A mathematical model and forecast for the coronavirus disease COVID-19 in Germany
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.N. Grabovoi, V.A, Dilenko, O.I. Laiko, Z.N. Sokolovska)
Forecast monitor
31.05.2020. No 85.
(https://www.facebook.com/ab.alyokhin/posts/146528506990053)
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. On May 25, 2020 the analysis of the forecast’s accuracy was published (https://www.facebook.com/ab.alyokhin/posts/144090053900565) considering actual data available for the period from May16 till May 24, 2020. Then the accuracy estimations have exceeded our expectations.
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 16–30, 2020. Thus, the forecasting period of the estimated forecast makes 15 days.
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.
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 COVID-19 outbreak in Germany in a week (for the period from May 25 till May 30, 2020) has not changed and remains extremely high.
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 30, 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 coronavirus outbreak in Germany;
– calculated trajectory of these indicators throughout the entire period of observation (until May 30, 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.
The high accuracy of the forecast of COVID-19 outbreak’s development in Germany for such a long period indicates the outbreak’s trends stability in this country and that these trends are accurately identified and extrapolated by the model, developed by our group.
Source of statistics:
https://www.worldometers.info/coronavirus/#countries
https://www.pravda.com.ua/cdn/covid-19/cpa/
Our publications:
https://www.facebook.com/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