Modeling and forecasting the spread tendency of the COVID-19 in China

Abstract

To forecast the spread tendency of the COVID-19 in China and provide effective strategies to prevent the disease, an improved SEIR model was established. The parameters of our model were estimated based on collected data that were issued by the National Health Commission of China (NHCC) from January 10 to March 3. The model was used to forecast the spread tendency of the disease. The key factors influencing the epidemic were explored through modulation of the parameters, including the removal rate, the average number of the infected contacting the susceptible per day and the average number of the exposed contacting the susceptible per day. The correlation of the infected is 99.9% between established model data in this study and issued data by NHCC from January 10 to February 15. The correlation of the removed, the death and the cured are 99.8%, 99.8% and 99.6%, respectively. The average forecasting error rates of the infected, the removed, the death and the cured are 0.78%, 0.75%, 0.35% and 0.83%, respectively, from February 16 to March 3. The peak time of the epidemic forecast by our established model coincided with the issued data by NHCC. Therefore, our study established a mathematical model with high accuracy. The aforementioned parameters significantly affected the trend of the epidemic, suggesting that the exposed and the infected population should be strictly isolated. If the removal rate increases to 0.12, the epidemic will come to an end on May 25. In conclusion, the proposed mathematical model accurately forecast the spread tendency of COVID-19 in China and the model can be applied for other countries with appropriate modifications.

Keywords: COVID-19; Control strategy; Forecasting; Mathematical modeling; Parameter estimation.

Figure 1

The transmission mechanism of COVID-19

Figure 2

Dynamic trends of the susceptible

Figure 3

Dynamic trends of the exposed

Figure 4

Dynamic trends of the infected. The blue line represents the simulation of SEIR model. The red line represents the data issued by NHCC. The green line represents the intervention 1. The light blue line represents the intervention 2. The black line represents that the government began to implement new diagnostic criteria

Figure 5

Dynamic trends of the removed. The removed consist of the cures and the death. The blue line represents the simulation of SEIR model. The red line represents the data issued by NHCC

Figure 6

Dynamic trends of the death. The blue line represents the simulation of SEIR model, and the red line represents the data issued by NHCC

Figure 7

Dynamic trends of the cured. The blue line represents the simulation of SEIR model, and the red line represents the data issued by NHCC

Figure 8

Dynamic trends of the infected with different removal rates (γ). The solid line represents the trends of the infected with the current γ. The purple dotted line represents the trends of the infected when $\gamma =0.12$. The orange dotted line represents the trends of the infected when $\gamma =0.06$. The blue dotted line represents the trends of the infected when $\gamma =0.04$. The green dotted line represents the trends of the infected when $\gamma =0.02$

Figure 9

Dynamic trends of the removed with different removal rates (γ). The solid line represents the trends of the removed with the current γ. The purple dotted line represents the trends of the removed when $\gamma =0.12$. The orange dotted line represents the trends of the removed when $\gamma =0.06$. The blue dotted line represents the trends of the removed when $\gamma =0.04$. The green dotted line represents the trends of the removed when $\gamma =0.02$

Figure 10

Dynamic trends of the infected with different r. The solid line represents the trends of the infected with the current r. The orange dotted line represents the trends of the infected when $r=1$. The yellow dotted line represents the trends of the infected when $r=3$. The purple dotted line represents the trends of the infected when $r=5$

Figure 11

Dynamic trends of the removed with different r. The solid line represents the trends of the removed with the current r. The orange dotted line represents the trends of the removed when $r=1$. The yellow dotted line represents the trends of the removed when $r=3$. The purple dotted line represents the trends of the removed when $r=5$

Figure 12

Dynamic trends of the infected with different $r_2$. The solid line represents the trends of the infected with the current $r_2$. The orange dotted line represents the trends of the infected when $r_2=1$. The yellow dotted line represents the trends of the infected when $r_2=2$. The purple dotted line represents the trends of the infected when $r_2=2.5$. The green dotted line represents the trends of the infected when $r_2=3$

Figure 13

Dynamic trends of the removed with different $r_2$. The solid line represents the trends of the removed with the current $r_2$. The orange dotted line represents the trends of the removed when $r_2=1$. The yellow dotted line represents the trends of the removed when $r_2=2$. The purple dotted line represents the trends of the removed when $r_2=2.5$. The green dotted line represents the trends of the removed when $r_2=3$