### SEIAR and SEIA-CQFH models simulated two-period epidemics

The numbers of newly confirmed cases, cumulative-confirmed cases, and deaths (0, 50,005, and 2496) until March 18, 2020 reported in Wuhan are basically consistent with the models simulated results (21, 50,926, and 2590), indicating that the real data and values predicted by the model were well simulated (Fig. 2 a-c). In addition, after adopting various prevention and control measures, although the BRN fluctuated slightly from February 3, 2020 to February 9, 2020, the overall trend was as follows: the BRN decreased from 4.50 on January 22, 2020 to 0.18 on March 18, 2020. Specifically, the BRNs of symptomatic infected individuals, asymptomatic infected individuals, and exposed individuals decreased from 3.57, 0.18, and 0.75 on January 23, 2020 to 0.04, 0.02, and 0.10 on March 18, 2020. In addition, although the BRN of community-isolation symptomatic infected individuals increased slightly from 0.24 on January 24, 2020 to 0.41 on February 2, 2020, the BRN continued to decrease from 0.27 on February 8, 2020 to 0.02 on March 18, 2020 (Fig. 2d). In addition, the SEIAR-CQFH model simulated the transmission rule of the epidemic after January 23, 2020, and found that the increase in the numbers of cumulative confirmed cases and deaths was smooth, except for February 12, 2020 (Fig. 2a). The reason for the surge was that on February 12, 2020, clinical diagnosis cases were enrolled as confirmed cases.

### Assessment of Fangcang shelter hospitals

The SEIAR-CQFH model simulated the number of beds in Fangcang shelter hospitals. With this model, we confirmed that if the number of beds was reduced by 1/2 or 3/4, the growth ranges of the numbers of cumulative confirmed cases and deaths increased obviously, especially the cumulative deaths. Specifically, if the numbers of beds in Fangcang shelter hospitals were 0, 1/4, 1/2, and normal, the cumulative number of cases on March 18, 2020 would be 60,389, 56,924, 54,430, and 50,925 (real data: 50,005), respectively. By March 18, 2020, there would be 18.58, 11.78, and 6.88% more cumulative confirmed cases in the cases of 0, 1/4, and 1/2 beds, compared to the condition with normal beds (Fig. 3a). Compared to the cumulative number (425) of cases on January 23, 2020, the month-on-month growths in the cases of 0, 1/4, 1/2, and normal beds were 12,533.73, 12,082.60, 11,683.11, and 11,049.31%, respectively (Fig. 3a). In addition, if the numbers of beds in Fangcang shelter hospitals were 0, 1/4, 1/2, and normal, the numbers of deaths on 18 March, 2020 were 3929, 3399, 3019, and 2590 (real data: 2495), respectively. By March 18, 2020, there would be 51.73, 31.25, and 16.59% more cumulative deaths in the cases of 0, 1/4, and 1/2 beds, respectively, compared to the condition with normal beds. Compared to the death number (190) on January 23, 2020, the month-on-month growths in the cases of 0, 1/4, 1/2, and normal beds were 954.56, 927.92, 872.48, and 779.35%, respectively (Fig. 3b ).

### Assessment of designated hospitals

The impact of the number of beds in designated hospitals is similar to that in Fangcang shelter hospitals in the COVID-19 epidemic; however, it is important to note that reducing the number of beds in designated hospitals would lead to a more significant increase in confirmed cases. Specifically, if the numbers of beds in designated hospitals are 1/4, 1/2, and normal, the cumulative numbers of confirmed cases on March 18, 2020 would be 141,594, 97,829, and 50,926 (real data: 50,005), respectively. By March 18, 2020, there would be 178.04 and 92.1% more cumulative confirmed cases for 1/4 and 1/2 beds, respectively, compared to the condition with normal beds. Compared to the cumulative number of cases (425) on January 23, 2020, the month-on-month growths for 1/4, 1/2, and normal beds were 23,234.81, 18,784.59, and 11,049.31%, respectively. Although the number of cases increased slightly with the increase in bed size in the early period, the increase in the number of beds significantly inhibited the increase in the number of cases in the later period (Fig. 4).

### Assessment of the joint measures led by Fangcang shelter hospitals

We used the SEIAR-CQFH model to estimate the impact of the time interval from illness onset to hospital visit at 1 day, 2 days, and 4 days in the COVID-19 epidemic and found that the time interval from illness onset to hospital visit was of importance for the epidemic. Compared to 1 and 2 days, the time interval from illness onset to hospital visit was 4 days, resulting in a significant increase in the number of confirmed cases and deaths. Specifically, the cumulative numbers of cases and deaths as of March 18, 2020 were 54,350 and 2750, respectively, an increase of 6.73, 4.29 and 6.19%, 3.31% in comparison with that of 1 day and 2 days, respectively (Fig. 5a-b).

The increased impact of the time interval from hospital visit to diagnosis was more pronounced on the numbers of confirmed cases and deaths. Specifically, before February 12, 2020, the time interval from hospital visit to diagnosis had lesser effect on the cumulative numbers of cases and deaths. After February 12, 2020, the shorter the time interval from hospital visit to diagnosis, the fewer the accumulated cases. As of March 18, 2020, the cumulative numbers of cases were 50,926, 55,334, and 64,863, respectively, for 1 day, 2 days, and 4 days, respectively. In addition, the cases were more significantly affected after February 22, 2020, that is, the shorter the time interval from hospital visit to diagnosis, the fewer the number of deaths, and the gap increased with time. As of March 18, 2020, the total numbers of deaths were 2590 (real data: 2496), 26,280 and 27,740 for 1, 2, 4 days, respectively (Fig. 5c-d).

In general, in view of the severity and public concern of the COVID-19 epidemic, the onset individuals usually visit the hospitals soon; other medical services including the time for diagnosis, number of beds in Fangcang shelter hospitals, and number of beds in designated hospitals were evaluated and required by the Chinese government. Therefore, we put the dynamic change of the above variables, except the variables for illness onset to visit hospitals, into the model to simulate the effect of changes of multiple variables on the cumulative number of cases to evaluate the joint measures. The results indicate that the numbers of beds in Fangcang hospitals and designated hospitals are normal, and both time intervals from illness onset to hospital visit and diagnosis are 1 day; the cumulative number of cases is the fewest and basically consistent with the real data (50,926; real data: 50,005). The number of Fangcang shelter hospitals is 0, the number of beds in designated hospitals is 1/4, the time interval from onset to hospital visit is 1 day, and the time interval from hospital visit to diagnosis is 4 days, the cumulative number of cases would be the highest (187,904). For the other combinations’ types of medical services, the cumulative number of cases caused is higher than the actual number of prevention and control measures (Fig. 6).