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

(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.I. Laiko, Z.N. Sokolovska)

Forecast monitor

20.05.2020. No 76.


Today’s issue of forecast monitor is devoted to the analysis of accuracy of the 8-day forecast of the COVID-19 outbreak in Russia, which was compiled according to statistics as of May 11th, 2020, inclusive, and published on May 12th (см. https://www.facebook.com/ab.alyokhin/posts/138886377754266).

The forecast results and their degree of compliance with the statistical data are stated in tables and graphs Fig. 1–15.

Evaluation of the forecast accuracy is shown in table.1 and 2 (see Fig. 1, 2).

In table. 1 the calculated and actual values of the main indicators of coronavirus outbreak in Russia for 8-day forecast period are indicated, absolute and relative errors of daily forecasts and mean absolute error MAE and mean absolute percentage error MAPE of 8-day forecast as a whole.

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

The data contained in these tables, including error of estimates, indicate a high level of the 8-day forecast accuracy.

The following graphs are placed in the monitor in addition to the tables (see Fig.3–15).

Fig. 3–6 indicate as follows:

– actual trajectories of the main indicators of the coronavirus outbreak in Russia;

– calculated trajectory of these indicators with 8-day forecast (May12–19, 2020);

– confidence intervals limits (ranges of possible deviations of the 8-days point forecast with a significance level of p=0.01).

As can be seen from graphs, Fig. 3–6, all indicators of the outbreak are deviated upward from forecasted values, but remained within the confidence intervals. Despite relatively high accuracy of the forecast, this fact highlights the need for new forecasts which is envisaged in the rolling forecasting concept that we follow.

It also follows from these graphs, that the quality of the actual data approximation by the theoretical curves (the whole pre-forecast period) is rather high (the lowest value of determination coefficient R2 for the indicators, as presented in fig. 3–6, exceeds 0.998).

The graphs in Fig. 7–10 reflect as follows:

– actual trajectories of the indicators’ daily changes of the outbreak in Russia;

– calculated trajectory of these indicators for the entire observed period and 30-day forecast period;

– confidence intervals limits (p=0,3), corresponding to the 10- day forecast (for the period of May 12–21, 2020).

Note that the daily indicators because of their great variability, due to the complexity of the predictable processes that are extremely difficult to predict future object. This explains the wide confidence intervals of the forecasts of these indicators and a relatively high probability of error of the forecasts.

As can be seen, the actual values of the daily indicators remained within the confidence intervals, although deviated from the model trend.

Fig.11–13 reflect the following parameters of the coronavirus outbreak in Russia:

– actual trajectory of the fatality rates I(TC) and I(CC) and IP progress indicator for the entire observed period (until May 19, 2020 inclusive);

– calculated trajectories of the indicators of the same period.

It follows from the graphs as above mentioned, the accuracy of reproduction by the model of the actual values of case fatality rates and indicator of progress, as well as the forecast accuracy of these indicators are very high.

Based on the results of the forecast accuracy assessment as of May 11, 2020 for 8-day forecast period (May 19–20, 2020), the deviations from the calculated actual data as observed, it can be concluded that the epidemiological situation in Russia within 8-day forecast period has deteriorated slightly but remained within the margin of error. Nevertheless, there is every reason for the new forecast calculations in order to take account of changes in trends in of the COVID-19 outbreak in Russia, and to clarify the short-term forecast.


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