Phase adjusted estimation of the number of 2019 novel coronavirus cases in Wuhan, China

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. 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. After implementation of strict prevention and control measures in China, new estimation is needed. 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. In the first assumption, Rt was assumed to maintain over 1. 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. The number of infections would reach 11,044, 70,258 and 227,989, respectively, by 29 February 2020. 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 heath intervention. Several phases were divided by the dates when various levels of prevention and control measures were taken in effect in Wuhan. The estimated number of infections would reach the peak in late February, which is 58,077-84,520 or 55,869-81,393. 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. 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.


Introduction
2019 novel coronavirus (2019-nCoV / SARS-CoV-2) has given rise to an outbreak of viral pneumonia in Wuhan, China since December 2019. 1,2 World Health Organization (WHO) now has named the disease COVID-19, short for "coronavirus disease 2019". 3 Most cases from the initial cluster had an epidemiological link to the Huanan Seafood Wholesale Market. 4 Patients have clinical manifestations including fever, cough, shortness of breath, muscle ache, confusion, headache, sore throat, rhinorrhoea, chest pain, diarrhoea, and nausea and vomiting. 5,6 As of 17 February 2020, a cumulative total of 72,436 confirmed cases (including 11,741 currently severe cases), 6,242 currently suspect cases, a cumulative total of 1,868 deaths and 12,552 cases discharged from hospital were reported by National Health Commission of the People's Republic of China (NHC) in mainland China. 7 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 Concern. 8 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, R0, 9 and the actual average number of secondary cases per infected case at time t is called effective reproduction number, Rt. [10][11][12] Rt shows timedependent variation with the implementation of control measures. 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 stop. 9 Over the past month, several groups reported estimated R0 of COVID-19 and generated All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.02. 18.20024281 doi: medRxiv preprint 4 valuable prediction for the early phase of this outbreak. 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. Other authors estimated R0 to be 3.8, 13 6.47, 14 2.2, 15 and 2.68. 16 These predictions were very alerting and suggestions have been made for very strict public health measures to contain the epidemics.
In response to the outbreak of COVID-19, a series of prompt public health measures have been taken. On 1 January, the Huanan Seafood Wholesale Market was closed in the hope of eliminating zoonotic source of the virus. 5 On 11 January, upon isolation of the viral strain for COVID-19 and establishment of its whole genome sequences, 17 RT-PCR reagents were developed and provided to Wuhan, which ensured the fast ascertainment of infection. 15 On 21 January, Emergency Response System was activated to better provide ongoing support to the COVID-19 response. 18 Ever since the outbreak, the work of intensive surveillance, epidemiological investigations and isolation of suspect cases gradually improved. Those having had close contacts with infections were asked to receive medical observation and quarantine for 14 days. 19 Travel from and to Wuhan City as well as other medium-sized cities in Hubei Province has been restricted since 23 January 2020. 20 The 2019-nCoV / SARS-CoV-2 has at least 79.5% similarity in genetic sequence to SARS-CoV. 5,17 Riley estimated that 2.7 secondary infections were generated per case on average (R0 = 2.7) at the start of the SARS epidemic without controlling. 21 After isolating the patients and controlling the infection by the authority, the value of Rt for SARS decreased to 0.25. 22 As Li et al. mentioned, it is possible that subsequent control measures in Wuhan, and elsewhere in mainland China, have reduced transmissibility. 15 A new estimation of the epidemic dynamics All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.02. 18.20024281 doi: medRxiv preprint taking the unprecedentedly strict prevention and control measures in China into consideration is required to better guide the future prevention decisions.
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). 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.

Estimation of the epidemic trend assuming that the prevention and control measures are insufficient in Wuhan, China
Assuming the epidemic continues to develop with R0 = 1.9, 2.6 and 3.1 9 from 1 December 2019, the number of infections will continue to rise (Fig. 1). 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. Detailed calculation process is included in the Materials and Methods part. The second phase (24 January 2020-2 February 2020): From 23 January 2020 on, public All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is Our model predicted 2,323-3,381 deaths in Wuhan, China when we assumed Rt as 0.9 and the percent of deaths as 4%; 2,235-3,256 deaths when we assumed Rt as 0.5 at the fourth phase.
An average of 2,279-3,318 deaths were also estimated ( Table 1).
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 epidemic, 6 our model predicted 5,808-8,452 deaths in Wuhan, China; 5,587-8,139 deaths when we assumed Rt as 0.5 at the fourth phase. An average of 5,697-8,296 deaths were also estimated. All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is there were more zoonotic sources), the epidemic might continue to develop at a high speed. 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. The curve continued to go up throughout February without any indication of dropping, indicating the need for further All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is to 23 January 2020, there was no limitation of population flow and gathering. When the humanto-human transmission was confirmed, an important decision was made to isolate Wuhan from other parts of the country. 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.
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. 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 All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
Rt is therefore assumed to decrease gradually from 3.1 to 0.5 in Wuhan, China in the current study. The trend of the estimated cases is in accordance with the trend of currently the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is However, independent self-sustaining human-to-human spread is estimated to already present in multiple major Chinese cities including Beijing, Shanghai, Guangzhou, and Shenzhen. 16 In addition, pressure on transmission control caused by the population migration after Spring Festival holidays may occur soon, especially in some densely-populated cities. 25 . Necessary strict measures should still be maintained even when the current measures turn out to be effective.
Our study has some limitations. Firstly, the SEIR model was set up based on a number of necessary assumptions. For example, we assumed that no super-spreaders exist in the model, but there is currently no supportive evidence. Secondly, the accuracy of the estimation model All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.02.18.20024281 doi: medRxiv preprint 11 depends largely on the accuracy of the parameters it used such as incubation period. With more precise parameters obtained as the epidemic progresses, our estimation model will also be more precise. Our estimates of the reproductive number from 3.1 to 0.5 are based on previous studies and experience from SARS control. However, this measure may change substantially over the course of this epidemic and as additional data arrives. Besides, using a fixed Rt value in each phase may incur potential bias because Rt is essentially a dynamic parameter. Thirdly, these estimated data may not be sustained if unforeseeable factors occurred. For example, if some infections were caused by multiple exposures to animals, these estimates will be exposed to a big uncertainty. Fourthly, the epidemic trend shows great difference between Wuhan and Hubei 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.
Whether current prevention and control measures are sufficient or not may be evaluated through the occurrence of the infection number peak in February. Rigorous measures should still be All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.02. 18.20024281 doi: medRxiv preprint maintained even when the current measures turn out to be effective by the end of February to prevent further spread of the virus.

Model
We employed an infectious disease dynamics model (Susceptible, Exposed, Infectious and Removed model; SEIR model) for the purpose of modeling and predicting the number of COVID-19 cases in Wuhan, China. 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 SARS. 22,[26][27][28][29][30][31] 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.
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. 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). The total population size (N) is given by N = S+E+I+R. 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. The differential equations of the SEIR model are given as: 32,33 All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.02.18.20024281 doi: medRxiv preprint 13 dS / dt = -β S I / N dE / dt = β S I / N -σ E dI / dt = σ E -γ I dR / dt = γ I β = R0 γ where β is the transmission rate; σ is the infection rate calculated by the inverse of the mean latent period; γ is the recovery rate calculated by the inverse of infectious period. R software (Version 3.6.2) was applied for all the calculations and estimates in the current study.

Estimation of the epidemic trend assuming the prevention and control measures are insufficient
We first estimated the epidemic trend in Wuhan, China assuming the current prevention and control measures are insufficient. In this process, S was assumed to be the population of Wuhan City (11 million). 15,34 The initial assumed number of cases caused by zoonotic exposure was 40 (I) according to Imai et al.'s estimation. 9 We proposed E at 20 times of I in accordance with Read et al. 13 R was set as 0. σ was set as 1/5.2 according to the latest article by Li et at. 15  the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is Chinese authorities mobilized more medical resources to support Wuhan ever since. 36 The newly constructed hospital "Huoshenshan" come into service on this day 37 and "Leishenshan"， mobile cabin hospitals several days later. 38 And also, more and more medical teams arrived in Wuhan. So the third phase began on 3 February and Rt was set as 1.9 consistent with Imai et al.'s estimation of low transmission level. 9 All of these measures may need one longest incubation period to take effect. So the last phase began on 16 February and Rt was set as 0.9 All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.  All rights reserved. No reuse allowed without permission.
the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is . https://doi.org/10.1101/2020.02. 18 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. All rights reserved. No reuse allowed without permission. the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is 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.