A mathematical model and forecast for the coronavirus disease COVID-19 in Russia
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)
Forecast Monitor
06/17/2020. No 97.
The latest forecast for the development of the coronavirus epidemic COVID-19 in Russia for 10 and 30 days was published by us on June 6 (see https://www.facebook.com/ab.alyokhin/posts/148843413425229). Today we have the opportunity to analyze the accuracy of this forecast using statistical data for the period from June 6 to June 16, 2020 with an actual lead time of 11 days.
The results of the analysis of the forecast of June 6, 2020 and the degree of its compliance with actual data are shown in Fig. 1–15.
The accuracy estimates for the 11-day forecast are shown in Tables 1 and 2 (see Fig. 1, 2).
The table. Figure 1 shows the calculated and actual values of the main indicators of the epidemic of the coronavirus COVID-19 in Russia for 11 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 * cumulative estimate 11-day forecast in general.
The table. Figure 2 shows the same data on mortality rates I (TC), I (CC) and the IP progress indicator.
In fig. 3–6, as is usually accepted in our forecast monitors, are indicated:
- actual trajectories of the main indicators of the coronavirus epidemic in Russia;
- calculated trajectories of these indicators;
- the boundaries of confidence intervals (ranges of possible deviations of the point 10-day forecast (for the period from June 6 to June 15) with a significance level of p = 0.01.
Diagrams fig. 7, 8 indicate the values of the total number of infected and dead at the time the epidemic in Russia reached a progress level (IP indicator) of 75.11% (see the value of the progress indicator in Fig. 15).
Diagrams fig. 9–12 reflect the following parameters of the coronavirus epidemic in Russia:
- actual trajectories of changes in daily indicators of the coronavirus epidemic in Russia;
- calculated trajectories of these indicators over a significant part of the life cycle (from 0% to 75%);
- boundaries of confidence intervals (p = 0.3), corresponding to the forecast for 10 days in advance (for the period from June 6 to June 15, 2020).
Recall that the daily performance due to their significant variability due to the complexity of the predicted processes, are extremely difficult to predict the object. 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. 13–15 depicted:
- actual trajectories of mortality rates I (TC) and I (CC);
- the actual trajectory of the IP progress indicator;
- calculated trajectories of these mortality rates for the majority (up to 75%) of the epidemic life cycle;
- the calculated trajectory of the progress indicator.
As the analysis of the data in Table 1 shows (Fig. 1), as well as Fig. 3, 4, the forecast accuracy of the indicators of the total number of infected and dead is very high (0.41% and 2.80%, respectively).
The accuracy of predicting the indicators of the total number of recovered and current patients (Table 1, Fig. 5.6) is noticeably lower, but according to the level of MAPE * estimates, it is very high. So, we want to pay attention to Fig. 5. In this figure, it is clearly seen that the deviation of the actual data from the calculated ones appeared even before the start of the forecast period. If we compare this diagram with a similar one (see Fig. 12 of the forecast monitor that was published (https://www.facebook.com/ab.alyokhin/posts/148843413425229)), we can find that there is no such deviation in Fig. 12. This is due to the fact that while making the forecast, was a minor technical error about entering the actual data on the number of people who recovered before calibrating the model. This influenced the sought values of the model parameters responsible for the “recovery” block, and, as a result, the predicted values of this indicator.
When analyzing the accuracy of this forecast, these errors in the actual data were discovered and eliminated. As a result, the actual curve of the total number of people recovered on the days preceding the forecast period changed its shape, and the calculated trajectory remained unchanged. We see the same in the level of MAPE * estimates in the first days of the forecast period (see Table 1 in Fig. 1 and Table 2 of us in Fig. 2). With the right calibration, the accuracy of our forecasts in the early days is extremely high. In fact, the value of the MAPE * estimates on the first forecast day just characterizes the level of error introduced into the forecasts of these indicators by the inaccuracy that was made when entering the actual data.
We see the main source of a lower level of accuracy in predicting the indicator of the total number of patients recovered, as well as the indicator of the number of current patients directly associated with it (Fig. 6).
Despite the error allowed when entering the statistics for calibrating the model, in general, the accuracy of the forecast for the development of the epidemic of the coronavirus COVID-19 remained at a high level. This is evidenced by the diagrams in Fig. 6, 7, which reflect the forecasted values of the total number of infected and fatal cases, and the diagrams of daily increments of the main indicators (Fig. 9–12). In fact, the values of which did not go beyond the confidence intervals, despite the high variability, and the diagrams of Fig. 13–15, demonstrating a high level of consistency of the actual and estimated values of mortality and progress indicators.
Comment.
It is well known from foreign press that statistics on the problem of coronavirus in the Russian Federation are not a sample of statistical accounting. There is a discrepancy in the data contained in different monitoring systems for the distribution of the coronavirus COVID-19. While analyzing the accuracy of our forecasts, we never make retroactive changes to the database. Therefore, the actual data presented in the tables of Fig. 1, 2 may not correspond to updated data from different sources for the same past period. If facts of changes in statistics are discovered retroactively, we consider it appropriate to continue developing forecasts for such countries, update our databases only before new forecast calculations.
Sources of statistics:
https://www.worldometers.info/coronavirus/#countries
Our materials also:
https://www.facebook.com/MATHMODELCOVID19
Our initiative group and mission:
https://www.facebook.com/ab.alyokhin/posts/117804769862427
Publications on Mortality and Progress Indicators
https://www.facebook.com/ab.alyokhin/posts/105684827741088