A mathematical model and forecast for the coronavirus disease COVID-19 in France

5 min readJul 10, 2020

(A.B. Alyokhin, B.V. Burkynskyi, A.N. Grabovoi, V.A, Dilenko, N.I. Khumarova)

Forecast Monitor

07/10/2020. No 112.

https://www.facebook.com/ab.alyokhin/posts/160856195557284

On June 30, 2020, we published the next predictive monitor (see https://www.facebook.com/ab.alyokhin/posts/157423242567246) dedicated to the COVID-19 coronavirus epidemic in France, the statistics of which have repeatedly presented surprises, associated with significant (fatal in scale for forecasting) changes in indicators for the past period. At the same time, interest in this country and in the development of the epidemic of the coronavirus COVID-19 in France never left us. In this regard, we went to the loss of time associated with updating databases and developing new forecasts.

As usual, our forecast includes the main 10-day and auxiliary (approximate) 30-day forecasts. Today we have statistics on the basic forecast and can evaluate its accuracy. However, this time, such an opportunity almost eluded us. For three days, within the 10-day forecast period, France did not provide statistics to international organizations and systems for monitoring the spread of the coronavirus epidemic. Fortunately, a few days ago, this gap was filled, and we were fully rewarded with one of the highest estimates of forecast accuracy for the entire more than 3-month period of practical forecasting of coronavirus epidemics.

The results of the analysis of this forecast are presenting in Fig. 1–15.

Fig. 1, 2 contain, as is customary in our predictive analytical monitors, quantitative estimates of the accuracy of the forecast.

Figure 1. shows the calculated and actual values of the main indicators of the epidemic in France over the past 10 days of the main 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.

Figure 2. shows the same data on mortality rates I (TC), I (CC) and IP progress indicator.

As can be seen from the data in these tables, the error level of all the main indicators of the coronavirus epidemic is extremely low. Therefore, the forecast error of the total number of infected people is 0.16%, the dead — 0.54%, recovered — 0.12%, active cases — 0.77%.

In fig. 3–6 are given:

- actual trajectories of the main indicators of the coronavirus epidemic in France for the entire observation period, including the main 10-day forecast period;

- calculated trajectories of these indicators for the same period;

- boundaries of confidence intervals (ranges of possible deviations of the point 10-day forecast with a significance level of p = 0.01).

These diagrams, as well as all subsequent ones, allow you to visualize quantitative estimates of accuracy of forecasts contained in the table. 1 and table 2, and to demonstrate the exceptional forecasting accuracy.

Diagrams Fig. 7, 8 are analogues of the diagrams in Fig. 3, 4 and, in contrast to them, contain forecast values of the corresponding indicators for an estimated 30-day forecast period. The almost complete coincidence of the actual and calculated trajectories during the 10-day forecast period allows us to hope that the predicted values of the total number of infected and deceased at the end of the 30-day lead-time given in these diagrams will slightly differ from the actual ones.

Diagrams Fig. 9–12 reflect:

- actual trajectories of changes in the daily indicators of the coronavirus epidemic in France for the entire observation period, including a 10-day forecast period;

- calculated trajectories of these indicators for the same period, as well as for the 30-day lead-time period;

- boundaries of confidence intervals (p = 0.3) corresponding to a 10-day basic forecast.

Despite the fact that the daily epidemic indicators are usually characterized by extremely high variability and are a difficult object to predict, these charts show that the model trends of these indicators extremely accurately revealed and predicted the main trends of their change.

The foregoing fully relates to the accuracy of forecasting mortality rates in France and an indicator of progress in the development of the epidemic in that country (see diagrams Fig. 13–15). Given the patterns of change in these mortality rates, it can be expecting that by the end of the 30-day forecast period, the mortality rate in France will range from 17.24% (Fig. 13) to 27.28% (Fig. 14), and this will correspond to a progress level of 64.20% (Fig. 15).

The indicators, however, are shocking, although they cannot be directly (without additional research) comparing with similar indicators of other countries due to possible differences in national methods for determining the number of deaths.

In general, analyzing the above diagrams, it should be noted that the COVID-19 coronavirus epidemic in France is moving very slowly towards its final, is under control (this country has so far managed to avoid significant outbreaks of the epidemic in the quarantine weakening phase), which is one of the key factors for good predictability of ongoing epidemiological processes. Even the drastic updates of the statistics did not have a significant impact on the predictability of the epidemic in France and the accuracy of our forecasts both before and after the statistical shocks. This may serve in favor of the quality of statistics in this country.

Nevertheless, the delayed development of the COVID-19 coronavirus epidemic in time, as the diagrams demonstrate, inevitably results in the growth of new infections and deaths for the country. We do not doubt that in the minds of the relatives of the victims, but in fact, people who could not (did not want to) protect the state, all these cunning strategies for managing epidemics will not be justified.

Sources of statistics:

https://www.worldometers.info/coronavirus/#countries

Our materials also:

https://www.facebook.com/MATHMODELCOVID19

https://t.me/mathmodelcovid19

The accuracy of our forecasts:

https://www.facebook.com/ab.alyokhin/posts/154698732839697 (Germany)

https://www.facebook.com/ab.alyokhin/posts/142548897388014 (Spain)

https://www.facebook.com/ab.alyokhin/posts/150095069966730 (Italy)

https://www.facebook.com/ab.alyokhin/posts/148450556797848 (USA)

https://www.facebook.com/ab.alyokhin/posts/154364292873141 (Ukraine)

https://www.facebook.com/ab.alyokhin/posts/144983953811175 (France)