A mathematical model and forecast for the coronavirus disease COVID-19 in Ukraine
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.I. Laiko, Z.N. Sokolovska)
Математическая модель и прогноз эпидемии коронавируса COVID-19 в Украине
18.05.2020. No 73.
This issue of the forecast monitor provides the final analysis of 10-day forecast accuracy of COVID-19 outbreak in Ukraine, which was prepared and published on May 8th, 2020
Now there is the possibility to assess the forecast accuracy for the period from May9th till May 18th, 2020 on the actual data reported for the entire period as specified.
The forecast results and their compliance with the statistical data are shown in Fig. 1–15.
The estimates of forecasts accuracy are shown in table.1 and table. 2 (see Fig. 1, 2).
In the table of Fig. 1, there are calculated and actual values of the main indicators of coronavirus outbreak in Ukraine for the entire forecast period, absolute and relative errors of daily forecasts and mean absolute error MAE and mean absolute percentage error MAPE of the forecast as a whole.
In table. 2 the same data are shown but relative to the case fatality rates I(TC) and I (CC), as well as the progress indicator IP.
The data, contained in these tables, including the errors estimates, confirm a relatively high level of accuracy of 10-day forecast.
In addition to these tables, there’re the following graphs (see Fig. 3–15).
Fig. 3–6 show:
– actual trajectories of the main indicators of the coronavirus outbreak in Ukraine;
— calculated trajectory of these indicators with 10 — day forecast (May 9–18, 2020);
— confidence intervals limit (ranges of possible deviations of the point forecast with a significance level of p=0,15).
Fig. 3–6 provide a visual representation of the degree of correspondence between the estimated and actual data. We would like to note again that the forecast of the cumulative reported recovered (Recovered), starting from the May 10th,2020, turned out to be slightly more optimistic. As can be seen from Fig. 5, the value of this indicator deviated from the forecasted level on this day, following parallel the calculated trajectory almost all the time. Only at the end of the forecast period the situation has deteriorated somewhat. The same trend, far from encouraging, is observed in the trend of the cumulative reported deaths (Fig. 4) in recent days.
It also follows from these graphs, the quality of the actual data approximation by the theoretical curves (all pre-forecast period) is very high (the lowest value of determination coefficient R2, for the indicators as presented in Fig. 1–4, exceeds 0.998).
The Fig. 7, 8 indicate the cumulative reported cases and death by the time the outbreak in Ukraine reaches the level of progress (indicator IP) in 63% (see the progress indicator in Fig. 13).
Fig. 9–12 contain the following:
– actual trajectories of indicators’ daily changes of the coronavirus outbreak in Ukraine;
– calculated trajectory of these indicators in significant part of the outbreak’s life cycle (from 0% to 63 %);
– confidence intervals limit (p=0,3), corresponding to 10 — day forecast (for the period of May 9–18, 2020).
Let’s note that the daily indicators are extremely difficult object for the forecasting, because of their great variability due to the complexity of the forecasted processes. This explains both the wide confidence intervals for the forecasts of these indicators and the relatively high probability of forecast errors.
However, as can be seen, none of the indicators have passed the confidence intervals limit, reflecting that the model correctly fixed the trends in Ukraine during the pre-forecast period.
Fig. 13–15 show the following parameters of the coronavirus outbreak in Ukraine:
- actual trajectories of case fatality rates I (TC) and I (CC) and progress indicator to IP for the entire observation period;
- calculated trajectory of these indicators over the same period.
It follows from these graphs that 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 is also relatively high.
Based on the results of the forecast accuracy assessment as of May 8th, 2020 for the entire 10-day pre-emption period, the observed deviations of the actual data from the calculated ones, it can be concluded that the patterns of the COVID-19 outbreak in Ukraine undergo minor changes for the worse (see figure. 4, 5, 6, 8, 10, 11, 12, 15) in recent days.