We use sequence diagrams and autocorrelation functions of the original data to determine the stationarity of these time series, and to smooth the series whose average and variance are not always constant. In the exponential smoothing method, we perform a natural logarithmic transformation on the series to omplete the smoothing process. In the ARIMA and ARIMAX models, we use the first-order difference or the second- order difference to smooth the original sequence. Using the above processing, we can obtain the time series analysis model summary information of the number of confirmed cases in mainland China as shown in Table 2.

As shown in Table 2, we have established multiple time series analysis models for the number of confirmed cases in mainland China. By comparing, we can initially find that the Brown model is a natural logarithmic transformation of the original sequence and the second order ARIMAX (0,1,0) model for difference processing seems to be more suitable. Among them, the Brown model has a stationary R-square of 0.605, the Ljung-Box Q (18) test statistic has a value of 0.958, the stationary R-square of the ARIMAX (0,1,0) model is 0.977, and the value of the Ljung-Box Q (18) test statistic is 0.987. According to Table 2, we find that ARIMAX (0,1,0) model is the best of the six time series models in terms of goodness of fit and Ljung box Q (18) test results. We preliminarily think that Brown model and ARIMAX (0,1,0) model should have good statistical significance, and they should be able to predict the number of confirmed cases of new coronavirus pneumonia in mainland China in the next week. To further diagnose the results of these time series models, we make their autocorrelation function diagrams of the residuals as shown in Figure 2.

In the function graph, we can judge whether the residuals still contain valid information of the time series. Through Figure 2, we can intuitively find that there may still be some valid information in the residuals of model 3. After observing the Residual ACF of other models, we think the residual sequences of Model 2 and Model 5 can be regarded as white noise sequences.29 That is, to a certain extent, the Brown model with natural logarithmic transformation of the original sequence and ARIMAX (0,1,0) models can be used to predict the short-term development of the confirmed number of patients with new type of coronavirus pneumonia in mainland China. As shown in Figure 3 and Figure 4 below, we have made a short-term prediction of the number of confirmed cases of new coronavirus pneumonia in mainland China based on Brown model and ARIMAX (0,1,0) model after second-order difference processing. We can clearly see from Figure 3 and Figure 4 that the prediction of the exact number of cases diagnosed in the past time by these two models is in good agreement with the real value, while the ARIMAX (0,1,0) model processed by second-order difference is more consistent with the historical data. The predictions of these two models for the number of confirmed cases of new coronavirus pneumonia in the next week are relatively close, but we noticed that under the 95% confidence interval, the ARIMAX (0,1,0) after second-order difference processing the upper and lower limits of the model's prediction of the number of confirmed cases are very small, so we finally selected the ARIMAX (0,1,0) model that was subjected to second-order difference processing in six time series models.

Then the number of confirmed cases in mainland China is predicted. Based on the predictions in Figure 4, we believe that the number of confirmed cases of new coronavirus pneumonia in mainland China in a week (February 8, 2020) may be as high as 36,343.

We also made six time series models of cumulative confirmed cases in Hubei Province as shown in Table 3 below and the autocorrelation function diagrams of the residuals of these 6 models are shown in Figure 5. Based on the information in Table 3 and Figure 5, we selected the ARIMAX (0,0,0) model made a short- term prediction of the number of confirmed cases of pneumonitis of the new coronavirus in Hubei Province, and plotted the prediction of the ARIMAX (0,0,0) model as shown in Figure 6.

According to Figure 6, we believe that the number of confirmed cases of pneumonitis with new coronavirus in Hubei Province will rise to 26,455 in a week (February 8, 2020). It is worth mentioning that because the time series model is based on the original sequence itself time series models based on different mathematical formulas may not be suitable for long-term prediction of the spread of the COVID-19 epidemic, but these models can provide rapid prediction of short-term transmission of the COVID-19 epidemic. So as to provide reference value for all levels of departments and hospitals in the next few days to implement effective intervention and prevention of the spread of new coronavirus.

According to the data released by the National Health Construction Commission of China, we set the data on January 10 as the initial value. On January 10, the transmission of COVID-19 only occurred in Hubei Province, of which 41 were confirmed, 0 were suspected, 2 were cured, 2 were infected with the COVID-19 but not yet sick, and 0 people were ill but not isolated, namely:

E(0) = 2 , I (0) = 0 , Q(0) = 0 , D(0) = 41 , R(0) = 2 .

Since COVID-19 originates from Wuhan, Hubei, the above initial value can also be used as the national initial value. Based on this, we use the least square method to calculate k and errors SSE of Hubei Province and Mainland China as follows:

k_H= 0.815 , SSE_H= 2236 .

k_N= 0.553 , SSE_N= 2527 .

Among them, kH means Hubei Province’s k value, kN means the k value of mainland China, because Hubei Province is the birthplace of the epidemic, with a large number of patients and limited medical resources, a large number of mild patients are self-isolated at home, which increases the transmission time after the incubation period. 30 The number of cases outside Hubei Province is small, and medical resources are sufficient, making the k value small. The latent can get timely treatment after the onset, and reduce the transmission time after the onset. It can be seen from the comparison of k value that it is a very correct and effective decision for medical staff from other provinces in mainland China to go to Wuhan and Hubei to fight the epidemic. It can be seen from Figure 7 that the SEIQDR model based on the dynamic propagation of COVID-19 has a good fitting effect with the original data in the duration period (from January 10, 2020 to February 9, 2020), and the fitting curve of the number of confirmed cases is basically consistent with the duration data.

We use SEIQDR model to predict the spread of COVID-19 in mainland China and Wuhan, and get the development trend of the cumulative number of confirmed cases in mainland China and Wuhan as shown in Figure 8. Based on the prediction results in Figure 8, we believe that the cumulative number of confirmed cases in Wuhan will continue to rise within 70 days from January 10, 2020, and the cumulative number of confirmed cases in Wuhan may reach a peak around March 20, 2020, the peak is 76982, that is to say, after the cumulative number of confirmed cases in Wuhan reached 76982 on March 20, there may no new confirmed cases appear.

To observe the development trend of the cumulative number of confirmed cases in mainland China, we believe that when the cumulative number of confirmed cases in Wuhan reaches a peak, the growth rate of confirmed cases in mainland China will decrease rapidly, and the cumulative number of confirmed cases in mainland China will peak around March 15, 2020, with a peak of 87,701. In order to give a clearer mathematical description of the spread of COVID-19 in Wuhan and Mainland China, we analyze the infection rate and basic regeneration number of the new coronavirus. Using the diachronic data and the calculation formula for the infection rate given above, the infection rate is fitted, we let the basic regeneration number of COVID-19 be R(t) , we use the following formula to calculate the basic regeneration number of COVID-19:

As can be seen from the above formula, there is a close relationship between the basic regeneration number and the infection rate. In the above formula, t is the average latency of the COVID-19, and we also set the initial value of the average latency to 7. From this, we can get the trend of infection rate and basic regeneration number of 2019 nCoV in Wuhan and Mainland China over time as shown in Figure 9 below. As shown in Figure 9, during the period from January 10 to February 9, 2020, No matter in mainland China or Wuhan, the infection rate and basic regeneration number of COVID-19 continue to decline, and may continue to decline in the future. In our opinion, this may indicate that the emergency intervention and special control measures taken by the Chinese government to block Wuhan City, restrict the flow of people in Hubei Province and enhance the medical resources in the severely affected areas in the early stage of COVID-19 transmission have played a crucial role in the spread of the epidemic. According to the results of SEIQDR model, we believe that during the period from January 10 to February 9, 2020, the average basic regeneration number of COVID-19 in mainland China is 4.01, while the average basic regeneration number in Wuhan is 4.3. The infection rate of COVID-19 in mainland China should be reduced to 0 in 45 days after January 10, 2020, that is, around February 25.

According to the results of the SEIQDR model, we can also study more about the development trend of the COVID-19 epidemic in mainland China, Hubei Province, and Wuhan. Without the loss of generality, other parameters in the SEIQDR model remain initially set. Under the circumstances, we analyze some parameters in mainland China to explore the possible changes in the cumulative number of confirmed diagnoses. We have made a trend chart of the number of confirmed cases in mainland China when the average time required for the suspected population to be transformed into the confirmed population changes as shown in Figure 10.

In Figure 10, The reciprocal of s indicates that it takes the average time for the suspected population to be diagnosed as the confirmed population, that is  = dqd , as shown in Figure 10, at that time of = 1 / 5 , it took an average of 5 days for suspected cases to be diagnosed as confirmed cases for necessary isolation and treatment. If the various preventive measures remain unchanged, the cumulative number of confirmed patients in mainland China will reach a peak after 73 days on January 1, 2020. The peak time was 94731 people. At that time of = 1 / 3 , patients can get relatively timely isolation and treatment after the onset of the disease, in which case the peak number of cumulative diagnoses will be reduced to 87701, a relative decrease of 7030. According to Figure 10, we can find that the peak number increases as gets smaller of cumulative diagnoses, which means that if the number of patients diagnosed with suspected patients will increase rapidly if they are not diagnosed in time. We believe that this trend may not be obvious enough within 30 days after January 10, however, once the epidemic situation becomes serious, the rapid increase in the number of confirmed cases and the difficulty in timely diagnosis and treatment may bring great challenges to the prevention and control of the epidemic in mainland China.

Finally, we analyzed the sensitivity of mortality  and cure rate in SEIQDR model. The Figure 11 shows the change in the cumulative number of confirmed cases with mortality and cure rate in mainland China. In Figure 11, on the left is the cumulative number of confirmed diagnoses with death during the transmission of COVID-19 in mainland China, the change of the cure rate is the change of the cumulative number of diagnoses with the cure rate on the right.

We found that when the mortality rate gradually increased from 2% to 10%, the cumulative number of diagnoses increased by about 2,000. We believe that ,this means that the bodies of patients killed by COVID 19 may still carry a certain number of new infectious coronaviruses. According to the results of this simulation, we suggest that mainland China, especially Hubei Province and Wuhan City, should pay attention to the treatment of the dead bodies of the dead patients, try to ensure that the body itself and the handling process do not cause additional contagion. We also gradually increased the cure rate from 2% to 10%, and found that the cumulative number of confirmed diagnoses has almost no fluctuation. We think this means that once the pneumonia patients with the new coronavirus are cured, the antibodies left in their bodies may make them no longer a member of the susceptible population infected with the new coronavirus. In the early stage of COVID-19 transmission, as we did not know about COVID-19 and clinical trials were difficult to proceed immediately, our modeling and results provided reference values for intervention and prevention and clinical trials at all levels.

There is no doubt that the propagation of COVID-19 in the population will be affected by the intricacies of many factors. In the early stage of the COVID-19 propagation, it is difficult to establish a dynamic propagation model with parameters to be estimated and obtain fairly accurate simulation results, but the preliminary estimation of parameters such as average latency and mortality through existing data may be helpful for solving important parameters such as infection rate and rehabilitation rate, which will help us have a more accurate grasp of the transmission trend of COVID-19. On the other hand, statistical modeling of the spread of new coronavirus pneumonia in the population based on time series analysis is a thing that can be done immediately after getting the latest data every day, because the dynamic model of the time series is based on the law of the data itself. Although this method often requires sufficient data to support it, in the early stages of epidemic transmission, this method can still be used to more accurately predict the indicators of epidemic transmission in the short term, so as to provide intervention control at all levels of the departments and Policy implementation provides short-term emergency prevention programs.