Fangcang shelter hospitals during the COVID-19 epidemic, Wuhan, China

Abstract Objective To design models of the spread of coronavirus disease-2019 (COVID-19) in Wuhan and the effect of Fangcang shelter hospitals (rapidly-built temporary hospitals) on the control of the epidemic. Methods We used data on daily reported confirmed cases of COVID-19, recovered cases and deaths from the official website of the Wuhan Municipal Health Commission to build compartmental models for three phases of the COVID-19 epidemic. We incorporated the hospital-bed capacity of both designated and Fangcang shelter hospitals. We used the models to assess the success of the strategy adopted in Wuhan to control the COVID-19 epidemic. Findings Based on the 13 348 Fangcang shelter hospitals beds used in practice, our models show that if the Fangcang shelter hospitals had been opened on 6 February (a day after their actual opening), the total number of COVID-19 cases would have reached 7 413 798 (instead of 50 844) with 1 396 017 deaths (instead of 5003), and the epidemic would have lasted for 179 days (instead of 71). Conclusion While the designated hospitals saved lives of patients with severe COVID-19, it was the increased hospital-bed capacity of the large number of Fangcang shelter hospitals that helped slow and eventually stop the COVID-19 epidemic in Wuhan. Given the current global pandemic of COVID-19, our study suggests that increasing hospital-bed capacity, especially through temporary hospitals such as Fangcang shelter hospitals, to isolate groups of people with mild symptoms within an affected region could help curb and eventually stop COVID-19 outbreaks in communities where effective household isolation is not possible.


Introduction
On 30 January 2020, the World Health Organization declared coronavirus disease-2019 (COVID-19) a public health emergency of international concern. 1 The disease was first reported in Wuhan, China, in December 2019. To control the COVID-19 epidemic, Wuhan, a city with an estimated population of 10 million, started a lockdown on 23 January 2020. 2 The city itself was quarantined and turned into an isolation ward. 3 To alleviate the shortage of doctors and medical resources, medical teams and materials were dispatched in batches to Wuhan from other parts of China. 4 Several hospitals in Wuhan were designated as COVID-19 hospitals and their capacity to accept daily confirmed cases of COVID-19 was increased. 5,6 However, the number of confirmed cases continued to grow even though quarantine and social-distancing policies were strictly enforced. 7 The situation with the epidemic did not improve until the opening of Fangcang shelter hospitals on 5 February 2020. Fangcang shelter hospitals are rapidly built temporary hospitals composed of several movable shelters; they are equipped to provide services such as emergency treatment, surgical treatment and clinical examination. 8 To effectively control the spread of COVID-19, the government of Wuhan decided to move all COVID-19 patients together, enlist all experts in infectious diseases and doctors (health-care personnel) and centralize all resources. 9,10 To implement these policies, on 3 February, the decision was taken to treat patients by severity of infection and to start building Fangcang shelter hospitals for mild cases, who did not need intensive care. This approach effectively changed the family-based quarantine approach into group isolation of mild confirmed cases. 11 Wuhan continued to build more Fangcang shelter hospitals and by the middle of February, the daily number of new confirmed cases started to decrease (Fig. 1). While the availability of hospital beds in both designated hospitals and Fangcang shelter hospitals and sufficient health-care personnel were important in minimizing the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in the city, it was recognized that front-line health-care personnel in close contact with infectious patients had a much higher risk of infection. By 11 February, 3019 health-care personnel had been infected and five had died. 13 Here, we build compartmental models to mimic the spread of CO-VID-19 in Wuhan and examine how the lockdown policy controlled the epidemic. We computed the basic reproduction numbers to assess the risk of infection in health-care personnel and the general public. We also estimated the number of hospital beds needed to control the COVID-19 epidemic. Many modelling studies of COVID-19 in Wuhan have been done; [14][15][16][17] however, these models did not consider the roles played by the beds in the Fangcang shelter hospitals and health-care personnel in the infection dynamic.

Data used
The epidemic of COVID-19 in Wuhan resulted in 50 003 infections and 2469 deaths as of 15 March 2020. 18 We obtained data on the reported daily new confirmed cases of COVID-19, recovered cases and deaths from 23 January to 17 March from the official website of the Wuhan Municipal Health Commission. 12 When lockdown started, testing resources and health-care personnel were limited. As a result, the data are affected by a testing time lag from the date of onset of symptoms to the date of the test result and, therefore, the number of confirmed cases reported in the data are not the actual number of infections on a specific day. In addition, the diagnostic criteria for COVID-19 were updated five times. As shown in Fig. 1, the daily number of confirmed cases increased substantially on 13 February, reaching about 12 000. This sudden jump can be attributed to a change in national test standards. 19 Hence, we used data only from 12 February onwards to estimate the model parameters and initial variables.
In our models, we treated healthcare personnel separately from the general public. We extracted data on the cumulative number of infected health-care personnel in Wuhan, Hubei province (excluding Wuhan) and daily infected health-care personnel in the whole country 13,20,21 to calculate the daily infection of health-care personnel in Wuhan from 23 January to 11 February. When the lockdown started, many health-care personnel were infected because of the limited hospital capacity to handle the large number of patients (Fig. 1). The number of reported cases among health-care personnel started to decrease in the middle of February when a large number of hospital beds were added through the building of the Fangcang shelter hospitals. As an indication of the effectiveness of control measures, we estimated the bed capacity of the des-ignated hospitals and Fangcang shelter hospitals from data in public reports for Wuhan. 13,22 We denoted T 0 as the date when the lockdown started (23 January 2020), T 1 as the date when the first bed in the Fangcang shelter hospitals opened (5 February) and T 2 as the date when no new Fangcang shelter hospital beds were installed and more of the beds became free (22 February). We defined phase I of the epidemic as the period from T 0 to T 1 , phase II as the period from T 1 to T 2 , and phase III as the period from T 2 to the time that our simulations were terminated. We denoted B 1 (t) as the total number of designated-hospital beds. Thus, if b 1 (t) is the number of new beds for COVID-19 patients installed a day in the designated hospitals, then Similarly, we defined the total number of beds in Fangcang shelter hospitals as: where b 2 (t) is the number of new beds installed per day in Fangcang shelter hospitals.  27 29 31 2 4 6 8 10 12 14 16 18 20 22 24 26  In a standard designated hospital or Fangcang shelter hospital, given the limited resources, the ratio of number of beds to number of health-care personnel is usually fixed to ensure proper care. We use k 1 and k 2 to denote these ratios in designated hospitals and Fangcang shelter hospitals, respectively. With information from the Wuhan Municipal Health Commission 22 and news report, 23,24 we calculated k 1 as 2.486 and k 2 as 1.107, from which we deter-mined the total number of health-care personnel. With the construction and assignment of designated and Fangcang shelter hospitals, the number of hospital beds used became an important quantity to reflect the progression and severity of the epidemic. We defined V 1 (t) and V 2 (t) as the number of available beds in designated hospitals and Fangcang shelter hospitals, respectively. The number of beds started to increase on 15 February and the cumulative number of new confirmed cases started to decrease on 22 February. Therefore, we did not count the extra beds installed after 22 February, even though the plan to build more Fangcang shelter hospitals continued. We thus determined B 2 (22) as 13 348, the limit of B 2 (t). In addition, we defined the end date of the COVID-19 epidemic in Wuhan to coincide with the date that satisfies B i (t) = V i (t), I = 1,2, when empty beds in the designated hospitals and Fangcang shelter hospitals are available to admit new patients. Note that the daily number of newly built beds planned was not the actual number opened and all beds were opened on a day to day basis as needed. 25- 27 We used the moving average method to smooth the cumulative number of beds to calculate the daily number of new beds put into use (available in the data repository). 28

Models
We developed deterministic susceptible-exposed-asymptomatic-infectious-recovered models for the three phases of the epidemic based on the assumptions listed in Box 1 (available at: http:// www .who .int/ bulletin/ volumes/ 98/ 12/ 20 -258152). We divided the population into three groups: non-health-care personnel (subscript w), health-care personnel in designated hospitals (subscript h) and health-care personnel in Fangcang shelter hospitals (subscript g). We further classified these groups as: susceptible (S i (t)), exposed (E i (t)), asymptomatic (subclinical) infection (A i (t)), infectious pre-symptomatic (will eventually show symptoms) (I i1 (t)), infectious symptomatic (I i2 (t)) and recovered (R i (t)). Based on the flowcharts for the three phases of the epidemic (data repository), 28 we established model equations accordingly (data repository). 28 We estimated model parameters and calculated the basic reproduction number R 0 for phase III using the nextgeneration matrix method. 30 Using R 0 , we defined the instantaneous risk index as R 0 (t). 30, 31 The formulas for R 0 and R 0 (t) are given in the data repository. 28

Sensitivity analysis
Given the uncertainty of the model parameters, we did a sensitivity analysis of key parameters, including the transmission rates (βs), the proportion of subclinical infections (a) and the number of beds in the designated hospitals and Fangcang shelter hospitals (b 1 ,b 2 ). We used the Latin hypercube sampling and partial rank correlation coefficient method. 32 To examine how these parameters affected the transmission over the three phases of the epidemic, we generated 3000 samples of these parameters, using Latin hypercube sampling and varied them between 80% and 120% of their estimated values. We then verified the monotonic relationships between the parameters and the outcomes of the models. We calculated the values of the partial rank correlation coefficient, which determine the significance (partial rank correlation coefficient magnitude > 0.5 required) of each parameter to variations in the model outcomes.

Simulations
We set the initial values and some parameters for each phase using the data available. On dayT 0 , we set the initial values for variables for Fangcang shelter hospitals to zero (Table 1; available at: http:// www .who .int/ bulletin/ volumes/ 98/ 12/ 20 -258152). We estimated the initial values for the six state variables for non-health-care personnel and the 14 parameters associated with transmission using Bayesian methods. We assumed prior distributions of the parameters were multivariate Gaussian. We determined the values of the parameters as the mean of the posterior distributions, which we obtained using Markov chain Monte Carlo methods and used the adaptive Metropolis-Hastings algorithm with 150 000 iterations and a 90 000 iteration burn-in reference. 33 We assessed chain convergence by the Geweke statistic with values greater than 0.9 indicating a satisfactory chain convergence.
To further assess the effect of medical resources in controlling the COVID-19 epidemic in Wuhan, we calculated the hospital beds per 1000-infected-person ratios 34 to quantify the minimum number of beds required in different scenarios. In the case of sufficient or increasing medical resources, we estimated the hospital beds per 1000-infected-person ratio as: where Pop is the total population in Wuhan and the maximum number of inpatients daily (In max ) is determined by I wB1 (t) + I wB2 (t). Larger values of the hospital beds per 1000-infected-person ratio mean more beds are needed to mitigate the epidemic.

Results
Using the daily numbers of new beds in the designated hospital (23 January-25 February) and the Fangcang shelter hospitals (5-22 February), we fitted our model to the data of cumulative confirmed cases, recovered cases and deaths from 23 January to 17 March, and the cumulative number of cases among health-care personnel from 23 January to 11 February. The estimated parameters and highest density intervals are shown in Table 1 and  Our models fitted well with the normalized mean square error 0.97. We estimated that 0.95% (95% CI: 0.95-0.96) of the total exposed cases progressed to symptomatic infections (  Control of the COVID-19 epidemic in Wuhan, China Juan Li et al. is higher than the previously reported value of 1.20%. 13 The results of our model simulation show the peak value of the epidemic of 39 771 cases (95% CI: 39 727-39 827) on 21 February, 30 days after the lockdown on 23 January (Table 3). The total number of infections is 50 844 (95% CI: 50 757-50 915), the total number of hospital deaths is 2920 (95% CI: 2817-2985) and overall deaths (including those who died because they could not get treatment in time) is 5003 (95% CI: 4888-5065). Our model shows that the number of new cases a day falls to zero after 2 April, (95% CI: 2 April-3 April), corresponding to 71 days after implementation of the lockdown.

Shelter hospital beds
Simulations shown in Fig. 6 and  Table 3). Furthermore, in our model, if Wuhan started to build the Fangcang shelter hospitals the day the lockdown started on 23 January, the epidemic would reach its peak on 29 January with a daily peak of only 8976 infections, the total number of infections would decrease by 74.96% ((50 844−12 729)/50 844), the length of the epidemic would be 36 days shorter and the cumulative number of deaths would be reduced by 93.52% ((5003−324)/5003).
Wuhan planned to provide 30 000 Fangcang shelter hospital beds, 27 Fig. 6 and Fig. 7 (scenario 2) and Table 3 (t) is reduced to 0.8b 2 (t), the epidemic will not be effectively controlled ( Fig. 6 and Fig. 7 (scenario 2) and Table 3). If all 13 348 beds in the Fangcang shelter hospitals were gradually used in 1 week with 1907 beds a day, our simulations indicate that the number of COVID-19 cases would peak 11 days earlier with 28 818 cases, there would be 25.47% fewer cases in total ((50 844-37 892)/50 844), the epidemic time would be shortened by 12 days, and the cumulative number of deaths would be reduced by 52.79% ((5003-2362)/5003). However, if the 13 348 beds had been opened in 2 weeks with 953 beds a day, Wuhan would have missed the opportunity of isolating the large number of confirmed cases, which would have led to over 7.4 million infections in total ( Table 3).
The values of the hospital beds per 1000-infected-person ratio in different hypothetical scenarios are given in Table 3, Table 4 and Table 5. If the available hospital beds are too few to control the epidemic, it is not possible to estimate the hospital beds per 1000-infectedperson ratio in the absence of additional data on the time, number of beds and method of replenishing beds in the For all the scenarios with NA (not applicable), the public health system will collapse, and the original model is not applicable anymore. We simulate the case by modifying the model accordingly, considering possible herd immunity and variation of parameters for the non-healthcare group due to a lack of hospital resources.
Control of the COVID-19 epidemic in Wuhan, China Juan Li et al.
Fangcang shelter hospitals. In general, the earlier beds in the Fangcang shelter hospitals are opened, the smaller the hospital beds per 1000-infected-person ratio needed to control the scale of the epidemic (Table 3 and Table 4). We also found that if the Fangcang shelter hospitals are not opened promptly, the hospital beds per 1000-infected-person ratio increases and does not guarantee effective control.

Absence of shelter hospitals
Before the establishment of the Fangcang shelter hospitals, most patients were asked to quarantine or isolate at home because medical resources were insufficient. We analysed the effect of home isolation in the absence of the Fangcang shelter hospitals.
Without the Fangcang shelter hospitals, the epidemic could still be effectively controlled. Fig. 6 and Fig. 7 (scenario 3) show that medium to substantial reductions in contact transmission rates can reduce the peak number of daily infections and the final size of the epidemic, delay the peak time, and reduce the length of the epidemic. However, the total number of deaths will increase because of insufficient resources in the designated hospitals and the inability to provide immediate treatment to some critically ill patients (Table 5).    Table 5 show that an increase in the capacity of designated hospitals can also effectively control the epidemic in the absence of the Fangcang shelter hospitals. When the number of designated-hospital beds is increased by 1.5 times the actual number, the peak number of daily infections is reduced to 13 287, the total number of infections is reduced to 15 942, the epidemic duration shortened to 42 days, and the total number of deaths reduced to 1113. In contrast, if the number of designated-hospital beds is reduced by 20%, the epidemic will spread on a much larger scale and last longer.

Instantaneous risk indices
We assessed the instantaneous risk index of COVID-19 in each phase of the epidemic. In phase I with the increasing number of designatedhospital beds, the risk of transmission was significantly reduced, R 0 (t) < 1, compared with the early stage of the outbreak (Fig. 8). However, the number of designated-hospital beds was not enough to cope with the increasing number of new infections, so the risk of infection to the general population, R w (t), was still increasing with a possibility of exceeding 1 if no more beds were added. When the Fangcang shelter hospitals were opened with a steadily increasing number of beds in phase II, R w (t) decreased (Fig. 9), although the risk to health-care personnel in designated hospitals and Fangcang shelter hospital, R h (t) and R g (t), respectively, continued to increase slightly until phase III when R w (t), R h (t) and R g (t) all decreased (Fig. 10, Fig. 11 and Fig. 12, all available at: http:// www .who .int/ bulletin/ volumes/ 98/ 12/ 20 -258152).

Discussion
The lockdown of Wuhan provided a valuable opportunity to prevent and control the spread of SARS-CoV-2 in China and some other countries of the world. 38 Our threephase models mimicked and revealed how the Fangcang shelter hospitals and the group isolation policy helped to stop the epidemic in Wuhan. Our study suggests that, in lockdown cities such as Wuhan that have implemented social distancing and effective testing, if household isolation is not sufficient to inhibit the transmission of the virus, then effective group isolation of large numbers of people with mild infection in Fangcang type of facilities can curb an epidemic of COVID-19.
The success in tackling the COV-ID-19 epidemic in Wuhan, particularly the use of shelter hospitals, has been acknowledged and many countries have adopted a similar approach. 8,39 For example, Italy, New Zealand and the United States of America have built temporary hospitals by transformation of caravans, ferries, trains and buses, and city squares to set up tents based on local conditions. As the pandemic has become more widespread and may last for years to come, 40 we suggest, whenever possible and if needed, countries build more temporary hospitals such as the Fangcang shelter hospitals.
Our modelling has some limitations. Because our focus was on hospital beds and their role in mitigating and controlling the epidemic, our models are based on simplified assumptions. In addition, the data on the number of daily beds are not accurate because of counting processes and reporting. More accurate data on hospital beds will improve estimation of the parameters, but the main results of our work will not be significantly affected.
Our findings may provide policymakers with useful information on combatting COVID-19 by considering increasing hospital-bed capacity to enhance isolation of cases where home quarantine is insufficient. ■
Resultados Teniendo en cuenta las 13 348 camas de los hospitales de confinamiento Fangcang que se emplearon en la práctica, los modelos indican que si los hospitales de confinamiento Fangcang se hubieran abierto el 6 de febrero (un día después de su apertura efectiva), el número total de los casos de la COVID-19 habría alcanzado los 7 413 798 (en lugar de 50 844) y se habrían producido 1 396 017 muertes (en lugar de 5003), por lo que la epidemia habría durado 179 días (en lugar de 71). Conclusión Si bien los hospitales designados salvaron vidas de pacientes que padecían la COVID-19 grave, fue el aumento de la capacidad de las camas en los hospitales de confinamiento Fangcang lo que ayudó a frenar y finalmente detener la epidemia de la COVID-19 en Wuhan. Dada la actual pandemia mundial de la COVID-19, el presente estudio sugiere que el aumento de la capacidad de las camas en los hospitales, en especial en los hospitales temporales como los hospitales de confinamiento Fangcang, para aislar a los grupos de personas con síntomas leves dentro de una región afectada podría ayudar a frenar y finalmente detener los brotes de la COVID-19 en las comunidades donde el aislamiento doméstico eficaz no es posible.  CI: confidence interval; COVID-19: coronavirus disease-2019; T 2 : date when the first bed in the Fangcang shelter hospitals opened; E w , E h , E g : exposed people who are not health-care personnel, exposed health-care personnel who work in designated hospitals and exposed health-care personnel who work in Fangcang shelter hospitals, respectively; I w1 , I h1 , I g1 : asymptomatic people with COVID-19 (who will develop symptoms) who are not health-care personnel, asymptomatic health-care personnel with COVID-19 (who will develop symptoms) who work in designated hospitals and asymptomatic health-care personnel with COVID-19 (who will develop symptoms) who work in Fangcang shelter hospitals, respectively; NA: not applicable. a 95% highest posterior density interval. b The infection rate of susceptible health-care personnel in designated hospitals by infectious patients in phase I of the COVID-19 epidemic is different from that in phases II and III, because of the strict measures put in place to protect health-care personnel after the first phase. 37 c Because of the strict measures put in place to protect health-care personnel, the infection rate of susceptible health-care personnel in designated hospitals from asymptomatic infectious health-care personnel in designated hospitals in phases II and III is also different from that in phase I. d Including health-care personnel. e In phase III, the recovery and death rates in designated hospitals are different from those in phases I and II because there are enough hospital beds. f Excluding health-care personnel on the assumption that health-care personnel will be given priority in use of designated hospital beds.