Figure 1. Two processes constituting multiple symmetrical breakings in population dynamics. Blue indicates susceptible population, light yellow indicates exposed population, orange is infected cases, green is recovered cases, gray is severe cases, and black is deaths. (a) Popular SEIR model viewed from a symmetry-breaking perspective. (b) Three types of social interventions led to symmetry breaking in corresponding populations.

Figure 1. Two processes constituting multiple symmetrical breakings in population dynamics. Blue indicates susceptible population, light yellow indicates exposed population, orange is infected cases, green is recovered cases, gray is severe cases, and black is deaths. (a) Popular SEIR model viewed from a symmetry-breaking perspective. (b) Three types of social interventions led to symmetry breaking in corresponding populations.

Figure 2. Schematic representation of SHR model.

Figure 2. Schematic representation of SHR model.

Figure 3. Comparison of evolution of first wave of the epidemic in Hubei Province and Italy. Red and blue circles indicate data collected by Hubei Provincial Health Commission and Johns Hopkins University real-time epidemic surveillance system, respectively (as of 2 June 2020), triangles indicate resulting calculated rate data, and solid line indicates simulation results of SHR model. Simulation parameters are shown in Table 1. (a) Separating degree, (b) healing degree, and (c) rescuing degree; (d) infection rate, (e) cure rate, and (f) death rate; (g) number of daily confirmed, (h) number of daily recovered, and (i) number of daily deaths. Figure 3. Comparison of evolution of first wave of the epidemic in Hubei Province and Italy. Red and blue circles indicate data collected by Hubei Provincial Health Commission and Johns Hopkins University real-time epidemic surveillance system, respectively (as of 2 June 2020), triangles indicate resulting calculated rate data, and solid line indicates simulation results of SHR model. Simulation parameters are shown in Table 1. (a) Separating degree, (b) healing degree, and (c) rescuing degree; (d) infection rate, (e) cure rate, and (f) death rate; (g) number of daily confirmed, (h) number of daily recovered, and (i) number of daily deaths.

Figure 4. Simulation for 23 areas of mainland China in first wave of the epidemic, compared to data. Circles indicate cumulative data (as of 1 April 2020) collected from Johns Hopkins University real-time epidemic surveillance system, triangles indicate daily data calculated from that, and solid lines indicate simulation results from SHR model.

Figure 4. Simulation for 23 areas of mainland China in first wave of the epidemic, compared to data. Circles indicate cumulative data (as of 1 April 2020) collected from Johns Hopkins University real-time epidemic surveillance system, triangles indicate daily data calculated from that, and solid lines indicate simulation results from SHR model.

Figure 5. Two evolutionary patterns of healing degree among 17 areas of mainland China. Red represents pattern 1 and blue represents pattern 2. (a) Power laws of growth rate α and inflection point th. (b) Linear laws of initial healing degree H0 and saturation healing degree H1. (c) Distribution of duration.

Figure 5. Two evolutionary patterns of healing degree among 17 areas of mainland China. Red represents pattern 1 and blue represents pattern 2. (a) Power laws of growth rate α and inflection point th. (b) Linear laws of initial healing degree H0 and saturation healing degree H1. (c) Distribution of duration.

Figure 6. Comparison of Beijing in different epidemic waves. Red and blue circles indicate data collected by Johns Hopkins University real-time epidemic surveillance system (as of 2 July 2020). Triangles indicate resulting calculated rate data, and solid lines indicate results of SHR model simulations. (a) Separating degree, (b) infection rate, and (c) number of infected; (d) healing degree, (e) cure rate, and (f) number of cured.

Figure 6. Comparison of Beijing in different epidemic waves. Red and blue circles indicate data collected by Johns Hopkins University real-time epidemic surveillance system (as of 2 July 2020). Triangles indicate resulting calculated rate data, and solid lines indicate results of SHR model simulations. (a) Separating degree, (b) infection rate, and (c) number of infected; (d) healing degree, (e) cure rate, and (f) number of cured.

Figure 7. Third epidemic wave in Beijing under different intervention intensities. Black circles indicate data collected from Johns Hopkins University real-time epidemic surveillance system, triangles indicate resulting rate data, and solid lines indicate SHR model simulations, with different colors representing different saturation control efforts. (a) Evolution of separating degree, (b) infection rate, and (c) total predicted infected cases; (d) phase trajectory of separating degree by simulating with different sized datasets; (e) predicted evolution of infected cases by using different sized datasets.

Figure 7. Third epidemic wave in Beijing under different intervention intensities. Black circles indicate data collected from Johns Hopkins University real-time epidemic surveillance system, triangles indicate resulting rate data, and solid lines indicate SHR model simulations, with different colors representing different saturation control efforts. (a) Evolution of separating degree, (b) infection rate, and (c) total predicted infected cases; (d) phase trajectory of separating degree by simulating with different sized datasets; (e) predicted evolution of infected cases by using different sized datasets.

Table 1. Model parameters and initial values for Hubei (China) and Italy.

Table 1. Model parameters and initial values for Hubei (China) and Italy.

Order ParametersModel ParametersHubeiItalySeparating degree (S)VI0Initial infection rate0.48 ± 0.010.48 ± 0.02γGrowth rate of separating degree0.18 ± 0.020.10 ± 0.02S1Saturation value of separating degree1.00 ± 0.000.98 ± 0.01tsTime up to midpoint of S17.8 ± 0.417.0 ± 1.0Healing degree (H)αGrowth rate of healing degree0.08 ± 0.010.03 ± 0.01H1Saturation value of healing degree0.15 ± 0.010.09 ± 0.04thTime up to midpoint of H50 ± 296 ± 20Rescuing degree (R)VD0Initial death rate0.03 ± 0.010.03 ± 0.01μGrowth rate of rescuing degree0.16 ± 0.060.09 ± 0.03R1Saturation value of rescuing degree0.95 ± 0.020.80 ± 0.10trTime up to midpoint of R9 ± 532 ± 18

Table 2. Model parameters for 23 epidemic spillover areas during first wave in mainland China.

Table 2. Model parameters for 23 epidemic spillover areas during first wave in mainland China.

γtsαthInfectedDuration0.27 ± 0.096.5 ± 2.70.12 ± 0.0543.4 ± 18.9528 ± 39527 ± 5

Table 3. Comparison of model parameters and statistics for the two epidemic waves.

Table 3. Comparison of model parameters and statistics for the two epidemic waves.

WaveγS0αInfectedDurationFirst0.1553%0.0439530Second0.3521%0.3433525

Table 4. Mean values of model parameters obtained based on different sized datasets.

Table 4. Mean values of model parameters obtained based on different sized datasets.

γS0S1αH0Infected0.33 ± 0.0156.2% ± 0.1%96.5% ± 0.1%0.071 ± 0.0051.8% ± 0.1%1631 ± 166