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

5 min readJul 6, 2020

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

Forecast Monitor

07/05/2020. No 109.

https://www.facebook.com/ab.alyokhin/posts/159151129061124

On June 24, 2020, we published a forecast monitor dedicated to the COVID-19 coronavirus epidemic in Germany, which contained forecasts of the main epidemic indicators for the lead time of 10 and 30 days (see https://www.facebook.com/ab.alyokhin / posts / 155352992774271). For the development of forecasts, statistical data accumulated on June 23rd, 2020 inclusive were used.

To date, there is actual data for July 4, 2020. Thus, it is possible to assess the accuracy of this forecast based on actual data for an 11-day forecast period. However, before moving on to the results of the analysis of accuracy, we recall the intrigue of this forecast.

For the first time, in addition to the main point forecast and its confidence interval, focused on extrapolating the revealed trends for the future, the previous forecast monitor was supplemented by another forecast (forecast II). This was due to the fact that, due to the second wave of the spread of infection in Germany, different strategies for government behavior were possible.

In forecast II, it was assumed that the country would take the same (or similar) measures to contain the second wave of the coronavirus epidemic that were used in the initial phase of the epidemic in this country. Such an assumption implicitly contained another assumption, the assumption that the German government would not allow further deterioration of the epidemic development trends.

Taking into account the noted circumstances, we proceed to consider the results of the forecast accuracy assessment. The results of this analysis are presented in Fig. 1–14.

As usual, fig. 1–2 contain quantitative estimates of the accuracy of the forecast.

Fig. 1 shows the calculated and actual values of the main indicators of the epidemic of the coronavirus COVID-19 in Germany for 11 days of the forecast period, the absolute and relative errors of daily forecasts, as well as the average absolute error MAE and the average absolute error in percent MAPE of the 11-day forecast as a whole.

Fig. 2 shows the same data on mortality rates I (TC), I (CC) and IP progress indicator.

The data contained in these tables, including estimates of errors, indicate an extremely high level of forecast accuracy (the forecast error of the total number of infected people is 1.30%, of the dead — 0.14%, of those who recover — 0.69%).

In fig. 3–5 are given:

- actual trajectories of the main indicators of the coronavirus epidemic in Germany for the entire observation period, including an 11-day forecasting period;

- calculated trajectories of these indicators for the same period;

- boundaries of confidence intervals (ranges of possible deviations of the point 10-day basic forecast for the period from June 24 to July 3 with a significance level of p = 0.01).

These charts graphically illustrate the high quality of the forecast.

Diagrams fig. 6, 7 reflect:

- the actual trajectories of the values of the indicators of the total number of infected and dead for the entire observation period, including an 11-day forecast period;

- the calculated trajectories of these indicators for the entire observation period, as well as the 30-day forecast period for forecast I and forecast II;

- predicted values of the total number of infected and deceased at the end of the 30-day forecast period for both forecasts.

From these diagrams, it can be seen that the German government took advantage of the accumulated earlier and relatively quickly turned the trajectory of the epidemic in its usual direction, i.e. quickly stopped the second wave of the epidemic.

Charts 8–11 reflect:

- actual trajectories of changes in daily indicators of the coronavirus epidemic in Germany for the entire observation period, including an 11-day forecast period;

- calculated trajectories of these indicators for the same period, as well as for the 30-day lead-time period (for the main forecast and forecast-II);

- boundaries of confidence intervals (p = 0.3) corresponding to a 10-day basic forecast.

As usual, we note that daily indicators, due to their significant variability due to the complexity of the predicted processes, are an extremely difficult object to forecast. This also explains the relatively wide confidence intervals for the forecasts of these indicators, and the relatively high probability of error in point forecasts.

From these diagrams it follows that the dynamics of daily epidemic indicators also indicates that Germany was able to implement a scenario close to forecast scenario II.

Diagrams fig. 12–14 reflect the following parameters of the coronavirus epidemic in Germany:

- actual trajectories of mortality rates I (TC) and I (CC) and the progress indicator IP for the entire observation period;

- calculated trajectories of these indicators for the main forecast and forecast-II for the same period, as well as for the 30-day forecasting period.

These charts confirm the estimates made on the basis of the previous tables and figures, and indicate a high accuracy of forecasting, along with the main indicators, and derived indicators of the development of the epidemic, such as mortality rates and progress indicators.

In general, an analysis of the development of the coronavirus epidemic in Germany, in addition to confirming the high accuracy of the forecasts of our working group, provides a good example of how to stop the next wave of the epidemic if the quarantine weakening phase is not entirely successful. However, this experience can only be useful to the governments of those countries that have learned the lessons of the primary curbing of the epidemic, which was presented by the same Germany.

Sources of statistics:

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

Our materials also:

https://www.facebook.com/MATHMODELCOVID19

https://t.me/mathmodelcovid19

The 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)