A mathematical model and forecast for the coronavirus disease COVID-19 in Russia
(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)
22.08.2020. No F-151.
The latest forecast for the development of the COVID-19 coronavirus epidemic in Russia, compiled according to statistical data as of August 11, published on August 12, 2020 (see https://www.facebook.com/ab.alyokhin/posts / 171642154478688). The forecast based on Worldometers data (https://www.worldometers.info/coronavirus/#countries).
The results of a quantitative analysis of the accuracy of the forecast development of the COVID-19 coronavirus epidemic in Russia from August 12, 2020 and degree of its compliance with the actual data are shown in Fig. 1–2.
Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Russia for the 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 (Fig. 1), the forecast accuracy is extremely high. Mean absolute percentage errors (MAPE) for the main indicators of the epidemic are at the following level:
- total number of infected people — 0.13%;
- total number of deaths — 0.56%;
- total number of recovered — 0.35%;
- number of active cases — 0.80%.
The accuracy of forecasting derived indicators of the coronavirus epidemic in Russia, such as mortality indices I (TC), I (CC), and the IP progress indicator (Table 2, Fig. 2), is also high. The MAPE estimates for these metrics are as follows
- mortality rate I (TC) — 0.69%;
- mortality rate I (CC) — 0.89%;
- IP progress indicator — 0.20%;
Graphic materials (Fig. 3–14) allow you to visual assess the degree to which the forecasted trajectories of the main indicators of the COVID-19 coronavirus epidemic in Russia correspond to the actual ones. In all diagrams, the trajectories of the actual values of indicators are indicated in red, and the forecasted values are in blue.
In fig. 3–6 indicate:
- actual trajectories of the main indicators of the coronavirus epidemic in Russia for the entire observation period (red color of the graphs);
- calculated trajectories of these indicators for the forecast period (blue);
- boundaries of the confidence intervals (ranges of possible deviations of the point 10-day forecast (for the period from 12 to 21 August) with a significance level of p = 0.05).
As follows from the graphs in Fig. 3–6, as well as all subsequent charts presented, the values of the main indicators of the epidemic deviated slightly from the forecast. This indicates a high stability of the trends in the development of the epidemic in Russia and visually confirms the high quality of the forecast.
The diagrams in Fig. 7–10 characterize:
- actual trajectories of changes in the daily indicators of the coronavirus 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 12 to 21 August 2020).
As you can see, the actual values of daily indicators, despite their high variability, did not go beyond the confidence intervals; they consolidate the downward trend for the indicators of the daily increase in the number of infected, died and recovered and stabilize the number of active patients.
Unusually low level of variability in the growth rate of new infections (Fig. 7) persists, which, as we noted earlier, is uncharacteristic of coronavirus epidemics in other countries and may indicate a strict moderation of the corresponding statistics.
Diagrams Fig. 11–14 reflect the following parameters of the coronavirus epidemic in Russia:
- actual trajectories of mortality rates 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, which characterizes the growth potential of the epidemic (at a value of this indicator less than one, the epidemic begins to fade and eventually ends; the less one reproductive number, the faster the rate of attenuation of the epidemic), as well as the IP progress indicator for the entire period observations;
- calculated trajectories of the values of the same indicators for the 10-day forecast period.
The mortality rate in Russia is still very low (Fig. 11–12) and is explain, most likely, by the peculiarities of the statistical recording of deaths in the Russian Federation.
The level of the statistical reproductive number SR0 (Fig. 13) over the forecast period is at a level slightly below 1.00, which indicates a very slow decrease in the spread of coronavirus (this is clearly seen in the diagram in Fig. 1). Since the growth of new infections is still very high (Fig. 7), and the growth of those who recovered only slightly exceeds them (Fig. 9), the IP progress indicator slowly continues its extensive upward movement (Fig. 14), promising a protracted nature of the coronavirus epidemic in Russia.
In general, the tabular and graphical data provided indicate that the COVID-19 coronavirus epidemic in Russia continues to remain in a well-predictable course, the coronavirus is still showing high activity, and there are no signs of a qualitative change in the epidemic’s trends.
Sources of statistical data:
Our materials also:
Accuracy of our forecasts:
Publications on case fatality rates and progress indicator