phase from beginning of December 2019 to 23 January 2020, there was no limitation of population flow and gathering.
T97 13665-13797 Sentence denotes When the human-to-human transmission was confirmed, an important decision was made to isolate Wuhan from other parts of the country.
T98 13798-13961 Sentence denotes As a result, since 24 January 2020, all public transports from and to Wuhan, as well as public transports and people’s gathering events within Wuhan, were stopped.
T99 13962-14309 Sentence denotes Since 2 February 2020, strict public health measures were taken to prevent population flow among distinct communities, whereas since 9 February 2020, public health interventions including quarantine of each building in the urban area and each village in the rural area were implemented in order to block the transmission chain among the household.
T100 14310-14540 Sentence denotes Therefore, strong efforts of authorities and people in Wuhan with the support of the central government and people from all over China, as well as the WHO and the international society, may have gradually braked COVID-19 outbreak.
T101 14541-14640 Sentence denotes Rt is therefore assumed to decrease gradually from 3.1 to 0.5 in Wuhan, China in the current study.
T102 14641-14735 Sentence denotes The trend of the estimated cases is in accordance with the trend of currently confirmed cases.
T103 14736-14914 Sentence denotes The relatively big difference in number may be due to the possible existence of a large number of mild and asymptomatic cases and the imperfection of current diagnostic measures.
T104 14915-15122 Sentence denotes According to NHC, before 12 February 2020, the confirmed cases were diagnosed according to contact history, clinical manifestations, chest X-ray, or computer-assisted tomography (CT) and RT-PCR for COVID-19.
T105 15123-15376 Sentence denotes Since 12 February 2020, the diagnosis has been mainly based on contact history, clinical manifestation, and imaging evidence of pulmonary lesion suggestive of pneumonia, while viral detection with RT-PCR is still being performed in a part of patients23.
T106 15377-15616 Sentence denotes After the diagnosis method was changed, a large number of cases that were previously missed and piled up for testing were reported in Wuhan, which greatly increased the number of existing cases and made it approaching our estimated number.
T107 15617-15713 Sentence denotes A peak of the estimated number of infections would occur in late February under this assumption.
T108 15714-15872 Sentence denotes If the peak does occur in February, the very strong measures China has taken may have already received success in controlling the COVID-19 infection in Wuhan.
T109 15873-15963 Sentence denotes The number of deaths in the current study was estimated based on previously reported CFRs.
T110 15964-16059 Sentence denotes Chen et al.6 calculated it to be 11% based on 99 cases at the very early stage of the outbreak.
T111 16060-16234 Sentence denotes This mortality rate might not be representative of the whole patients’ population due to the relatively small sample size and scarce knowledge about the virus at early stage.
T112 16235-16363 Sentence denotes More recently, Yang et al.24 estimated the overall adjusted CFR among confirmed patients to be 3.06% with a sample size of 8866.
T113 16364-16442 Sentence denotes The number of deaths estimated accordingly might be more close to the reality.
T114 16443-16545 Sentence denotes Our estimation of the number of deaths only provides a possible range based on currently reported CFR.
T115 16546-16720 Sentence denotes The actual number of deaths might be lower with more mild and asymptomatic cases being detected and the improvement of clinical care and treatment as the epidemic progresses.
T116 16721-16876 Sentence denotes Hubei Province, of which Wuhan is the capital city, accounts for more than 80% of newly confirmed cases all over the country according to NHC daily report.
T117 16877-16955 Sentence denotes The current epidemic trend in Hubei Province is similar to that in Wuhan City.
T118 16956-17273 Sentence denotes Considering the high number of confirmed cases in the province, the currently strict measures should be continuously implemented both in Wuhan and other cities in Hubei Province no matter whether the peak of number of infections would occur or not, in order to reduce Rt to an ideal level and to control the epidemic.
T119 17274-17557 Sentence denotes Owing to the timely transportation restriction in Hubei Province and other measures, the number of newly confirmed cases remains relatively low and has decreased for 13 days in a row in other provinces, autonomous regions, and municipalities in mainland China outside Hubei Province.
T120 17558-17738 Sentence denotes However, independent self-sustaining human-to-human spread is estimated to already present in multiple major Chinese cities, including Beijing, Shanghai, Guangzhou, and Shenzhen16.
T121 17739-17913 Sentence denotes In addition, pressure on transmission control caused by the population migration after Spring Festival holidays may occur soon, especially in some densely populated cities25.
T122 17914-18023 Sentence denotes Necessary strict measures should still be maintained even when the current measures turn out to be effective.
T123 18024-18055 Sentence denotes Our study has some limitations.
T124 18056-18134 Sentence denotes Firstly, the SEIR model was set up based on a number of necessary assumptions.
T125 18135-18249 Sentence denotes For example, we assumed that no super-spreaders exist in the model, but there is currently no supportive evidence.
T126 18250-18382 Sentence denotes Secondly, the accuracy of the estimation model depends largely on the accuracy of the parameters it used, such as incubation period.
T127 18383-18496 Sentence denotes With more precise parameters obtained as the epidemic progresses, our estimation model will also be more precise.
T128 18497-18617 Sentence denotes Our estimates of the reproductive number from 3.1 to 0.5 are based on previous studies and experience from SARS control.
T129 18618-18729 Sentence denotes However, this measure may change substantially over the course of this epidemic and as additional data arrives.
T130 18730-18847 Sentence denotes Besides, using a fixed Rt value in each phase may incur potential bias because Rt is essentially a dynamic parameter.
T131 18848-18933 Sentence denotes Thirdly, these estimated data may not be sustained if unforeseeable factors occurred.
T132 18934-19065 Sentence denotes For example, if some infections were caused by multiple exposures to animals, these estimates will be exposed to a big uncertainty.
T133 19066-19239 Sentence denotes Fourthly, the epidemic trend shows great difference between Wuhan and Hubei Province and regions in mainland China outside Hubei Province according to the NHC reported data.
T134 19240-19356 Sentence denotes It is thus inappropriate to generalize the estimations in Wuhan to regions in mainland China outside Hubei Province.
T135 19357-19487 Sentence denotes The dynamics model for the other locations in mainland China remains to be developed and specific parameters need to be redefined.
T136 19488-19557 Sentence denotes Lastly, we do not provide model fit information in the current study.
T137 19558-19642 Sentence denotes SEIR model is a prediction model forecasting the number of infections in the future.
T138 19643-19788 Sentence denotes The data corresponding to actual situation in the future cannot be determined and this makes model fitting almost impossible during the outbreak.
T139 19789-19963 Sentence denotes We would carry out model fitting according to the real data in pace with more information and knowledge about the characteristics of COVID-19 and the epidemics in the future.
T140 19964-20148 Sentence denotes Despite the limitations mentioned above, the current study is the first to provide estimation for epidemic trend after strict prevention and control measures were implemented in China.
T141 20149-20300 Sentence denotes Whether current prevention and control measures are sufficient or not may be evaluated through the occurrence of the infection number peak in February.
T142 20301-20464 Sentence denotes Rigorous measures should still be maintained even when the current measures turn out to be effective by the end of February to prevent further spread of the virus.
T143 20466-20487 Sentence denotes Materials and methods
T144 20489-20494 Sentence denotes Model
T145 20495-20645 Sentence denotes We employed an infectious disease dynamics model (SEIR model) for the purpose of modeling and predicting the number of COVID-19 cases in Wuhan, China.
T146 20646-20874 Sentence denotes The model is a classic epidemic method to analyze the infectious disease, which has a definite latent period, and has proved to be predictive for a variety of acute infectious diseases in the past such as Ebola and SARS22,26–31.
T147 20875-21105 Sentence denotes Application of the mathematical model is of great guiding significance to assess the impact of isolation of symptomatic cases as well as observation of asymptomatic contact cases and to promote evidence-based decisions and policy.
T148 21106-21364 Sentence denotes We assumed no new transmissions from animals, no differences in individual immunity, the time-scale of the epidemic is much faster than characteristic times for demographic processes (natural birth and death), and no differences in natural births and deaths.
T149 21365-21635 Sentence denotes In this model, individuals are classified into four types: susceptible (S; at risk of contracting the disease), exposed (E; infected but not yet infectious), infectious (I; capable of transmitting the disease), and removed (R; those who recover or die from the disease).
T150 21636-21696 Sentence denotes The total population size (N) is given by N = S + E + I + R.
T151 21697-21855 Sentence denotes It is assumed that susceptible individuals who have been infected first enter a latent (exposed) stage, during which they may have a low level of infectivity.
T152 21856-22741 Sentence denotes The differential equations of the SEIR model are given as:32,33\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{l}{\mathrm{d}}S/{\mathrm{d}}t = - {\beta}\,{S}\,{I}/{N},\\ {\mathrm{d}}E/{\mathrm{d}}t = {\beta}\,{S}\,{I}/{N} - {\sigma}\,{E},\\ {\mathrm{d}}I/{\mathrm{d}}t = {\sigma}\,{E} - {\gamma}\,{I},\\ {\mathrm{d}}R/{\mathrm{d}}t = {\gamma}\,{I},\\ {\beta} = {R}_{\mathrm{0}}{\gamma},\end{array}$$\end{document}dS∕dt=−βSI∕N,dE∕dt=βSI∕N−σE,dI∕dt=σE−γI,dR∕dt=γI,β=R0γ,where β is the transmission rate, σ is the infection rate calculated by the inverse of the mean latent period, and γ is the recovery rate calculated by the inverse of infectious period.
T153 22742-22841 Sentence denotes R software (version 3.6.2) was applied for all the calculations and estimates in the current study.
T154 22843-22879 Sentence denotes Data collection and parameter values
T155 22881-22975 Sentence denotes Estimation of the epidemic trend assuming the prevention and control measures are insufficient
T156 22976-23100 Sentence denotes We first estimated the epidemic trend in Wuhan, China assuming the current prevention and control measures are insufficient.
T157 23101-23185 Sentence denotes In this process, S was assumed to be the population of Wuhan City (11 million)15,34.
T158 23186-23300 Sentence denotes The initial assumed number of cases caused by zoonotic exposure was 40 (I) according to Imai et al.’s9 estimation.
T159 23301-23365 Sentence denotes We proposed E at 20 times of I in accordance with Read et al.13.
T160 23366-23520 Sentence denotes R was set as 0. σ was set as 1/5.2 according to the latest article by Li et al.15, which calculated the mean incubation period of COVID-19 to be 5.2 days.
T161 23521-23630 Sentence denotes Chen et al.6 calculated the average hospitalization period of 31 discharged patients to be 12.39 ± 4.77 days.
T162 23631-23797 Sentence denotes Yang et al.24 calculated the median time from disease onset to diagnosis among confirmed patients to be 5. γ was accordingly set as 1/18 (ceiling of 12.39 ± 5 is 18).
T163 23798-23915 Sentence denotes R0 was chosen based on Imai et al.’s9 estimation 2.6 (1.9–3.1) assuming 4000 (1000–9700) infections as of 18 January.
T164 23917-24009 Sentence denotes Estimation of the epidemic trend assuming the prevention and control measures are sufficient
T165 24010-24111 Sentence denotes This section discussed the scenario where the current prevention and control measures are sufficient.
T166 24112-24292 Sentence denotes The set of S, E, I, R, σ, and γ is the same as the first section except that we also explored the model with E at 30 times of I to provide a possible range of number of infections.
T167 24293-24391 Sentence denotes The absence of fever in COVID-19 cases is more frequent than in SARS-CoV and MERS-CoV infection35.
T168 24392-24501 Sentence denotes Such patients may be missed since the current surveillance case definition focused mainly on fever detection.
T169 24502-24572 Sentence denotes Accordingly, the possibility of E at 30 times of I cannot be excluded.
T170 24573-24613 Sentence denotes R0 in this section was chosen by phases.
T171 24614-24792 Sentence denotes The first phase ranges from 1 December 2019 to 23 January 2020 and can be regarded as the early phase of the epidemic when a few prevention and control measures were implemented.
T172 24793-24880 Sentence denotes R0 was set as 3.1 consistent with Imai et al.’s9 estimation of high transmission level.
T173 24881-25097 Sentence denotes On 23 January 2020, airplanes, trains, and other public transportation within the city were restricted and other prevention and control measures such as quarantine and isolation were gradually established in Wuhan20.
T174 25098-25234 Sentence denotes So, the second phase began on 24 January and Rt was set as 2.6 consistent with Imai et al.’s9 estimation of moderate transmission level.
T175 25235-25395 Sentence denotes Second February was the last day of the extended Spring Festival holiday and Chinese authorities mobilized more medical resources to support Wuhan ever since36.
T176 25396-25536 Sentence denotes The newly constructed hospital “Huoshenshan” came into service on this day37 and “Leishenshan,” mobile cabin hospitals several days later38.
T177 25537-25588 Sentence denotes Also, more and more medical teams arrived in Wuhan.
T178 25589-25718 Sentence denotes So the third phase began on 3 February and Rt was set as 1.9 consistent with Imai et al.’s9 estimation of low transmission level.
T179 25719-25795 Sentence denotes All of these measures may need one longest incubation period to take effect.
T180 25796-26049 Sentence denotes So, the last phase began on 16 February and Rt was set as 0.9 and 0.5, respectively, assuming the prevention and control measures are sufficient and effective to depict two different levels of effect of the measures in reducing transmission probability.
T181 26051-26186 Sentence denotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
T182 26187-26221 Sentence denotes These authors contributed equally:
T183 26222-26325 Sentence denotes Huwen Wang, Zezhou Wang, Yinqiao Dong, Ruijie Chang, Chen Xu, Xiaoyue Yu, Shuxian Zhang, Lhakpa Tsamlag
T184 26327-26343 Sentence denotes Acknowledgements
T185 26344-26733 Sentence denotes This work is funded by Medicine and Engineering Interdisciplinary Research Fund of Shanghai Jiao Tong University (YG2020YQ06), the National Key Research and Development Project (2018YFC1705100, 2018YFC1705103), and the National Natural Science Foundation of China (71673187), which had no role in study design, data collection, data analysis, data interpretation, or writing of the report.
T186 26734-26842 Sentence denotes We acknowledge all health-care workers involved in the diagnosis and treatment of patients all around China.
T187 26843-26983 Sentence denotes We thank National Health Commission of the People’s Republic of China for coordinating data collection for patients with COVID-19 infection.
T188 26985-27005 Sentence denotes Author contributions
T189 27006-27216 Sentence denotes Y.C., X.Z., H.W., Z.W., and Y.D. had the idea for and designed the study and had full access to all data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis.
T190 27217-27315 Sentence denotes Y.C., H.W., Z.W., Y.D., R.C., S.Z., C.X., L.T., and X.Y. contributed to writing of the manuscript.
T191 27316-27408 Sentence denotes H.W., Y.C., J.H., G.X., T.S., Y.W., and X.Z. contributed to critical revision of the report.
T192 27409-27536 Sentence denotes Y.C., X.Z., H.W., Z.W., Y.D., M.S., R.C., S.Z., C.X., L.T., G.X., T.S., Y.W., and X.Y. contributed to the statistical analysis.
T193 27537-27665 Sentence denotes All authors contributed to data acquisition, data analysis, or data interpretation, and reviewed and approved the final version.
T194 27667-27687 Sentence denotes Conflict of interest
T195 27688-27747 Sentence denotes The authors declare that they have no conflict of interest.