Results

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 3.19 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 section.
Fig. 1 Estimation of the number of COVID-19 cases in Wuhan, China (December 2019–February 2020, R0 = 1.9, 2.6, and 3.1).
In all, 11,044, 70,258, and 227,989 represent the estimated number of COVID-19 cases by the end of February 2020 in Wuhan, China, with R0 = 1.9, 2.6, and 3.1, respectively.

Estimation of the epidemic trend assuming that the prevention and control measures are sufficient in Wuhan, China
The first phase (1 December 2019–23 January 2020): It was the early phase of the epidemic when a few prevention and control measures were implemented. The number of infections in Wuhan, China reached 17,656–25,875 by the end of this phase with R0 as 3.1.
The second phase (24 January 2020–2 February 2020): From 23 January 2020 on, public transportations to and from Wuhan, as well as public transportation within Wuhan were stopped. While gathering events inside Wuhan was banned, quarantine and isolation were gradually established in Wuhan. The number of infections was 32,061–46,905 by the end of this phase as Rt decreased to 2.6.
The third phase (3 February 2020–15 February 2020): New infectious disease hospitals and mobile cabin hospitals came into service and many medical and public health teams from other provinces and cities in China arrived in Wuhan. The quarantine and isolation at the community level were further enhanced. The number of infections would reach 53,070–77,390 if Rt could be reduced sequentially to 1.9.
The fourth phase (from 15 February 2020 on): All of the most restrict public health measures may need a longest incubation period to take effect. If Rt could be gradually reduced to 0.9 or 0.5 in the fourth phase, the epidemic peaks and inflection points might occur in Wuhan, China on 23 February or 19 February. The number of infections would be 58,077–84,520 or 55,869–81,393 with Rt = 0.9 or 0.5, respectively (Figs. 2 and 3).
Fig. 2 Phase-adjusted estimation of the number of COVID-19 cases in Wuhan, China (1 December 2019–30 April 2020, E = 20I).
In all, 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.
Fig. 3 Phase-adjusted estimation of the number of COVID-19 cases in Wuhan, China (1 December 2019–30 April 2020, E = 30I).
In all, 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.
Our model predicted 2323–3381 deaths in Wuhan, China when we assumed Rt as 0.9 and the percent of deaths as 4%; 2235–3256 deaths when we assumed Rt as 0.5 at the fourth phase. An average of 2279–3318 deaths were also estimated (Table 1).
Table 1 Estimating the number of deaths of COVID-19 cases in Wuhan, China (Rt = 0.9 or 0.5).
Rt = 0.9 Rt = 0.5 Average
Total cases 58,077–84,520 55,869–81,393 56,973–82,957
Deaths (4%) 2323–3381 2235–3256 2279–3318
Deaths (10%) 5808–8452 5587–8139 5697–8296
The estimated percent of deaths is about 4–10%6,24.
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 epidemic6, our model predicted 5808–8452 deaths in Wuhan, China; 5587–8139 deaths when we assumed Rt as 0.5 at the fourth phase. An average of 5697–8296 deaths were also estimated.