A mathematical model and forecast for the coronavirus disease COVID-19 in Ukraine
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)
06/21/2020. No 99.
The latest published forecast for the development of the epidemic of the coronavirus COVID-19 in Ukraine is a forecast for 10 and 30 days from June 6 (see https://www.facebook.com/ab.alyokhin/posts/148972766745627). Today we publish the results of a final analysis of the accuracy of this fact of a 15-day forecast based on statistical data for the period from June 7 to June 21, 2020.
Estimates of the accuracy of the 15-day forecast for the development of the coronavirus epidemic in Ukraine are giving in Table 1 and Table. 2 (see Fig. 1, 2).
In the Table 1 shows the calculating and actual values of the main indicators of the epidemic for 15 days of the forecast period, the absolute and relative errors of daily forecasts, as well as the average absolute error MAE and the average absolute error in percent of MAPE, including the same MAPE* estimate on an accrual basis.
In the table. Figure 2 shows the same data on mortality rates I (TC), I (CC) and IP progress indicator.
In fig. 3–6, as is usually accepted in our forecast monitors, are indicating:
- actual trajectories of the main indicators of the coronavirus epidemic in Ukraine;
- calculated trajectories of these indicators;
- boundaries of confidence intervals (ranges of possible deviations of the point 10-day forecast (for the period from June 7 to 16) with a significance level of p = 0.01.
These, like other diagrams placed in the forecast monitor, allow you to visualize the degree of consistency (mismatch) of the actual and calculated data.
Diagrams fig. 7–10 reflect the following parameters of the coronavirus epidemic in Ukraine:
- actual trajectories of changes in daily epidemic indicators;
- calculated trajectories of these indicators for a 30-day forecast period;
- boundaries of confidence intervals (p = 0.3) corresponding to the forecast for 10 days (for the period from June 7 to June 16, 2020).
Recall that daily indicators, due to their significant variability due to the complexity of the predicted processes, are an extremely difficult object to predict. This explains both the wide confidence intervals for the forecasts of these indicators and the relatively high probability of forecast errors.
In the diagrams of Fig. 11–13 displayed:
- actual trajectories of mortality rates I (TC) and I (CC) for the entire observation period;
- actual trajectory of the IP progress indicator for the entire observation period;
- calculated trajectories of these mortality rates for a period including the observation period and the 30-day lead time for this forecast;
- calculated trajectory of the progress indicator for a period, including the observation period and the 30-day lead-time period.
Based on the data of Table 1 (Fig. 1), as well as Fig. 3, 4 and 6, we can conclude that the accuracy of prediction of the total number of infected and deceased, as well as active patients is very high (1.61%, 0.96% and 2.95%, respectively) and by the end of the analysis period for the first two indicators are even increasing. The accuracy of predicting the indicator of the number of convalesced people (Table 1, Fig. 5) is noticeably lower, but according to the level of MAPE * estimates it is very high.
An analysis of the reasons for the lower accuracy in predicting the total number of survivors, performed by specialists of the working group, shows that their reasons are solely due to the specifics of statistical accounting of this category of patients on weekends and holidays. (We have repeatedly pointed out this phenomenon in our forecast monitors.)
As can be seen in the diagram in fig. 5 (see the actual curve indicated in red), the curve growth rate slows down every weekend, and after the weekend it resumes in strict accordance with the theoretical curve, but with a certain deviation in absolute value. This has nothing to do with the regularities of the epidemic and the accuracy of their forecasting, but it directly affects the formal estimates of the accuracy of forecasts.
The consequence of this is a slightly increased (compared to other indicators) error level due to the total number of recovered patients, the number of active patients (see Fig. 6). This is the main reason for a certain deviation of the calculated values of the mortality rate I (CC) and, especially, the progress indicator IP, which are determined, among other things, by the number of people who have recovered (see Fig. 12–13). Despite this, however, the accuracy of forecasting mortality rates and, to a somewhat lesser extent, the progress indicator remains very high (see Table 2, Fig. 1 and Fig. 11–13).
Despite the traditionally high level of variability of daily epidemic indicators (see Fig. 6–10), model trends and their corresponding confidence intervals describe their excellent dynamics. As seen in fig. 3–6 and fig. 7–10, the actual values of all indicators within the framework of the regular 10-day forecast did not go beyond confidence limits.
The results of this analysis, like many others that we previously published for epidemics in Ukraine and other countries of the world, including Germany, Spain, Italy, the USA, France, and South Korea, indicate the level of accuracy of the forecasts of the interagency working group better than they could tell the developers of these forecasts themselves.
Sources of statistics:
Our materials also:
Publications on Mortality and Progress Indicators