A mathematical model and forecast for the coronavirus disease COVID-19 in Ukraine (M1)
(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)
25/09/2020. No F-204
Yesterday, the 7-day forecast period of the coronavirus epidemic COVID-19 development, using the M1 model in Ukraine, according to statistical data, inclusive September 17 for the period from September 18 to September 27, and published by us on September 17, 2020, expired. (see https://www.facebook.com/ab.alyokhin/posts/181624583480445).
The results of evaluating the forecast accuracy are presenting in table. 1–2 and Fig. 1–11.
Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Ukraine for the 7-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, including the same estimate of MAPE * growing the result, the forecast as a whole.
Table 2 shows the same data for case fatality rates I (TC), I (CC) and the IP progress indicator.
The average absolute percentage errors (MAPE * estimates) for the main indicators of the coronavirus epidemic in Ukraine are at the following level:
- total number of infected — 0.25%;
- total number of deaths — 1.70%;
- total number of recovered — 1.14%;
- number of active cases — 1.11%.
The errors in forecasting the most important derived indicators of the coronavirus epidemic in Ukraine (MAPE * estimates) are as shown in Table. 2:
- mortality rate I (TC) — 1.56%;
- mortality rate I (CC) — 2.62%;
- IP progress indicator — 1.10%,
Visually, the degree of correspondence between statistical and forecast data is showing in Fig. 1–11.
In Fig. 1–4 indicate:
- actual trajectories of the main indicators of the coronavirus epidemic in Ukraine;
- calculated trajectories of these indicators for the same period, as well as for a lead-time period of 10 days;
- boundaries of confidence intervals (ranges of possible deviations of a point forecast with a significance level of p = 0.01).
In Fig. 1 the boundaries of the confidence interval are hidden due to their imposition on the main graphs.
The past week did not show record values of the increase in the number of deaths, in contrast to the pre-forecast period, and therefore the forecast for this indicator turned out to be more pessimistic (Fig. 2). At the same time, Ukraine has shown record high rates of growth in the number of recovered, and therefore slightly deviated from the forecast trajectory and the value of this indicator (Fig. 3). After it, (automatically) the same thing happened with the number of active cases (Fig. 4), which also turned out to be more optimistic than the forecast.
The diagrams in Fig. 5–8 are reflecting:
- actual trajectories of changes in the daily indicators of the coronavirus epidemic in Ukraine over the entire observation period;
- calculated trajectories of these indicators for the entire observation period, as well as for a 10-day forecast period;
- boundaries of the confidence intervals of the 10-day forecast (p = 0.3).
Daily indicators confirm the above circumstance, namely: a decrease in daily increments in the number of deaths (Fig. 6) and the number of active cases (Fig. 8). In this case, the variation of the values of all daily indicators was carried out within the confidence intervals around or near the model trends.
Diagrams Fig. 9–11 reflect:
- actual trajectories of lethality indicators I (TC) and I (CC), as well as the IP progress indicator for the entire observation period;
- calculated trajectories of these indicators for the entire observation period, as well as for a forecasting period of 30 days.
These diagrams indicate a high level of correspondence of the forecast of the indicated synthetic data to the actual data.
In general, the epidemic of the coronavirus COVID-19 in Ukraine continues to be in an active phase, the forces of the coronavirus seem inexhaustible against the backdrop of the impotence of the authorities to stop its spread.
Sources of statistical data:
Our materials also:
Accuracy of our forecasts:
Publications on case fatality rates and progress indicator