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

5 min readAug 3, 2020

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

Forecast Monitor

08/03/2020. No 126.

https://www.facebook.com/ab.alyokhin/posts/168608294782074

On June 24, 2020, the German COVID-19 coronavirus outbreak forecast monitor was publishing, which contained forecasts of the main epidemic indicators for a 10 and 30-day lead-time (see https://www.facebook.com/ab.alyokhin / posts / 155352992774271). For the development of forecasts, statistical data were using for June 23, 2020 inclusive.

On July 24, 2020, another analysis of this forecast was publishing, which showed its extremely high level of accuracy in a 30-day lead period (see https://www.facebook.com/ab.alyokhin/posts/165417025101201).

Today, the actual data is available as of August 2, 2020, i.e. for a 40-day forecast period. In addition, as we will show later (see Figure 1–13), this forecast continues to demonstrate the highest accuracy.

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Germany for 40 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 on case fatality rates I (TC), I (CC) and the IP progress indicator.

In these tables, in order to reduce their size, data rows are hiding that repeat the table data from the previous analysis (see https://www.facebook.com/ab.alyokhin/posts/165417025101201).

From the data table. 1 it follows that, despite the long lead time (40 days), the error in predicting the main indicators of the epidemic remains very low:

- for the total number of infected people — 1.30%;

- for the total number of deaths — 1.20%;

- for the total number of recovered –0.82%.

The accuracy of predicting mortality rates and progress indicator is also very high (see MAPE estimates?):

- mortality rate I (TC) — 1.42%;

- mortality rate I (CC) — 1.65%;

- progress indicator — 1.98%.

These are clearly exceptionally high numbers for the 40-day lead-in period when predicting the COVID-19 coronavirus epidemic.

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, the values of all the main indicators of the epidemic deviated only slightly from the predicted ones. This indicates the stability of the trends in the development of the epidemic in Germany, despite the appearance of a weak second wave of infected, and clearly confirms the high quality of forecasting.

Diagram fig. 6 reflects the dynamics of the values of the indicator of the average absolute increase in infected. In our opinion, the dynamics of this absolute indicator, together with the dynamics of the absolute indicator of daily increments (see Fig. 7 below), characterizes the patterns of development of coronavirus epidemics much better than the notorious reproduction rate R0 (relative indicator). So beloved by analysts and forecasters of epidemics, despite serious criticism in the scientific literature against its informative and content.

We share this critical position and will continue to use the reproductive number R0 (and only its statistical analogue, the calculation method for which we have proposed) only when it is productive.

The diagrams in Fig. 7–10 characterize:

- actual trajectories of changes in the daily indicators of the coronavirus epidemic in Germany for the entire observation period, including the 30-day forecast period;

- calculated trajectories of these indicators for the same period.

Diagrams Fig. 6 and fig. 7 show how in Germany, over time, it was possible to overcome the increase in the number of infected and to achieve not only a significant decrease in the number of new (daily) infected, but a decrease in the average (over the entire period of the existence of the epidemic) values of absolute growth. Many countries, including Ukraine, are still very far from such a development of events, and these curves cannot be achieving in such classical forms.

In general, this group of diagrams clearly demonstrates that the actual values of the daily indicators of the epidemic varied around model trends, confirming the high quality of forecasts, which is largely due to the high stability of the patterns of development of the COVID-19 coronavirus epidemic in Germany.

Diagrams Fig. 11–13 reflect such 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 2, 2020 inclusive), including the 40-day forecast period;

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