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

4 min readOct 11, 2020

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

Forecast Monitor

10/10/2020. No F-227.

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

The previous 10-day forecast of the COVID-19 epidemic development in Russia, compiled according to statistical data of September 30 for the period from October 1 to October 10, published on October 1, 2020 (see https: //www.facebook.com/ab.alyokhin/posts/185406746435562).

Recall that we presented two forecasts: one made on the assumption that the current trends will continue, the other on the assumption that effective measures will take to counter the spread of coronavirus. By taking such measures, we mean not the implementation of them, but exclusively their effect, which would clearly manifested in statistical data. If the statistics do not record the effect of such measures, it does not matter whether any measures taken or not.

As a result, it turned out that the first forecast came true. The results of a quantitative analysis of its accuracy and degree of compliance with the actual data are showing in table 1–2.

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Russia for a 10-day 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, including the same estimate cumulative total (MAPE *).

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

As shown in the table. 1, the accuracy of this forecast is very high. The mean absolute percentage errors (MAPE) for the main indicators of the epidemic are at the following level:

- total number of infected people — 0.41%;

- total number of deaths — 0.89%;

- total number of recovered — 0.23%;

- number of active cases — 1.20%.

The accuracy of predicting derived indicators of the coronavirus epidemic in Russia, such as the mortality indices I (TC), I (CC) and the IP progress indicator, is also very high. The MAPE estimates for these indicators are at the following level (Table 2):

- mortality rate I (TC) — 0.48%;

- mortality rate I (CC) — 0.84%;

- IP progress indicator — 0.18%;

Graphs (Fig. 1–12) allow you to visual assess the degree to which the predicted trajectories of the main indicators of the COVID-19 epidemic in Russia correspond to the actual ones. In all diagrams, the trajectories of the actual values of indicators are red, and the forecasted values are blue.

In fig. 1–4 indicate:

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

- calculated trajectories of these indicators for the forecast period.

As follows from these diagrams, only the indicators of the total number of infected and deaths (Fig. 1–2) during the forecast period slightly deviated from the forecast trajectory. They followed by the resulting indicator of the number of active cases (Fig. 4)

The diagrams in Fig. 5–8 presented:

- actual trajectories of changes in the daily indicators of the COVID-19 epidemic in Russia over the entire observation period, including the 10-day forecast period;

- calculated trajectories of these indicators for the forecast period;

- boundaries of the confidence intervals (p = 0.05) corresponding to the forecast for 10 days (for the period from October 1 to October 10, 2020).

Fig. 5 shows an increase in the number of infected people at the upper limit of the confidence interval. Other daily measures (Fig. 6–8) showed very high levels of variability around model trends within the forecast confidence intervals.

Diagrams Fig. 9–12 reflect:

- actual trajectories of lethality indicators I (TC) and I (CC) for the entire observation period, including the 10-day forecast period;

- calculated trajectories of the specified indicators for the forecast period;

- actual trajectories of the statistical reproductive number SR0;

- calculated trajectories of the values of the same indicators for the 10-day forecast period.

The forecast of the dynamics indicators, with the exception of the reproductive number (Fig. 11), also turned out to be very accurate. Only the trajectory of this indicator temporarily deviated from the forecasted one within the lead period.

The high accuracy of the main one of the two forecasts developed a decade ago unambiguously indicates that nothing has done in Russia during this time in order to reverse the negative trends in the spread of coronavirus in the country.

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)