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

7 min readJun 24, 2020

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

Forecast Monitor

06/24/2020. No 102.

https://www.facebook.com/ab.alyokhin/posts/155352992774271

On May 16, 2020, we published a prognostic 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 / 140481370928100). For the development of forecasts, statistical data accumulated on May 15, 2020 inclusive were using.

On June 9th and 22nd, the results of the penultimate and final analyzes of this forecast were published (see https://www.facebook.com/ab.alyokhin/posts/150015603308010 and https://www.facebook.com/ab. alyokhin / posts / 154698732839697) for 24- and 37-day forecast periods, which have demonstrated extremely high accuracy in predicting all the main indicators of the epidemic.

As we have repeatedly noted in our statistical monitors, as well as in the analytical forecast monitors mentioned above, Germany, like many other countries, experiences certain difficulties with the implementation of the quarantine-weakening regime. This indicates that the coronavirus epidemic in Germany as a system is in a transitional mode, which is characterizing by changes in the patterns of processes occurring in the system, requiring their consideration in the model and updating forecasts.

However, before proceeding to the description of new forecast calculations performed taking into account the data accumulated to date, i.e. as of June 23, 2020, we present tables with estimates of the accuracy of the previous forecast, taking into account, the actual values for the forecast period with a lead-time of 39 days (see Fig. 1 and Fig. 2). This is all the more pleasant because it is difficult to expect the same high accuracy in predicting the development of the epidemic in Germany in the future, given the transitional nature of the epidemic development process.

From the data in these tables, we can see despite the emergence of new trends, the forecast accuracy of the main indicators of the coronavirus epidemic in Germany throughout the entire forecast period remained extremely high and reached the following level on the 39th forecast day: 2.37% for the total number of infected; 0.41% — for the total number of deaths; 0.62% — for the total number of recovered.

Such information gives confidence in the strength of the forecast designer in our abilities. Therefore, we will go on to characterize the main parameters (actual and estimated) of the COVID-19 coronavirus epidemic in Germany for the next 10 and 30 days, starting from June 24, 2020 (see 3- 15).

In fig. 3–6 are given:

- 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 well as for a 10-day forecasting 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).

All subsequent diagrams in this release are different from similar diagrams of previous forecast monitors.

In addition to the main point forecast and its confidence interval, the diagrams show the results of another forecast (forecast-II), made under certain assumptions. This is because of different strategies for government behavior are possible due to the second wave of the spread of infection in Germany. In this regard, before proceeding to the description of the assumption underlying the development of forecast II, we will point out a number of methodological provisions that we adhere to when conducting scenario calculations.

Methodological notes.

We clearly distinguish between forecasting itself and scenario calculations as one of the types of forecasting in the general sense of the goals and objectives, as well as the tools used.

Actually forecasting in a strictly scientific sense is focuses on point (single-valued) forecasts with corresponding confidence intervals and allows a complete quantitative assessment of the accuracy of forecasts according to generally accepted accuracy criteria.

Scenario calculations are a type of computer analysis of the properties of the model and are aimed at studying the consequences of the implementation of various epidemic development scenarios. The effectiveness of the scenario approach depends on the quality of the scenarios, the key to the development of which is close cooperation with professional representatives of the customer of scenario forecasts.

An unambiguous scientifically based quantitative assessment of the accuracy of scenario forecasts is usually complicated and, from the point of view of the goals and objectives of such calculations, is often not necessary.

These circumstances (especially the three of those listed above) formed the basis for the choice of our group of high-precision forecasting strategies with confidence intervals.

The nature of the development of the coronavirus epidemic in Germany makes us take a cautious step from our main position towards scenario forecasting.

Therefore, taking into account these remarks, a forecast for the development of the coronavirus epidemic in Germany, the following scenario was using as a representative scenario. Prediction II suggests that the same (or similar) measures will be taking to contain the second wave of the coronavirus epidemic, which were using in the initial phase of the epidemic in this country. (As you can see, there are no exaggerations in such an assumption.) As a result, any deviations from this strategy, i.e. the implementation of softer approaches will lead to scenarios that fit into the framework indicated by the main forecast and forecast-II. The second assumption is implicit here — the German government will not allow further deterioration of trends.

At the same time, there is reason to believe that the German government will not resort to such radical measures again, since both the population and the country’s economy are experiencing a certain “fatigue” from such measures. The consequences of any intermediate strategies by the end of the 30-day forecast period can be expecting to fit into the framework indicated in Fig. 7, 8.

We note in connection with the figures given in these diagrams that the insignificant difference in the number of deaths (insignificant for the soulless statistics, but not for the relatives of the deceased) of the two forecasts is due to the extremely long time lag between the moment of infection (registration of the disease) and the lethal outcome. On the 30-day forecast period, the remote effect of the growth in the number of infected people is not yet manifesting.

Charts 9–12 reflect:

actual trajectories of changes in daily indicators of the coronavirus epidemic in Germany for the entire observation 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 predict. This also explains the relatively wide confidence intervals for the forecasts of these indicators, and the relatively high probability of error in point forecasts.

As follows from these diagrams, here the range of possible scenarios is very large.

Diagrams fig. 13–15 reflect the following parameters of the coronavirus epidemic in Germany:

- actual trajectories of mortality rates I (TC) and I (CC) and IP progress indicator 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.

As usual, our forecasts are basing on high-quality approximation of statistical data by the model, which graphs in Fig. 1–4. The approximation accuracy (values of the determination coefficients) in our calculations never fall below the level of 0.99.

From the above charts characterizing the parameters of the two forecast options, it can be concluded that the epidemiological situation in Germany, if not taken emergency effective measures, can significantly deteriorate in the near future, which will manifest itself in a significant increase in the number of infected, dead and active (current) patients.

The choice, which is typical for the development of the epidemic of the coronavirus COVID-19, remains with the government and citizens of this country.

These findings are more than relevant for the government and for the citizens of our country.

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)