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)
Forecast Monitor
07/27/2020. No 119.
https://www.facebook.com/ab.alyokhin/posts/166709051638665
The latest forecast for the development of the COVID-19 coronavirus epidemic in Ukraine, compiled according to statistical data as of July 21, was published on the same day (see https://www.facebook.com/ab.alyokhin/posts/164310981878472) … This forecast was developed using a different approach and a different model, which are in the testing stage. Therefore, it was completing for 7 days and is considering by us as a trial, approximate.
When analyzing the results obtained, first, we note that the epidemic of the coronavirus COVID-19 in Ukraine in the last forecast week sought to set anti-records. It would be useful to remind that she did it with the tacit consent of those on whom it depends whether to be such anti-records in our country or not.
The results of the analysis of the 7-day forecast for the development of the COVID-19 coronavirus epidemic in Ukraine dated July 21, 2020 and the degree of its compliance with the actual data are showing in the tables in Fig. 1–2.
Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Ukraine for the entire forecast period. The absolute and relative errors of daily forecasts, as well as the average absolute error of MAE and the average absolute error in percent MAPE, including the same MAPE * estimate on a cumulative total, the forecast as a whole.
Table 2 shows the same data for case fatality rates I (TC), I (CC) and the IP progress indicator.
As the data in Table 1 shows (Fig. 1), the forecast accuracy is very high. The mean absolute percentage errors (MAPE estimates) for the main indicators of the epidemic are at the following level:
- total number of infected — 1.06%;
- total number of deaths — 0.22%;
- total number of recovered — 0.65%.
The accuracy of predicting derived indicators of the coronavirus epidemic in Ukraine, such as mortality indices I (TC), I (CC) and the IP progress indicator (Table 2, Fig. 2), are just as high. The MAPE estimates for these indicators are 0.87%, 0.45% and 0.89%, respectively.
The quality of forecasting can be visually assesse using the diagrams in Fig. 3–14. Due to the high forecasting accuracy and, as a consequence, the coincidence of the calculated and actual curves, we emphasize that on all charts, the forecast trajectories of the predicted indicators are indicated in dark blue in the 7-day forecast period.
In fig. 3–6 are given:
- actual trajectories of the main indicators of the coronavirus epidemic in Ukraine for the entire observation period, including the forecasting period;
- calculated trajectories of these indicators for the forecast period;
- boundaries of confidence intervals (ranges of possible deviations of the 7 point forecast with a significance level of p = 0.05) for the forecast of the number of active cases (Fig. 6).
In fig. The 3–5 confidence intervals were omitted due to their narrowness and overlapping on the graphs of the main indicators.
As you can see, only the deviation of the actual values of the number of active cases (Fig. 6), which are a consequence of abnormally low values of the number of recovered in the last days of the forecast period, are visually distinguishable on the diagrams.
Diagrams Fig. 7–10 reflect:
- actual trajectories of changes in daily indicators of the coronavirus epidemic in Ukraine for the entire observation period, including the forecast period;
- calculated trajectories of these indicators for the forecast period;
- boundaries of the confidence intervals (p = 0.05), corresponding to the 7-day forecast.
Despite the abnormal values of a number of daily indicators, in general, their trajectories corresponds to trends, were within confidence intervals or in close proximity to them, and did not have a noticeable effect on the accuracy of forecasting the main indicators of the epidemic.
This conclusion is confirming by the diagrams in Fig. 11–14, which reflect:
- actual trajectories of lethality indicators I (TC) and I (CC), reproductive number R0 and IP progress indicator for the entire observation and forecasting period;
- calculated trajectories of the specified indicators for the forecast period.
Overall, the data in the tables and diagrams provided indicate a high quality of the forecast, despite the anomalous (anti-record) bursts of individual indicators.
Unfortunately, apart from the accuracy of the forecast of their authors, nothing else pleases in the presented picture, and, above all, it is not encouraging that there are no signs of curbing the epidemic in our country in the short term, at least.
Source of statistics:
https://www.worldometers.info/coronavirus/#countries
https://www.pravda.com.ua/cdn/covid-19/cpa/
Our materials also:
https://www.facebook.com/MATHMODELCOVID19
Our initiative group and mission:
https://www.facebook.com/ab.alyokhin/posts/117804769862427
Publications on case fatality rates and progress indicator
https://www.facebook.com/ab.alyokhin/posts/105684827741088