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Id Subject Object Predicate Lexical cue
T1 0-136 Sentence denotes A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action
T2 138-148 Sentence denotes Highlights
T3 149-348 Sentence denotes • For the ongoing novel coronavirus disease (CODID-19) outbreak in Wuhan, China, the Chinese government has implemented control measures such as city lockdown to mitigate the impact of the epidemic.
T4 349-581 Sentence denotes • We model the outbreak in Wuhan with individual reaction and governmental action (holiday extension, city lockdown, hospitalisation and quarantine) based on some parameters of the 1918 influenza pandemic in London, United Kingdom.
T5 582-720 Sentence denotes • We show the different effects of individual reaction and governmental action and preliminarily estimate the magnitude of these effects.
T6 721-788 Sentence denotes • We also preliminarily estimate the time-varying reporting ratio.
T7 790-798 Sentence denotes Abstract
T8 799-1005 Sentence denotes The ongoing coronavirus disease 2019 (COVID-19) outbreak, emerged in Wuhan, China in the end of 2019, has claimed more than 2600 lives as of 24 February 2020 and posed a huge threat to global public health.
T9 1006-1147 Sentence denotes The Chinese government has implemented control measures including setting up special hospitals and travel restriction to mitigate the spread.
T10 1148-1372 Sentence denotes We propose conceptual models for the COVID-19 outbreak in Wuhan with the consideration of individual behavioural reaction and governmental actions, e.g., holiday extension, travel restriction, hospitalisation and quarantine.
T11 1373-1597 Sentence denotes We employe the estimates of these two key components from the 1918 influenza pandemic in London, United Kingdom, incorporated zoonotic introductions and the emigration, and then compute future trends and the reporting ratio.
T12 1598-1764 Sentence denotes The model is concise in structure, and it successfully captures the course of the COVID-19 outbreak, and thus sheds light on understanding the trends of the outbreak.
T13 1766-1778 Sentence denotes Introduction
T14 1779-2064 Sentence denotes The ongoing outbreak of coronavirus disease 2019 (COVID-19), has claimed 2663 lives, along with 77,658 confirmed cases and 2824 suspected cases in China, as of 24 February 2020 (24:00 GMT+8), according to the National Health Commission of the People's Republic of China (NHCPRC, 2020).
T15 2065-2403 Sentence denotes The number of deaths associated with COVID-19 greatly exceeds the other two coronaviruses (severe acure respiratory syndrome coronavirus, SARS-CoV, and Middle East respiratory syndrome coronavirus, MERS-CoV), and the outbreak is still ongoing, which posed a huge threat to the global public health and economics (Bogoch et al., 2020, J.T.
T16 2404-2421 Sentence denotes Wu et al., 2020).
T17 2422-2619 Sentence denotes The emergence of COVID-19 coincided with the largest annual human migration in the world, i.e., the Spring Festival travel season, which resulted in a rapid national and global spread of the virus.
T18 2620-2743 Sentence denotes At the early stage of the outbreak, most cases were scattered, and some linked to the Huanan Seafood Wholesale Market (J.T.
T19 2744-2761 Sentence denotes Wu et al., 2020).
T20 2762-2835 Sentence denotes The Chinese government has adopted extreme measures to mitigate outbreak.
T21 2836-2984 Sentence denotes On 23 January 2020, the local government of Wuhan suspended all public traffics within the city, and closed all inbound and outbound transportation.
T22 2985-3098 Sentence denotes Other cities in Hubei province announced similar traffic control measures following Wuhan shortly, see Figure 1 .
T23 3099-3204 Sentence denotes The resumption date in Wuhan remains unclear as of the submission date of this study on 25 February 2020.
T24 3205-3337 Sentence denotes Figure 1 The timeline of the facts of COVID-19 and control measures implemented in Wuhan, China from December 2019 to February 2020.
T25 3338-3435 Sentence denotes The red dots are the events in the COVID-19 outbreak, and the blue dots are the control measures.
T26 3436-3574 Sentence denotes The public panic in face of the ongoing COVID-19 outbreak reminds us the history of the 1918 influenza pandemic in London, United Kingdom.
T27 3575-3796 Sentence denotes Furthermore, its characteristics of mild symptoms in most cases and short serial interval (i.e., 4–5 days) (You et al., 2002; Zhao et al., 2020c) are similar to pandemic influenza, rather than the other two coronaviruses.
T28 3797-3894 Sentence denotes In 1918, a significant proportion of the deaths were from pneumonia followed influenza infection.
T29 3895-4105 Sentence denotes Thus, it might be reasonable to revisit the modelling framework of 1918 influenza pandemic, and in particular, to capture the effects of the individual reaction (to the risk of infection) and government action.
T30 4106-4379 Sentence denotes In (He et al., 2013), the study proposed a model incorporating individual reaction, holiday effects as well as weather conditions (temperature in London, United Kingdom), which successfully captured the multiple-wave feature in the influenza-associated mortality in London.
T31 4380-4618 Sentence denotes In this study, we followed the form of individual reaction and governmental action effects in (He et al., 2013), except for the effects of weather condition due to limited knowledge on weather effects on the transmission of coronaviruses.
T32 4619-4799 Sentence denotes We note that the governmental action, in both 1918 and current time, summarized all measures including holiday extension, city lockdown, hospitalisation and quarantine of patients.
T33 4800-4903 Sentence denotes We presume it will last for the next few months for the moment, and will update later if things change.
T34 4904-4976 Sentence denotes The parameter values may be improved when more information is available.
T35 4977-5152 Sentence denotes We argue that all prevention and control measures may be categorised into two large groups, which are described by either a step function or a response function, respectively.
T36 5153-5271 Sentence denotes We also consider zoonotic transmission period of one month and a huge emigration from Wuhan (35.7% of the population).
T37 5272-5498 Sentence denotes Nevertheless, our model is a preliminary conceptual model, intending to lay a foundation for further modelling studies, but we can easily tune our model so that the outcomes of our model are in line with previous studies (J.T.
T38 5499-5530 Sentence denotes Wu et al., 2020, Mahase, 2020).
T39 5532-5550 Sentence denotes A conceptual model
T40 5551-5877 Sentence denotes We adopt the ‘Susceptible-Exposed-Infectious-Removed’ (SEIR) framework with the total population size N with two extra classes (1) “D” mimicking the public perception of risk regarding the number of severe and critical cases and deaths; and (2) “C” representing the number of cumulative cases (both reported and not reported).
T41 5878-6021 Sentence denotes Let S, E, and I represent the susceptible, exposed and infectious populations and R represent the removed population (i.e., recovered or dead).
T42 6022-6324 Sentence denotes In a recent study (Wu and McGoogan, 2020), Wu and McGoogan found that 81% of cases were of mild symptom (without pneumonia or only mild pneumonia), 14% were severe case with difficulty breathing, and 5% were critical with respiratory failure, septic shock, and/or multiple organ dysfunction or failure.
T43 6325-6396 Sentence denotes We adopt the transmission rate function formulated in He et al. (2013).
T44 6397-6504 Sentence denotes We rename the school term effect as the governmental action effect, since the former belongs to the latter.
T45 6505-6575 Sentence denotes We also assume a period of zoonotic transmission during December 2019.
T46 6576-6724 Sentence denotes We model the zoonotic transmission (denoted as F) as a stepwise function, which takes zero after the shutdown of Huanan seafood market (presumably).
T47 6725-6938 Sentence denotes We then only model the sustained human-to-human transmission of COVID-19 after this date, along with the emigration of 5 million population before Wuhan was officially locked down (South China Morning Post, 2020).
T48 6939-7119 Sentence denotes Thus, a compartmental model is formulated as follows:(1) S'=-β0SFN-β(t)SIN-μS,E'=β0SFN+β(t)SIN-(σ+μ)E,I'=σE-(γ+μ)I,R'=γI-μR,N'=-μN,D'=d   γI-λD,andC'=σE,where(2) β(t)=β0(1−α)1−DNκ.
T49 7120-7385 Sentence denotes The transmission rate, β(t) in Eq. (2), incorporates the impact of governmental action (all actions which can be modelled as a step function), and the decreasing contacts among individuals responding to the proportion of deaths (i.e., the severity of the epidemic).
T50 7386-7470 Sentence denotes We also incorporate the individuals leaving Wuhan before the lock-down in the model.
T51 7471-7800 Sentence denotes We assume (i) the zoonotic cases only make impacts during December 2019 (Huang et al., 2020); (ii) the effect of governmental action starts on 23 January 2020 (in particular, α  = 0.4249 during 23–29 January 2020 and α  = 0.8478 after that); (iii) the emigration from Wuhan starts on 31 December 2019 and ends on 22 January 2020.
T52 7801-7847 Sentence denotes In this outbreak it seems children are spared.
T53 7848-7946 Sentence denotes Only 0.9% cases are from age 15 or less (Guan et al., 2020), while in China, 0–14 years are 17.2%.
T54 7947-8029 Sentence denotes To take this effect into account, we assume 10% of the population are ‘protected’.
T55 8030-8219 Sentence denotes Recent studies showed the serial interval of COVID-19 could be as short as 5 days (Nishiura et al., 2020a), and the median incubation period could be as short as 4 days (Guan et al., 2020).
T56 8220-8290 Sentence denotes These characteristics imply short latent period and infectious period.
T57 8291-8391 Sentence denotes Thus, we adopt a relatively shorter mean latent period (3 days) and mean infectious period (4 days).
T58 8392-8521 Sentence denotes Different from (He et al., 2013), we use the severe cases and deaths in the individual reaction function, instead of deaths only.
T59 8522-8682 Sentence denotes We also increase the intensity of the governmental action such that the model outcomes (increments in cases) largely match the observed, with a reporting ratio.
T60 8683-8765 Sentence denotes Namely only a proportion of the model generated cases will be reported in reality.
T61 8766-8910 Sentence denotes Many evidences and studies, e.g., (Tuite and Fisman, 2020, Zhao et al., 2020a, Zhao et al., 2020b), suggest the reporting ratio is time-varying.
T62 8911-8951 Sentence denotes We summarise our parameters in Table 1 .
T63 8952-9005 Sentence denotes Table 1 Summary table of the parameters in model (1).
T64 9006-9056 Sentence denotes Parameter Notation Value or range Remark Reference
T65 9057-9116 Sentence denotes Number of zoonotic cases F {0, 10} A stepwise function J.T.
T66 9117-9133 Sentence denotes Wu et al. (2020)
T67 9134-9212 Sentence denotes Initial population size N0 14 million Constant South China Morning Post (2020)
T68 9213-9269 Sentence denotes Initial susceptible population S0 0.9N0 Constant Assumed
T69 9270-9342 Sentence denotes Transmission rate β0 {0.5944, 1.68}a (day−1) A stepwise function Assumed
T70 9343-9428 Sentence denotes Governmental action strength α {0,0.4239,0.8478} A stepwise function He et al. (2013)
T71 9429-9485 Sentence denotes Intensity of responds κ 1117.3 Constant He et al. (2013)
T72 9486-9575 Sentence denotes Emigration rate μ {0, 0.0205} (day−1) A stepwise function South China Morning Post (2020)
T73 9576-9621 Sentence denotes Mean latent period σ−1 3 (days) Constant J.T.
T74 9622-9638 Sentence denotes Wu et al. (2020)
T75 9639-9688 Sentence denotes Mean infectious period γ−1 5 (days) Constant J.T.
T76 9689-9705 Sentence denotes Wu et al. (2020)
T77 9706-9768 Sentence denotes Proportion of severe cases d 0.2 Constant Worldometers. (2020)
T78 9769-9843 Sentence denotes Mean duration of public reaction λ−1 11.2 (days) Constant He et al. (2013)
T79 9844-9985 Sentence denotes a It is derived by assuming that the basic reproduction number, R0=β0γ·σσ+μ=2.8 (referring to Imai et al., 2020, Riou and Althaus, 2020, J.T.
T80 9986-10139 Sentence denotes Wu et al., 2020, Zhao et al., 2020a, Zhao et al., 2020b) when α = 0, by using the next generation matrix approach (van den Driessche and Watmough, 2002).
T81 10140-10182 Sentence denotes The time unit is in year if not mentioned.
T82 10184-10197 Sentence denotes Data analyses
T83 10198-10271 Sentence denotes We summarise the officially reported data from Wuhan, China in Figure 2 .
T84 10272-10339 Sentence denotes There is an increasing trend of daily new confirmations and deaths.
T85 10340-10447 Sentence denotes We argue that these data were heavily impacted by availability of medical supplies and health care workers.
T86 10448-10623 Sentence denotes Figure 2 The daily number of (a) cases or (b) deaths, cumulative number of (c) cases or (d) deaths, and the percentage of (e) cases or (f) deaths, of COVID-19 in Wuhan, China.
T87 10624-10693 Sentence denotes In panel (f), the 100% represents the count of deaths or cured cases.
T88 10694-10761 Sentence denotes The official data report was not available before January 15, 2020.
T89 10762-10834 Sentence denotes We fill the missing data before that from several retrospective studies.
T90 10835-10856 Sentence denotes Among them data in R.
T91 10857-10964 Sentence denotes Li et al. (2020) are daily symptom onset records, while those in Liu et al. (2020) are daily confirmations.
T92 10965-11155 Sentence denotes We notice that there is a delay of 14 days between symptom onset and laboratory confirmation of COVID-19 between the two datasets which are largely the same group of patients, see Figure 3 .
T93 11156-11189 Sentence denotes Namely, if we put back data in R.
T94 11190-11264 Sentence denotes Li et al. (2020) by 14 days, it largely matches data in Liu et al. (2020).
T95 11265-11445 Sentence denotes Thus, we assume a proportion of daily cases (reporting rate) will be reported after 14 days since their infectiousness onset (which is generally no later than their symptom onset).
T96 11446-11697 Sentence denotes Figure 3 Comparison between different sources of reported cases: official released data (NHCPRC, 2020) in red, data from Li et al. (denoted as NEJM) (Li et al., 2020) in green, from Liu et al. (denoted as GDCDC) (Liu et al., 2020) in blue, and from P.
T97 11698-11733 Sentence denotes Wu et al. (denoted as Eurosurv) (P.
T98 11734-11761 Sentence denotes Wu et al., 2020) in purple.
T99 11763-11779 Sentence denotes Model simulation
T100 11780-11817 Sentence denotes We show our simulations in Figure 4 .
T101 11818-11953 Sentence denotes Under the naive scenario, we assume governmental action strength α  = 0 and intensity of individual reaction κ  = 0, which is unlikely.
T102 11954-12103 Sentence denotes The second scenario is when we only consider “individual reaction”, both the peak value and the number of cumulative cases are substantially reduced.
T103 12104-12231 Sentence denotes The third scenario is considering both “individual reaction” and “governmental action”, and the reduction becomes even further.
T104 12232-12410 Sentence denotes We highlight the third scenario, as we know the individual reaction and governmental action existed and played important role in previous epidemic and pandemic (He et al., 2013).
T105 12411-12574 Sentence denotes Our third scenario implies that• The total number of zoonotic infections was 145 which corresponds to the reported 41 zoonotic cases with a reporting rate of ≈28%.
T106 12575-12678 Sentence denotes This level is largely in line with estimates of Riou and Althaus (2020), Nishiura et al. (2020), and Q.
T107 12679-12696 Sentence denotes Li et al. (2020).
T108 12697-12842 Sentence denotes • The cumulative number of cases in Wuhan was 4648 by January 18, 2020, which is in line with estimates of other teams (Bogoch et al., 2020, J.T.
T109 12843-12875 Sentence denotes Wu et al., 2020, NCPERET, 2020).
T110 12876-12949 Sentence denotes • The cumulative number of cases in Wuhan was 16,589 by 27 January, 2020.
T111 12950-12988 Sentence denotes Compared with estimates 25,630 (95%CI:
T112 12989-13112 Sentence denotes 12,260–44,440), announced by University of Hong Kong team on 27 January, 2020, our estimate is low but in their the 95% CI.
T113 13113-13191 Sentence denotes • The cumulative infections could be 84,116 in Wuhan by the end of April 2020.
T114 13192-13407 Sentence denotes • We compare simulated and reported numbers, and reconstruct the daily reporting ratio, which shows an improvement from a level of below 10% to around 50% from January 2020 to February 2020 and reflects the reality.
T115 13408-13637 Sentence denotes • Due to adjustment of the reporting policy, i.e., an effort to report all clinical cases accumulated in the past few days/weeks, there are a few days where the number of reported cases are artificially high than simulated cases.
T116 13638-13801 Sentence denotes The reason is that the reported cases in these few days included clinical cases but not laboratory confirmed that are accumulated in the past few days, also weeks.
T117 13802-14290 Sentence denotes Figure 4 (a) Daily new cases with a reporting delay of 14 days under three scenarios: naive (i.e., no action taken) as grey dotted curve, individual reaction regarding to the outbreak as red dashed curve, and individual reaction plus governmental action as green solid curve and reported cases (from official release and (Li et al., 2020) as grey curve with dotes. (b) The reporting ratio between reported cases and estimates when individual reaction and governmental action are involved.
T118 14291-14489 Sentence denotes The main purpose of this work is to propose a conceptual model to address the individual reaction (controlled by κ) and governmental action (controlled by α), as well as time-varying reporting rate.
T119 14490-14638 Sentence denotes We perform a simple sensitivity ity analyses on α and κ in Figure 5 , where we can see that both α and κ are needed to capture the observed pattern.
T120 14639-14743 Sentence denotes In particular, when α is around 0.9 and κ is greater than 110, the simulated largely match the observed.
T121 14744-14785 Sentence denotes Figure 5 Sensitivity analyses on α and κ.
T122 14786-14889 Sentence denotes We simulate the base model with both individual reaction and governmental action while varying α and κ.
T123 14890-15203 Sentence denotes We show model outcome when (a) α = 0.5 (black solid), 0.6 (red dashed), 0.7 (green dotted), 0.8 (blue dash-dotted) and 0.9 (cyan long dashed curve), while κ = 1117.3, when (b) κ = 100 (black solid), 500 (red dashed), 900 (green dotted), 1300 (blue dash-dotted) and 1700 (cyan long dashed curve), while α = 0.8478.
T124 15204-15238 Sentence denotes Grey dots show the reported cases.
T125 15240-15266 Sentence denotes Discussion and conclusions
T126 15267-15323 Sentence denotes We used some parameter estimates from (He et al., 2013).
T127 15324-15497 Sentence denotes The estimates were obtained via fitting a mechanistic model to the observed weekly influenza and pneumonia mortality in England and Wales during the 1918 influenza pandemic.
T128 15498-15554 Sentence denotes Recent studies showed that COVID-19 transmitted rapidly.
T129 15555-15611 Sentence denotes In this regard, it resembles influenza rather than SARS.
T130 15612-15803 Sentence denotes In our 1918 influenza work (He et al., 2013), we built a similar model as we introduced here, and we fitted that model to weekly influenza and pneumonia mortality in 334 administrative units.
T131 15804-15949 Sentence denotes Note that 1918 influenza had an infection-fatality-rate of 2%, which was at the same level of the case-fatality-rate of COVID-19 in Wuhan, China.
T132 15950-16185 Sentence denotes The merit of our model is that we considered some essential elements, including individual behavioural response, governmental actions, zoonotic transmission and emigration of a large proportion of the population in a short time period.
T133 16186-16302 Sentence denotes Meanwhile, our model is relatively simple and our estimates are in line with previous studies (Imai et al., 2020, P.
T134 16303-16320 Sentence denotes Wu et al., 2020).
T135 16321-16402 Sentence denotes Thus, our model should be considered as a baseline model for further improvement.
T136 16403-16453 Sentence denotes We avoid to fit model to data in conventional way.
T137 16454-16536 Sentence denotes Instead, we use a simple model framework to discuss what elements might be needed.
T138 16537-16811 Sentence denotes For instance, in order to achieve a good fitting performance, one obviously needs to include a time-varying report rate (as we reconstructed in Figure 4b), which was caused by the availability of medical supplies, hospital capacities and changing testing/reporting policies.
T139 16812-16932 Sentence denotes Thus it would be challenging given a relatively short time series, and several other unknown parameters to be estimated.
T140 16933-17120 Sentence denotes We employ some parameter estimates from the 1918 influenza pandemic, given the similar characteristics of COVID-19 and influenza (most cases are mild) and the similar level of mitigation.
T141 17121-17316 Sentence denotes Transmission from asymptotically infected cases is reported but the contribution of asymptomatic transmission is unclear (presumably small), which shall be further investigated in future studies.
T142 17317-17390 Sentence denotes In this work, we focused on the transmission of COVID-19 in Wuhan, China.
T143 17391-17548 Sentence denotes Our conceptual framework can be applied to other cities/countries, or be built into one multiple-patch model for modelling multiple cities/countries context.
T144 17549-17652 Sentence denotes Our model can be fitted to daily data when more information (e.g., daily number of tests) is available.
T145 17654-17696 Sentence denotes Ethics approval and consent to participate
T146 17697-17809 Sentence denotes Since no individual patient's data was collected, the ethical approval or individual consent was not applicable.
T147 17811-17845 Sentence denotes Availability of data and materials
T148 17846-17878 Sentence denotes All data are publicly available.
T149 17880-17887 Sentence denotes Funding
T150 17888-18192 Sentence denotes This research was supported by National Natural Science Foundation of China (Grant number 61672013 and 11601336), H uaian Key Laboratory for Infectious Diseases Control and Prevention (HAP201704), and General Research Fund (Grant Number 15205119) of the Research Grants Council (RGC) of Hong Kong, China.
T151 18194-18204 Sentence denotes Disclaimer
T152 18205-18449 Sentence denotes The funding agencies had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.
T153 18451-18473 Sentence denotes Authors’ contributions
T154 18474-18492 Sentence denotes Conceptualization:
T155 18493-18647 Sentence denotes Qianying Lin, Shi Zhao, Daozhou Gao, Yijun Lou, Salihu S Musa, Shu Yang, Maggie H Wang, Yongli Cai, Weiming Wang, Lin Yang and Daihai He; Formal analysis:
T156 18648-18788 Sentence denotes Qianying Lin, Shi Zhao, Daozhou Gao, Yijun Lou, Salihu S Musa, Shu Yang, Maggie H Wang, Weiming Wang, Lin Yang and Daihai He; Visualization:
T157 18789-18824 Sentence denotes Lin Yang; Writing – original draft:
T158 18825-19003 Sentence denotes Qianying Lin, Shi Zhao, Daozhou Gao, Yijun Lou, Salihu S Musa, Shu Yang, Maggie H Wang, Yongli Cai, Weiming Wang and Lin Yang; Writing – review & editing, Lin Yang and Daihai He.
T159 19005-19026 Sentence denotes Conflict of interests
T160 19027-19085 Sentence denotes The authors declare that they have no competing interests.