A mathematical model and forecast for the coronavirus disease COVID-19 in Germany
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.I. Laiko, Z.N. Sokolovska)
Forecast monitor
25.05.2020. No 81.
(https://www.facebook.com/ab.alyokhin/posts/144090053900565)
The latest forecast of the COVID-19 outbreak in Germany, was published on May 16 (see https://www.facebook.com/ab.alyokhin/posts/140481370928100), which was compiled by processing statistical data for the entire observation period up to May 15, 2020, inclusive.
Today we present the results of the evaluation of the forecast accuracy, based on a comparison of the estimated and actual values of main indicators of the COVID-19 outbreak in Germany for the period May 16–24, 2020.
Quantitative data of the analysis for the period are shown in the tables of Fig. 1, 2.
In table. 1 the calculated and actual values of the main indicators of coronavirus outbreak in Germany for the forecast period as mentioned above are indicated, absolute and relative errors of daily forecasts and mean absolute error MAE and mean absolute percentage error MAPE as a whole, as well as the coefficients of determination R2.
Table. 2 shows the same data (excluding coefficients of determination) for the case fatality rates I(TC) and I(CC), as well as the progress indicator IP
As can be see according to these tables, the forecast accuracy assessments of the main indicators of the outbreak are self-explanatory.
The degree of correspondence between the estimated (forecast) and actual data can be assessed using the diagrams, as presented in Fig. 3–15.
Fig. 3–6 indicate as follows:
– actual trajectories of the main indicators of the coronavirus outbreak in Germany until May 24, 2020 inclusive;
– calculated trajectory of these indicators with 10-day forecast (May 16–25, 2020);
– confidence intervals limits (ranges of possible deviations of the 10-day point forecast with a significance level of p=0.01).
Graphs Fig. 7 and 8 are analogues of the diagrams of Fig. 3 and 4 with long-term calculated trajectories of the cumulative reported cases and fatality cases. According to degree of compliance of the calculated data with the actual data, a high accuracy of long-term forecast and final values of the forecasted indicators, as indicated on the diagrams, can be expected.
The graphs in Fig. 9–12 reflect as follows:
– actual trajectories of the indicators’ daily changes of the outbreak in Germany;
– calculated trajectory of these indicators throughout the entire period of observation (until May 24, 2020 inclusive);
– confidence intervals limits (p=0,3), corresponding to the 10 — day forecast (for the period of May 16–25, 2020).
Let’s note, that the daily indicators are extremely difficult objects for forecasts, because of their great variability, due to the complexity of the forecasted processes. This explains the wide confidence intervals of the forecasts of these indicators, and a relatively high probability of error of the forecasts.
It can be seen from the graphs that the model trends in the values of these indicators reflect the trends, which, as the outbreak develops, fluctuate less and less around trends and getting closer to them.
Fig.13–15 reflect the following parameters of the coronavirus outbreak in Germany:
- actual trajectory of the fatality rates I(TC) and I(CC) and IP progress indicator for the entire observed period;
- calculated trajectories of the indicators for the same period.
It follows from table 2 and graphs fig.13–15 that the accuracy of the approximation and forecasting the fatality rates and the progress indicator is also very high.
Comment.
As is typical for forecasts, developed using models, whose identification is based on a series of statistical observations, such forecasts characterize the development of the outbreak in accordance with the trends as recorded in the statistical data. It follows that these forecasts are largely influenced by the methods of collecting and processing statistical data and, therefore, also reflect the features of the outbreaks’ statistical monitoring system in any given country.
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Source of statistics:
https://www.worldometers.info/coronavirus/#countries
Our publications:
https://www.facebook.com/MATHMODELCOVID19
https://t.me/mathmodelcovid19
Our initiative group and mission:
https://www.facebook.com/ab.alyokhin/posts/117804769862427
Our publications on case fatality rates and indicator of progress:
https://www.facebook.com/ab.alyokhin/posts/105684827741088