A mathematical model and forecast for the coronavirus disease COVID-19 in France
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, O.I. Laiko, Z.N. Sokolovska)
Forecast monitor
05/27/2020, No 83.
(https://www.facebook.com/ab.alyokhin/posts/144983953811175)
Today’s release of the forecast monitor is dedicated to the final analysis of the accuracy of the 14-day forecast for the development of the epidemic of the coronavirus COVID-19 in France, which was compiled according to statistics as of May 12 th, 2020 inclusive with a forecast horizon of 10 and 30 days and published on the May 13 th, 2020 (see https://www.facebook.com/ab.alyokhin/posts/139274657715438).
Today we planned to prepare a new forecast, however, retroactive changes began to be made to the statistics on France. This excludes the feasibility of new predictive calculations, since the calibration of our model is carried out solely on the basis of statistical series of observations. If they change, this requires a review of our database for this country and preparation of forecasts from scratch. In the framework of volunteer work, this work takes on a shade of nonsense. Therefore, we take the last opportunity to quantify the accuracy of the forecast for the development of the COVID-19 coronavirus epidemic in France by unchanged series of observations up to May 26 th, 2020 inclusive.
The results of predictive calculations and the degree of their compliance with statistical data characterize the tables and graphs in Fig. 1–15.
Estimates of the accuracy of the forecast are given in Tables 1 and 2 (Fig. 1, 2).
Table 1 shows the calculated and actual values of the main indicators of the coronavirus epidemic in France for 14-day forecast period, absolute and relative errors of daily forecasts and mean absolute error MAE and mean absolute percentage error MAPE as a whole.
Table. 2 shows the same data for the case fatality rates I(TC) and I(CC), as well as the progress indicator IP
The data contained in these tables, including estimates of error, indicate a very high level of forecast accuracy even for such a long (14-day) forecast period.
Fig. 3–6 indicate as follows:
– actual trajectories of the main indicators of the coronavirus outbreak in France;
– calculated trajectory of these indicators;
– confidence intervals limits (ranges of possible deviations of the 10-days point forecast with a significance level of p=0.01).
As can be seen from graphs Fig. 3–6, all indicators of the outbreak were slightly deviated from forecasted values, indicating the outbreak’s trends stability in this country and high quality of forecasts.
Graphs Fig. 7–8, demonstrating the calculated trajectories for the longer term along with the actual trajectories, show that a sufficiently high accuracy of both long-term forecast and forecasted final values of cumulative reported cases and deaths should be expected at such level of 14-day forecast’s accuracy.
The graphs in Fig. 9–12 reflect as follows:
– actual trajectories of the indicators’ daily changes of the outbreak in France;
– calculated trajectory of these indicators throughout the entire period of observation, including the forecast period;
– confidence intervals limits (p=0,3), corresponding to the 10 — day forecast (for the period of May 13–22, 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 France:
- actual trajectory of the fatality rates I(TC) and I(CC) and IP progress indicator for the entire observed period (until May 26, 2020 inclusive), and including 14-day forecast period;
- calculated trajectories of the indicators for this period.
It follows from the graphs fig.13–15 that the accuracy of reproduction by the model of the actual values of case fatality rates and indicator of progress as well as forecast accuracy of above stated indicators is quite high
Based on the results of the accuracy assessment for a 14-day forecast period (May 13–26, 2020) on May 12, 2020, the observed deviations of the actual data from the calculated ones, it can be concluded that the epidemiological situation in France is steadily and predictably developing towards the completion.
___
Source of statistics:
https://www.worldometers.info/coronavirus/#countries
https://www.pravda.com.ua/cdn/covid-19/cpa/
Our publications:
https://www.facebook.com/MATHMODELCOVID19
https://t.me/mathmodelcovid19
Our initiative group and mission:
https://www.facebook.com/ab.alyokhin/posts/117804769862427
Our publications on case fatality rates and indicator of progress:
https://www.facebook.com/ab.alyokhin/posts/105684827741088