### COVID-19 epidemic trend in the mainland of China

The final cumulative number of confirmed cases in the mainland of China would reach 86 763 (95% *CI:* 86 067–87 460) on May 2, 2020 (Fig. 2a). The cumulative number of confirmed cases would stabilize from April 1, 2020, which indicated that the number of new confirmed cases every day was minimal. Since March 13, 2020, the number of new confirmed cases would be less than 100 every day, and from April 1, 2020, the number of new confirmed cases would be less than 10 every day. The number of new daily confirmed cases began to decline since February 8, 2020. Up until March 15th, the cumulative number of deaths in the mainland of China would reach 5535 (95% *CI:* 5308–5763). Overall mortality rate due to disease was approximately 6.42% (95% *CI:* 6.16–6.68%) (Fig. 2b).

The number of existing confirmed cases in the mainland of China would reach its peak around February 23, 2020, and the number would reach 60 890 cases (95% *CI:* 60 350–61 431) (Fig. 3a). After the peak, the number of existing confirmed cases would decline slowly, following a chi-square distribution approximately.

Substituting the initial and parameter values in Table 1 into eq. (3), we can see that the effective reproduction number of COVID-19 on January 23, 2020 was about 2.620 (95% *CI:* 2.567–2.676). On February 5, 2020, the effective reproduction number had dropped below 1.0, which suggested that the number of new infections would gradually decline from February 5, 2020 (Fig. 3b).

### Impact of different prevention and control strategies on the COVID-19 epidemic trend

Before January 23, 2020, because there were no quarantine and close-contact tracing, so we reduced three compartments in model (1) and obtained a new SEIQR model (S1) (Supplementary p. 12). Based on the new model (S1), we found that there were no interventional measures that began on January 10, 2020, then the peak time of existing confirmed cases would have appeared around March 11, 2020, and the number at peak time would have reached 38 425 800, representing an increase of 38 364 910 cases compared with the current situation (Fig. 4a). Similarly, the cumulative number of confirmed cases and deaths in the mainland of China would have reached 58 613 197 and 7 117 271, respectively (Fig. 4b, c). In addition, the effective reproduction number would have reached 3.231 (95% *CI:* 3.117–3.348) on January 23, 2020 (Fig. 4d). The cumulative number of confirmed cases, existing confirmed cases at the peak time, and deaths would be reduced by 99.85, 99.84, and 99.84%, respectively, compared with the quarantine and prevention measures implemented by the Chinese government since January 23, 2020.

#### Impact of relaxing isolation

When discussing the impact of relaxing isolation, we assumed that the contact rate would no longer exponentially decline as in eq. (4) but would instead become a constant *c*. If the quarantine was relaxed from February 24, 2020 and the contact rate satisfied *c* > 4.356, then there would be a second peak of infection. Particularly, when *c* = 4.394, the number of existing confirmed cases would reach 433 100 at the time of the second peak on June 11, 2020 (Fig. 5a).

However, if the quarantine was relaxed from February 24, 2020 and the contact rate satisfied *c* ≤ 4.356, then the number of existing confirmed cases would continue to decline but the downward trend would be slower (when *c* = 4.334; see Fig. 5b). In Fig. 5, panels B and C, compared with the current situation, it was evident that when *c* = 4.334, if isolation was relaxed on February 24, March 2, March 9, March 16, and April 1, 2020, respectively, then on April 30, 2020, the number of existing confirmed cases would increase by 174.56%, 71.79%, 28.54%, 11.59%, and 2.59%, respectively; the cumulative number of confirmed cases would increase by 68.80%, 26.49%, 9.63%, 3.36%, and 0.26%, respectively.

Similarly, if the quarantine was relaxed on February 24, 2020, and the contact rate satisfied *c* = 4.394, then the cumulative number of deaths would reach 12 100 on April 30, 2020, representing an increase of 39.95% compared with the current situation. When *c* = 4.334, compared with the current situation, if the quarantine was relaxed from February 24, March 2, March 9, March 16 and April 1, 2020, respectively, then on April 30, 2020, the cumulative number of deaths would increase by 38.33%, 12.56%, 3.79%, 1.29%, and 0.48%, respectively (Fig. 5d).

#### Impact of delayed diagnosis

If infectious individuals in the free environment had a delayed diagnosis by 1 day after January 23, 2020, the transfer rate of undiagnosed infectious individuals to the confirmed class would become *d*_{iq} = 0.1176. Therefore, the number of existing confirmed cases at peak time (February 24, 2020) and the total number of confirmed cases would increase by 4250 and 7480, respectively, which would correspond to an increase of 7.07% and 8.72% (Fig. 6a, b). If the diagnosis was delayed by 2 days, with a *d*_{iq} = 0.1052, the number of existing confirmed cases at peak time (February 25, 2020) and the total number of confirmed cases would increase by 7970 and 14 410, respectively, corresponding to an increase of 13.26% and 16.80%. The peak time would then be slightly delayed due to delayed diagnosis.

Similarly, if infectious individuals in the free environment had a delayed diagnosis for 1 or 2 days, the cumulative number of deaths would increase by 1060 and 2050, corresponding to an increase of 9.44% and 18.26%, respectively (Fig. 6c).

#### Impact of external input of infected persons and quarantined rate (*q*)

If there was an external input of 1 or 10 free infected persons on January 23, 2020, then the number of existing confirmed cases at peak time compared with the current situation would increase by 40 and 400, respectively (Fig. 7a). The final cumulative number of confirmed cases would increase by 50 and 560, respectively (Fig. 7b), and the final cumulative number of deaths would increase by 10 and 80 cases, respectively (Fig. 7c).

In addition, if there was an exogenous input of 1 or 10 free infected persons every day since March 4, 2020, then the final cumulative number of confirmed cases compared with the current situation would increase by 50 and 610 cases, respectively (Figure S3D). The final cumulative number of deaths would increase by 40 and 410 cases, respectively (Figure S3E) (Supplementary p. 9–11).

Under the current situation, the quarantined rate of *q* was estimated to be 26.53%. If the quarantined rate of *q* was increased to 50%, then the number of existing confirmed cases at peak time would decrease by 37 220, equating to a decrease of 61.93%. Furthermore, the cumulative number of confirmed cases and deaths would decrease by 62.22% and 62.64%, respectively (Fig. 7d-f).

If the quarantined rate of *q* was increased by 100%, then the number of existing confirmed cases at peak time compared with the current situation would decrease by 52 718, equating to a decrease of 87.72%. The cumulative confirmed cases and deaths would decrease by 88.26% and 88.53%, respectively. Additionally, the peak time would be slightly ahead (Fig. 7d-f). Therefore, broad close-contact tracing played an important role in controlling COVID-19 transmission trends.

### COVID-19 epidemic trend in Hubei, China

The final cumulative number of confirmed cases in the Hubei Province would reach 72 023 (95% *CI:* 71 815–72 023). On January 23, 2020, the effective reproduction number of COVID-19 in the Hubei Province was 3.511 (95% *CI:* 3.489–3.534), and had dropped below 1.0 on February 7, 2020. The cumulative number of confirmed cases would begin to stabilize on April 1, 2020. Since March 13, 2020 the number of new confirmed cases would be less than 100 every day, and from April 1, 2020, newly confirmed cases would be less than 10 every day (Supplementary p. 15–20).

Similar to the entirety of the mainland of China, if isolation was relaxed compared with the current situation, then the number of existing confirmed cases would only increase by 3.36% by April 30, 2020. The cumulative number of confirmed cases and deaths would only increase by 0.02 and 0.17%, respectively. Based on the above analysis, we proposed a gradual relaxation of quarantine beginning on April 1st in the Hubei Province (Supplementary p. 20–22).