A mathematical model and forecast for the coronavirus disease COVID-19 in Spain
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.I. Laiko, Z.N. Sokolovska)
21.05.2020. No 78.
Today’s issue of forecast monitor is devoted to the analysis of accuracy of the 16-day forecast of the COVID-19 outbreak in Spain, which was compiled according to statistics as of May 4th, 2020, inclusive, and published on May 5th (see https://www.facebook.com/ab.alyokhin/posts/135852118057692). This analysis precedes the release of a new forecast of the outbreak in Spain, which is currently under preparation.
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 Spain for 16-day forecast period are indicated, absolute and relative errors of daily forecasts and mean absolute error MAE and mean absolute percentage error MAPE of 16-day forecast.
Table.2 shows the same data for the 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 forecast accuracy forecast for such a long period.
Fig. 3–6 indicate as follows:
– actual trajectories of the main indicators of the coronavirus outbreak in Spain;
– calculated trajectory of these indicators;
– confidence intervals limits (ranges of possible deviations of the 16-days point forecast with a significance level of p=0.05).
As can be seen from graphs, Fig. 3–6, all indicators of the outbreak are slightly deviated from forecasted values, indicating the stability of the outbreak’s trends in this country.
Graphs Fig. 7–8, on which the calculated trajectories for the longer term are displayed along with the actual trajectory, indicate that slightly higher final values of the cumulative reported cases and deaths should be expected, than envisaged in the forecast.
The graphs in Fig. 9–12 reflect as follows:
– actual trajectories of the indicators’ daily changes of the outbreak in Spain;
– calculated trajectory of these indicators for the entire observed period, including the forecast period;
– confidence intervals limits (p=0,3), corresponding to the 7- day forecast (for the period of May 5–11, 2020).
Let’s note, that the daily indicators are extremely difficult objects for forecasts, because of their great variability, due to the complexity of the forecasted processes. 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 daily indicators with a margin remained within confidence intervals and fluctuated around model trends.
Fig.13–15 reflect the following parameters of the coronavirus outbreak in Spain:
- actual trajectory of the fatality rates I(TC) and I(CC) and IP progress indicator for the entire observed period (until May 20, 2020 inclusive) and the forecast period;
- calculated trajectories of the indicators.
It follows from the 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 are very high.
Based on the results of the forecast accuracy assessment of May 5, 2020 for 16-day pre-emption period (May 5–20, 2020), deviations from the calculated actual data as observed, it can be concluded that the epidemiological situation in Spain is developing predictably and stably towards completion. Nevertheless, this doesn’t preclude updating the forecasts in order to improve their accuracy, as well as to increase the forecasting horizon.
Source of statistics:
Our initiative group and mission:
Our publications on case fatality rates and indicator of progress: