A mathematical model and forecast for the coronavirus disease COVID-19 in Germany
(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)
Forecast Monitor
06/22/2020. No 101.
https://www.facebook.com/ab.alyokhin/posts/154698732839697
Today’s release of the prognostic monitor is devoted to the analysis of the accuracy of the 37-day forecast of the development of the epidemic of the coronavirus COVID-19 in Germany, which was compiled from statistical data until May 15, 2020 inclusive with a forecast horizon of 10 and 30 days and published on May 16 (see https://www.facebook.com/ab.alyokhin/posts/140481370928100).
After 24 days, we analyzed the accuracy of this forecast, the results of which were published on June 9, 2020 (see https://www.facebook.com/ab.alyokhin/posts/150015603308010) and demonstrated the highest accuracy in predicting the development of the coronavirus epidemic in this country.
Recently, after Germany entered the quarantine weakening phase, which was first felt by the coronavirus COVID-19, and then by the people of Germany, the epidemic development trends in this country began to change. This served as a signal for revising the forecast and, as it has already entered our traditions, for a final analysis of its accuracy. As will be shown below, neither Germany nor our forecast failed us, demonstrating unprecedentedly high accuracy for a lead time of 37 days.
The results of forecast calculations and the degree of their compliance with statistical data characterize the tables and graphs of Fig. 1–12.
Estimates of the accuracy of the forecast are given in Tables 1 and 2 (Fig. 1, 2).
Table Figure 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Germany for the entire observation period, including the 37-day forecast period, the absolute and relative errors of daily forecasts, as well as the average absolute error of MAE, the average absolute error in percent of MAPE of the 37-day forecast as a whole, as well as cumulative total (MAPE * estimates). The last indicator allows you to see the dynamics of forecast accuracy with an increasing lead time.
Table Figure 2 shows the same data for the mortality rates I (TC), I (CC) and the IP progress indicator.
The data contained in these tables, including error estimates, indicate an extremely high level of forecast accuracy for such a long (37-day) forecast period.
In fig. 3–5 are indicated:
- actual trajectories of the main indicators of the coronavirus epidemic in Germany for the entire observation period, including a 37-day forecast period;
- calculated trajectories of these indicators;
- boundaries of confidence intervals (ranges of possible deviations of the point 10-day forecast (for the period from May 16 to May 25) with a significance level of p = 0.01).
As follows from the graphs of Fig. 3–5, all the main indicators of the epidemic slightly or practically did not deviate from the forecast values, which indicate a high stability of the epidemic development trend in this country over a long period and a high level of forecast accuracy.
The diagrams in fig. 6–9 reflect:
- actual trajectories of changes in daily indicators of the coronavirus epidemic in Germany throughout the entire observation period, including a 37-day forecast period;
- calculated trajectories of these indicators for the same period;
- boundaries of confidence intervals (p = 0.3) corresponding to the forecast for 10 days (for the period from May 16 to May 25, 2020).
As usual, we emphasize that daily indicators, due to their significant variability due to the complexity of the predicted processes, are the most 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.
As you can see, the actual values of daily indicators with a large margin remained within confidence intervals and fluctuated around model trends.
Diagrams fig. 10–12 reflect the parameters of the coronavirus epidemic in Germany, such as:
- actual trajectories of the mortality rates I (TC) and I (CC) and the IP progress indicator for the entire observation period, including a 37-day forecast period;
- calculated trajectories of these indicators for the same period.
From the graphs of Fig. 10–12 it follows that the accuracy of the model reproducing the actual values of mortality and the progress indicator, as well as the accuracy of the forecast of these indicators are also extremely high.
We also draw attention to the fact that Germany’s entry into the quarantine weakening phase, which was immediately followed by an increase in the spread of infection, was the only reason for a slight decrease in the forecast accuracy (see Fig. 3 and Fig. 6, which show how the actual period begins to move upward relative to the calculated trajectory). This is a classic example of a change in the mechanism (patterns) of the functioning of the system, to which the epidemic undoubtedly refers as an integral object, which indicates the need to make changes to the model and update forecast calculations.
We also note that the accuracy of forecasting other indicators of the epidemic has not been affected. This is a consequence of large time lags between the processes of infection, on the one hand, and the processes of formation of flows of convalescent and deceased, on the other hand. The response in the total number of people who recovered and died from the increased spread of coronavirus due to the weakening of quarantine will appear much later and, in the case of our forecast, goes beyond the planning horizon. However, we will certainly see this response in the new forecast for the development of the coronavirus epidemic in Germany, which is currently being prepared.
In general, based on the results of assessing the accuracy of the forecast from May 16, 2020 to the 37-day lead-time (May 16 — June 21, 2020), the observed deviations of the actual data from the calculated ones, we can conclude that the epidemiological situation in Germany is stable and predictable developed for a long time (a); a mathematical model for the development of the coronavirus epidemic accurately identified and extrapolated patterns that existed at the time of the forecast for a long time (b); In recent weeks, there has been a process of changing trends in the development of the epidemic in connection with the weakening of the quarantine regime ©, which indicates the feasibility of new forecast calculations taking into account these changes.
In conclusion, we note that the media, including foreign ones, including the USA, have repeatedly expressed complaints about the quality of forecasting the epidemics of the coronavirus COVID-19, as well as expressed doubts about the possibility of high-precision forecasting of the epidemic. It must be admitted that many forecast developers in different countries of the world provide good reasons for such judgments. With our forecasts, we try to refute this point of view, proving that problems should be sought in the used forecasting tools, its methodology and technique, in the experience and intuition of forecast developers, their desire to improve their professional level and quality of forecasts, rather than using a hot topic and forecasts their PR and PR of their organizations.
Sources of statistics:
https://www.worldometers.info/coronavirus/#countries
Our materials also:
https://www.facebook.com/MATHMODELCOVID19
Publications on Mortality and Progress Indicators
https://www.facebook.com/ab.alyokhin/posts/105684827741088