A mathematical model and forecast for the coronavirus disease COVID-19 in Germany

6 min readAug 27, 2020

(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)

Forecast Monitor

26.08.2020. No F-156.

https://www.facebook.com/ab.alyokhin/posts/175539657422271

The latest forecast for the development of the COVID-19 coronavirus epidemic in Germany published on June 24, 2020, which included 10-day and 30-day forecasts of the main indicators of the epidemic (see https://www.facebook.com/ab.alyokhin / posts / 155352992774271). To develop this forecast, was used statistics including 23-rd June 2020.

The latest estimates of its accuracy were published on August 14, 2020 after the 51-day forecast period (https://www.facebook.com/ab.alyokhin/posts/172209791088591), which showed that this forecast retained extremely high accuracy rates …

As you know, Germany is now experiencing a second wave of the spread of the epidemic, and this, undoubtedly, could not but effect of this forecast power. Therefore, the time has come to develop a new forecast for the development of the coronavirus epidemic in Germany, and we decided to preface its presentation with a final analysis of the accuracy of the current forecast.

The data in tables 1–2 (Fig. 1–2) and the illustrations in Fig. 1 show what indicators the 63-day lead-time period stood with (Fig. 3–14). To assess the forecast accuracy, statistical data inclusive August 25, 2020 used.

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Germany for 63 days of the 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 percentage of MAPE of the forecast as a whole.

Table 2 shows the same data for case fatality rates I (TC), I (CC) and the IP progress indicator.

In these tables, in order to reduce their size, rows with data are hiding, which repeat the data of tables from the previous analysis.

From the data table. 1 it follows that, despite such a long lead time of 63 days, the error in predicting the main indicators of the epidemic as a whole is still quite low:

- for the total number of infected — 3.36%;

- for the total number of deaths — 1.46%;

- for the total number of recovered — 1.34%.

The accuracy of forecasting mortality rates and the progress indicator is also relatively high (see MAPE estimates * Table 2, Fig. 2):

- mortality rate I (TC) — 4.43%;

- mortality rate I (CC) — 2.53%;

- progress indicator — 3.22%.

The forecast accuracy indicators after 63 days from the moment of its compilation differ markedly from the forecast accuracy indicators for the 51-day lead period. This is what serves as the basis for new forecast calculations taking into account changes in the patterns of development of the coronavirus epidemic in Germany.

In fig. 3–5 are indicating:

- actual trajectories of the main indicators of the coronavirus epidemic in Germany for the entire observation period;

- calculated trajectories of these indicators for the same period.

As follows from the graphs in Fig. 3–5, only the actual trajectory values of the total number of infected indicator deviated significantly from the forecast. In Fig. 3 also shows the actual and estimated values of the total number of infected. As you can see the cost of easing quarantine turned out to be very significant — almost 30 thousand new patients. Moreover, it is obvious that some of them will not add to the number of coronavirus victims.

The high accuracy of forecasting the total number of deaths and recovered patients indicates that trends in this subsystem have practically not changed over the past two months from the date of the forecast.

Diagrams Fig. 6–7 characterize the rate of expansion of the epidemic in Germany. Both charts show signs of some intensification of the spread of the coronavirus in Germany, which allows us to speak of a second wave.

The above tendencies clearly confirmed by the diagrams shown in Fig. 8–11. They characterize:

- actual trajectories of changes in the daily indicators of the coronavirus epidemic in Germany for the entire observation period, including the 63-day forecast period;

- calculated trajectories of these indicators for the same period.

It is the daily increase of the infect number (Fig. 8) that has clear growth trend. This also led to the activation of patients’ discharge (Fig. 10), which, in turn, made it possible to stabilize the number of active cases (Fig. 11), while maintaining its compliance with the prognosis. The high accuracy of predicting the daily increase in the number of deaths (Fig. 9) is due to the inertia of the corresponding processes, to which the second wave will come only after a certain time.

Diagrams Fig. 12–14 reflect such synthetic parameters of the coronavirus epidemic in Germany as:

- actual trajectories of lethality indicators I (TC), I (CC) and the IP progress indicator for the entire observation period (up to August 25, 2020 inclusive), including the 63-day forecast period;

- calculated trajectories of the indicated indicators for the same period.

As expected, the second wave of the spread of coronavirus in Germany was responded to by the case fatality rate, calculated by the total number of infected (Fig. 12), and the progress indicator (Fig. 14), which is also directly calculated based on the total number of infected. Both of these indicators have started counting down, indicating a certain setback in the development of the epidemic in this country.

The above data eloquently testifies to the effectiveness of the second attempt at the onset of the coronavirus in Germany, due to the obviously premature and inadequate epidemiological situation with quarantine relief. The payment for these indulgences is natural and accurately quantified.

For forecasting purposes, these data serve as an indication that the model no longer properly reflects the new features of the epidemic development, should be adjusting, and forecasts updated. The results of this work will be presenting today in the next forecast monitor.

Sources of statistical data:

https://www.worldometers.info/coronavirus/#countries

Our materials also:

https://www.facebook.com/MATHMODELCOVID19

https://t.me/mathmodelcovid19

Accuracy of our forecasts:

https://www.facebook.com/ab.alyokhin/posts/154698732839697 (Germany)

https://www.facebook.com/ab.alyokhin/posts/142548897388014 (Spain)

https://www.facebook.com/ab.alyokhin/posts/150095069966730 (Italy)

https://www.facebook.com/ab.alyokhin/posts/148450556797848 (USA)

https://www.facebook.com/ab.alyokhin/posts/154364292873141 (Ukraine)

https://www.facebook.com/ab.alyokhin/posts/144983953811175 (France)