Simulation and prediction of the COVID-19 disease variations
In this section, the variations of the COVID-19 in Guangdong province are simulated and predicted based on our SEIRQ model only considering the input population from the other provinces of China (excluding Hubei province). The simulated period are from Jan 27, 2019 to Feb 19, 2020. The parameter values and the initial values of our simulation and prediction are provided in Table 1 . The performance is evaluated by the data from Feb 20, 2020 to Feb 23, 2020, and R  *  2, AE, RE, RMSE, MPAE and DISO are employed to quantify the accuracy. The simulation and prediction results are displayed in Table 2 and Fig. 2 .
Table 1 Parameter estimates for COVID-19 in Guangdong province.
Parameter Definitions Esimated value Source
β Transmission incidence rate 2.45 × 10−8 Estimated
σ The fraction of transmission incidence rate for exposed individuals 0.63 Estimated
α Disease-induced death rate 0.00375 Estimated
ν Transmission rate of exposed individuals to the infected class 0.183 [Zhao et al., 2020a], [Zhao et al., 2020b]
γ(t) Recovery rate 0.008+0.19(1+e5.0126−0.1846t) Estimated
q1(t) Quarantined rate of susceptible individuals 0.28 Estimated
q2(t) Quarantined rate of exposed individuals 0.76 Estimated
q3 Quarantined rate of infected individuals 0.89 Estimated
A(t) Input number 86926 data
B1 Output number 21356 data
p1 The fraction of input population into susceptible class 0.9999927 Computed
p2 The fraction of input population into exposed class 0.0000073 Computed
p3 The fraction of input population into infected class 0 Assumed
Initial values Definitions Esimated value Source
N(0) Initial total population 113460000 GSY
S(0) Initial susceptible population 113346174 Estimated
E(0) Initial exposed population 31 Estimated
I(0) Initial infected population 19 Estimated
Sq(0) Initial quarantined susceptible population 113460 Estimated
Eq(0) Initial quarantined exposed population 128 data
Iq(0) Initial quarantined infected population 184 data
R(0 Initial recovered population 4 data
Note: GSY: Guangdong Statistical Yearbook, 2019.
Table 2 Evaluation results of the simulation and prediction in Guangdong province.
Different cases Simulation Prediction
R * 2 AE MAPE (%) DISO 20/2 21/2 22/2 23/2
RE (%) RE (%) RE (%) RE (%)
Cumulative confirmed cases 0.9973 −5.33 2.54 0.06 −0.38 −0.45 −0.37 −0.37
Confirmed cases 0.9898 −2.63 3.86 0.11 2.68 1.51 0.81 7.07
Recovered cases 0.9934 −3.38 43.32 0.17 −2.09 −1.38 −3.75 −10.41
Figure 2 Simulation and prediction of the COVID-19 in Guangdong province. (A) cumulative confirmed cases; (B) daily new confirmed cases and (C) difference of increased confirmed cases. The initial values and parameters are S(0) = 113346174, E(0) = 31, I(0) = 19, R(0) = 4, Sq(0) = 113460, Eq(0) = 128, Iq(0) = 184, A = 86926, B = 21356, p1 = 0.9999927, p2 = 0.0000073, p3 = 0, q1 = 0.28, q2 = 0.76, q3 = 0.89, α = 0.00375, β = 2.45 × 10−8, ν = 0.183, σ = 0.63, γ(t) = 0.008 + 0.19/(1 + e5.0126−0.1846t).
Our model has the ability to simulate and to predict the COVID-19 variations with the very high accuracy (Table 2 and Fig. 2). Particularly, the determinant coefficients R* of the cumulative confirmed cases, confirmed cases and recovered cases are highly to 0.9973, 0.9898 and 0.9934, respectively (Table 2). Very small estimations are obtained with the AE values of −5.33, −2.63 and −3.38 for the cumulative cases, confirmed cases and recovered cases. The comprehensive accuracies of our model are quantitatively measured by the DISO with the values of 0.06, 0.11 and 0.17 for the cumulative cases, confirmed cases and recovered cases. For the validation at Feb 20, Feb 21, Feb 22 and Feb 23, 2020, the very small RE values of the cumulative confirmed cases, confirmed cases and recovered cases indicate that our model also has very high accuracies and it can be employed to predict the future variations of the COVID-19 disease (Table 2).
Moreover, the largest number of cumulative confirmed cases is 1397 at May 7, 2020 which indicates that the COVID-19 disease will become extinction after 102 days in Guangdong province (Fig. 2A, STable 1). The peak value time of daily new confirmed cases is Feb 1, 2020 which is highly agrement with the reported time at Jan 31, 2020 (Fig. 2B). For the confirmed cases, the peak value and the corresponding time are both obtained by our model with the simulated values of 1002 at Feb 10, 2020 and reported values of 1007 at Feb 9, 2020 (Fig. 2C). The number of the recovered cases will reach about 1400 which is consist with the future changes of the cumulative confirmed cases (Fig. 2D).
In order to further explore the forecasting accuracy of our model, we have been compared the forecasting result with the observed data prolonged 11 days from Feb 24, 2020 to Mar 4, 2020. The absolute values of RE (relative error) of the cumulative confirmed cases are smaller than 1% (Table 3 ). The corresponding figures also display that our model can capture the temporal variations in a relative longer period (see SFigure 1 in the supplementary information).
Table 3 Evaluation results of the prediction in Guangdong province.
RE (%) 24/2 25/2 26/2 27/2 28/2 29/2 1/3 2/3 3/3 4/3
Cumulative confirmed cases −2.30 −0.41 0.12 0.20 0.25 0.37 0.40 0.49 0.58 0.66
Confirmed cases −14.98 −19.21 −24.22 −26.74 −27.64 −30.81 −36.19 −35.94 −33.52 −34.68
Recovered cases 9.60 11.35 13.09 12.57 10.88 10.67 11.35 9.35 7.08 6.31