A mathematical model and forecast for the coronavirus disease COVID-19 in France
(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.I. Laiko, Z.N. Sokolovska)
Forecast monitor
13.05.2020. No 65.
On April 22nd, 2020, we published a forecast of the COVID-19 outbreak in France (https://www.facebook.com/ab.alyokhin/posts/130244045285166). We’ll get to the analysis of the forecast accuracy, especially because this forecast is worthy of attention. However, in today’s forecast monitor, we present updated forecasts of the coronavirus outbreak in the country, considering statistics as of May 12th, 2020
The forecast results are shown in the fig. 1–12.
Fig. 1–4 indicate as follows:
— actual trajectories of the main indicators of the coronavirus outbreak in France;
— calculated trajectory of these indicators with 10 days forecast (as of May 13–22, 2020);
— confidence intervals limit (ranges of possible deviations of the point forecast with a significance level of p=0.01).
As can be seen from these diagrams, the quality of the actual data approximation by the theoretical curves to is very high (the lowest value of determination coefficient R2, for the indicators presented in figures 1–4, exceeds 0.998).
Fig. 5 and 6 indicate the total number of infected and dead by the time the outbreak reaches the level of progress (indicator IP) at 57% (see the progress indicator in Fig. 11).
Fig. 7–10 contain the following:
— actual trajectories of the indicators’ daily changes of the outbreak in France;
— calculated trajectory of these indicators in significant part of the outbreak life cycle (from 0% to 57 %);
— confidence intervals limit (p=0,15), corresponding to 10 days 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 the high probability of error of the forecasts.
Fig. 11 and 12 reflect the following parameters of the coronavirus outbreak in France:
— actual trajectory of the fatality rates I(TC) and I(CC);
— actual trajectory of progress indicator IP;
— calculated trajectory of the case fatality rates for a part (from 0% to 57%) of the outbreak’s life cycle;
— calculated trajectory of progress indicator.
It follows from these diagrams that the accuracy of reproduction by the model of the actual values of case fatality rates and indicator of progress is quite high. Theoretical trajectories of case fatality rates, in turn, indicate the forecasted values of these indicators by the end of the forecast period. It should be reminded that by the end of the outbreak indicators of fatality I(TC) and I (CC) should match. Thus, it is to be expected that the fatality rate in France at a progress indicator of 57% will be in the range from 15.47% (Fig. 12) to 26.90% (Fig. 11), which is a very high level compared to many other countries. In this regard, it should be noted that the fatality rate I (TC) is more inertial than the fatality rate I (CC). Therefore, it should be expected that the final fatality rate in France will be close to the lower limit of this range.
In conclusion, we wish to emphasize once again that these forecasts are aimed to identify trends at the time of making forecasts and extrapolating them using a systematic model of future outbreaks. This means that when the internal mechanisms (trends) of the outbreak development are changing, the forecasts will need to be clarified after making appropriate adjustments to the parameters or structure of the model.
Source of statistics:
https://www.worldometers.info/coronavirus/#countries
Our publications:
https://www.facebook.com/MATHMODELCOVID19
Our publications on case fatality rates and indicator of progress:
https://www.facebook.com/ab.alyokhin/posts/105684827741088
https://www.facebook.com/ab.alyokhin/posts/106831140959790
https://www.facebook.com/ab.alyokhin/posts/107444734231764
Our initiative group and mission: https://www.facebook.com/ab.alyokhin/posts/117804769862427