Quantitative assessment of the effectiveness of joint measures led by the Fangcang shelter hospitals in the response of COVID-19 epidemic in Wuhan, China


 Objective

To quantitatively evaluate the effectiveness of Fangcang shelter hospitals, designated hospitals, and time interval from illness onset to diagnosis in the prevention and control of COVID-19 epidemic.
Methods

We use SEIAR and SEIA-CQFH warehouse models to simulate the two-stage epidemic in Wuhan and calculate the time dependent basic reproduction number (BRN) of symptomatic infected individuals, asymptomatic infected individuals, exposed individuals and community isolated infected individuals. Scenarios that varied in the maximum numbers of open beds in Fangcang shelter hospitals and designated hospitals, the intervals from onset to visit hospitals and diagnosis, are considered to quantitatively assess the optimal measures.
Findings:

The BRN is decreased from 4.50 on Jan 22 to 0.18 on March 18. Without Fangcang shelter hospitals, the case number of cumulative and death will increase by 18.58% and 51.73%. If the number of beds in the designated hospitals decrease by 1/2 or 1/4, the number of cumulative cases will increase by 178.04% and 92.1%. If the time interval from illness onset to hospital visit is 4 days, the number of cumulative cases and deaths will increase by 2.79% and 6.19%. If Fangcang shelter hospitals are not established, the number of beds in designated hospitals reduce 1/4 and the time interval from visiting hospitals to diagnosis is 4 days, the cumulative number of cases will increase 268.97%.


Introduction
In December 2019, coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China. On Jan 31, 2020, World Health Organization (WHO) declared COVID-19 outbreak a public health emergency of international concern 1 . In view of the outbreak of COVID-19 in many countries around the world, WHO announced that the COVID-19 was a global pandemic 1 . In the early stage of the epidemic in Wuhan, thousands of cases rushed to hospitals, and the surge of infections placed huge pressure on the city's medical system 2 . In order to deal with the serious situation of COVID-19, the Chinese government has adopted strategies of joint prevention and control by means of triage, mild/moderate cases and close contacts were isolated at community and quarantine points, and severe and critical cases were admitted to designated hospitals.
Through the implementation of multiple prevention and control measures such as community isolation, quarantine point isolation, designated hospitals, and new diagnostic and intervention techniques, the rational allocation of medical resources and services is guaranteed during COVID-19 epidemic. However, there were still huge severity on treatment pressure, like lack of beds and medical resources. In order to relieve pressure, 86 designated hospitals providing about 24,000 beds were rebuilt and new-rebuilt 3 , and a total of 344 national medical teams had been dispatched, with 42,322 medical staffs 4 . In addition, from Feb 5, Wuhan has successively established and opened 16 Fangcang shelter hospitals providing about 13,000 beds to enroll mild/moderate cases. The This study mainly evaluates the effectiveness of joint measures led by the Fangcang shelter hospitals after the closure of Wuhan on Jan 23 3 . In addition, in order to include the asymptomatic individuals with infectiousness, we extend the classic SEIR (suspected-exposed-infected-recovered) transmission model to SEIAR model to describe the epidemiological characteristics. Four additional compartments (community isolation (C), quarantine point isolation (Q), Fangcang shelter hospitals (F) and designated hospitals (H)) are added to quantitatively assess the Fangcang shelter hospitals for COVID-19 epidemic in Wuhan from Jan 23 to March 18.

Data analysis SEIAR and SEIAR-CQFH model to stimulate two-stage epidemic in Wuhan
We use the date of Wuhan locked down to divide the Wuhan epidemic into two time periods, i.e., 2019 Dec 7 to 2020 Jan 22, and Jan 23 to March 18, and use SEIAR and SEIA-CQFH warehouse models to simulate the two-stage Wuhan epidemic, respectively. For the first stage epidemic from Dec 7 to Jan 22, we extend the basic SEIR (suspected-exposed-infected-recovered) model to SEIAR (suspected-exposed-symptomatic infected-asymptomatic infected-recovered) model by enrolling the asymptomatic infected individuals as follows ( Figure 1A-B) 6 .
are the number of susceptible, exposed, symptomatic infectious, asymptomatic infectious, recovered individuals and total population in Wuhan at time t , respectively. The functions ( ), ( ), ( ) S t E t I t ( ), ( ), ( ) A t R t N t dependent on t are simply denoted as , , , , , For the second stage epidemic from Jan 23 to March 18, we extend SEIAR model to enroll clinically diagnosed cases in community isolation (C), quarantine points isolation (Q), Fangcang shelter hospitals (F) and designated hospitals (H). The SEIAR-CQFH model is described as follows ( Figure   1C):   Table 1  Note: Reference=Ref Basic reproduction number for exposed, asymptomatic, symptomatic, and community

isolated infected individuals
The basic reproduction number, defined as the expected average number of secondary cases produced in a completely susceptible population by a typical infective individual during the infectious period, is one of the most significant concepts in population biology 13,14 . More importantly, it often determines the threshold behavior for many epidemic models. It is often the case that a disease will be died out if the basic reproduction number is less than unity and the disease will be established in the population if it is greater than unity. Hence, it is a commonly used to measure of the effort for controlling an infectious disease in epidemiology. We apply the next generation matrix to estimate the basic reproduction number 0 () t R with control measures in forcing as follows: In addition, the basic reproduction number of exposed, asymptomatic, symptomatic, and community isolated infected cases are respectively as: Before Jan 23, , Before Jan 23, , Before Jan 23, After Jan 23, , After Jan 23, , After Jan 23, The estimation of the basic reproduction numbers and their confidence intervals is calculated from the above formulas based on the estimated 1,000 groups of values.

Patient and Public Involvement
Patients were not involved in the design of this study.

SEIAR and SEIA-CQFH models simulated two-stage epidemics
The number of newly confirmed cases, cumulative confirmed and death cases (0, Figure 2D). In addition, SEIAR-CQFH model simulates the transmission rule of epidemic after Jan 23, and find that the increase range of number of cumulative confirmed cases and death cases is smooth, except for Feb 12 ( Figure   2A). The reason of surge is that on Feb 12 clinical diagnosis cases were enrolled as the confirmed cases.

Assessment of the joint measures led by the Fangcang shelter hospitals
we use SEIAR-CQFH model to estimate the impact of time interval from onset to visit hospital of 1 day, 2 days and 4 days on the COVID-19 epidemic and find that the time interval from illness onset to hospital visit is of importance for the epidemic. Compare to 1 and 2 days, the time interval from illness onset to hospital visit is 4 days, resulting in a significant increase in the number of confirmed cases and deaths. Specifically, the cumulative number of cases and deaths as of March 16 18 are 54,350 and 2,750, respectively, an increase of 6.73%, 4.29% and 6.19%, 3.31% compare with that of 1 day and 2 days ( Figure 5A-B).
The increased impact of the time interval from hospital visit to diagnosis is more pronounced on the number of confirmed cases and deaths. Specifically, before Feb 12, the time interval from hospital visit to diagnosis has less effect on the cumulative number of cases and deaths. After Feb 12, the shorter the time interval from visit hospital to diagnosis, the fewer cases are accumulated. As of   which are close to the data published by the government (0, 50,005 and 2,496) 1,3,5 . In addition, for any day from Dec 7 to March 18, the real data is matched with the simulated data, which indicates that the two-stage models are appropriate for COVID-19 transmission. Also, the BRN was decreased from 4.50 on Jan 23 to 0.18 on March 18, which is also consistent with other researches [15][16][17] . In addition, the BRN of symptomatic infected cases, asymptomatic infected cases, exposed individuals, and isolated infected cases decreased from Jan 23 to March 18. The time when the BRN began to decline was basically the same as the time when the national medical teams assisted Wuhan and the closure of Wuhan 18,19 and indicates that the effectiveness of joint prevention and control strategies adopted by the Chinese government. Therefore, we use SEIAR-CQFH model to quantitatively assess those measures of Fangcang shelter hospitals, designated hospitals, and time intervals from onset illness to diagnosis in COVID-19 epidemic after Jan 23 in Wuhan city in mainland China.
In the joint prevention and control of the COVID-19 epidemic, Fangcang shelter hospitals play important isolation and triage roles as the intermediate platform. At the beginning of Feb 2020, designated hospitals in Wuhan had not enough beds for COVID-19 patients, especially for 20 thousands of patients with mild to moderate COVID-19 2,3 . Mild and moderate patients could be isolated at community, however, epidemiological study showed that in China COVID -19 has a high rate of intrafamily transmission 2,10,20-23 , and more than 50% COVID-19 patients had at least one family member with the disease 2 . In addition, community isolation is difficult to monitor disease progress, and the asymptomatic infectious individuals may deteriorate to mild and moderate illness [21][22][23] . Our study also exhibits that the BRN for community isolation symptomatic infected individuals increased from Jan 24 to Feb 2, while other types of BRN was decreasing. This indicates that the effect of community isolation is not good. On Feb 2, Wuhan asked community isolation individuals, newly suspected individuals, and close contacts to designated points isolations. After three days, on Feb 5, 2020, Wuhan has successively opened 16 Fangcang shelter hospitals to treat mild and moderate patients. This implementation of this measure is conducive to the rapid isolation and triage of mild and moderate cases. Therefore, from Feb 5, the BRN of community isolation symptomatic infected individuals shows a continuous downward trend.
Beside isolation, triage, the basic medical care and frequent monitoring and rapid referral were also the original intention of the establishment of the Fangcang shelter hospitals 2,3 . Our study also confirms the important role of the Fangcang shelter hospitals in early treatment the COVID-19 cases, the results show that without Fancang shelter hospitals, the cumulative number of cases and deaths would increase by 18.58% and 51.73% by March 18. In addition, if the number of beds is reduced to 1/2 or 1/4, the cumulative number of cases and deaths would increase by 6.88%, 11.78% and 16.59%, 31.25%. Moreover, one of the important functions of the Fancang shelter hospitals was monitoring and rapid referral 2 , which is to enable severe COVID-19 cases to be treated in the shortest time and increase the survival possibility. The treatment of severe cases is inseparable from the designated hospitals, designated hospitals also play an important role as the high-level platform in hierarchical prevention and control. Our study also shows that, if the number of beds in the designated hospitals decrease by 1/2 or 1/4, the number of COVID-19 cases will increase significantly (from 50,926 to 97,829 and 141,594). After Jan 25, with progressively increasing medical materials and medical staff, the number of beds in designated hospitals was all expanded, which increased the treatment opportunities of severe cases, reduce the death of severe cases of COVID-19. This study has some limitations. Firstly, this study did not quantitatively assess the effectiveness of the community isolation and quarantine points isolation due to the difficulty for collection the related data set. Secondly, unable to collect the real-time number of beds in the central isolation point, and we used the fix ed number published by the National Health and Planning Commission.
In conclusion, our study provides a detailed quantitative assessment the effect of the Fangcang shelter hospitals, designated hospitals, and time intervals from illness onset to hospital visit and diagnosis of COVID-19 in Wuhan city of mainland China, especially the role of Fangcang shelter hospitals. The results showed that Fangcang shelter hospitals, like designated hospitals, played an irreplaceable contribution to the control of COVID-19 epidemic; moreover, the combination of measures, including the normal number of beds in Fangcang hospitals, is optimum, made the prevention and control strategies more effectiveness. Lastly, although the COVID-19 epidemic has been basically brought under control in China and Fangcang shelter hospitals have been closed, we still cannot take it lightly. We should sum up the prevention and control experience of COVID-19, and provide more scientific methods for Chinese and even global people in response to the outbreak of emerging infectious disease, especially for countries and regions with limited medical resources.

Ethical approval and consent to participate
Not applicable.

Consent for publication
Not applicable.

Availability of data and material
Our data are from publicly published data, have no privacy implications and can be founded in http://wjw.wuhan.gov.cn/.

Author contributions
Li W and Xu W conceived, designed, and supervised the study. Song P, Wang S, Zhu C and Cai C collected the data and cleaned the data. Jiang H and Song P analyzed the data. Jiang H and Song P wrote the drafts of the manuscript. Jiang H and Li W interpreted the findings. Li W and Xu W commented on and revised the drafts of the manuscript. All authors read and approved the final manuscript.       The cumulative number of COVID-19 cases varies with the number of beds in designated hospitals