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

5 min readJun 30, 2020

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

Forecast Monitor

06/30/2020. No 106.

https://www.facebook.com/ab.alyokhin/posts/157423242567246

On May 13, 2020, we last published the forecast for the development of the COVID-19 coronavirus epidemic in France (https://www.facebook.com/ab.alyokhin/posts/139274657715438). An analysis of the accuracy of this forecast was published on May 26-th and we were very pleased with the results of this analysis (see https://www.facebook.com/ab.alyokhin/posts/144983953811175). Unfortunately, the joy was relatively short-lived. The French Ministry of Health has made very significant adjustments to the previous statistics, which cast doubt on the advisability of further monitoring the epidemic in this country. Nevertheless, the interest in France as a country in which the epidemic of coronavirus became enormous, and the government of which was able to take control of it as a whole, prompted us to update the database of the epidemic in France and resume, at first, statistical monitoring, and today, forecasting the development of the epidemic.

The results of new forecast calculations based on updated data for the entire observation period, including data for June 29, 2020, are showing in the diagrams in Fig. 1–13. As usual, these figures provide data on 10-day and 30-day forecasts.

In the diagrams of Fig. 1- 4 are indicating:

- actual trajectories of the main indicators of the coronavirus epidemic in France;

- calculated trajectories of these indicators with a lead time of 10 days (June 30 — July 09, 2020);

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

As follows from these diagrams, the quality of approximation by theoretical curves of actual data is very high (the lowest value of the determination coefficient R2 for the indicators presented in diagrams 1–4 exceeds the level of 0.997).

Diagrams fig. 5, 6 indicate the values of the total number of infected and deceased at the end of the 30-day forecast period (180 thousand and 31 thousand, respectively).

Diagrams fig. 7–10 reflect:

- actual trajectories of changes in daily indicators of the coronavirus epidemic in France for the entire observation period;

- calculated trajectories of these indicators for the specified period, as well as for the period of the 30-day forecast;

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

Note that daily indicators, due to their significant variability due to the complexity of the forecasted processes, are an extremely difficult object to forecast. This explains both the wide confidence intervals for the forecasts of these indicators and the relatively high probability of forecast errors.

Diagrams fig. 11–13 reflect the following parameters of the coronavirus epidemic in France:

actual trajectories of mortality rates I (TC) and I (CC) for the entire observation period;
actual trajectory of the IP progress indicator for the same period;
calculated trajectories of these indicators for the entire observation period and a 30-day forecast period.

Diagrams of Fig. 11–13 are showing that the accuracy of the model reproducing the actual values of mortality rates is quite high. The theoretical trajectories of mortality indicators in turn indicate the forecast values of these indicators by the end of the forecast period. Recall that by the end of the epidemic, the mortality rates I (TC) and I (CC) coincide.

Thus, it should be expected that the mortality rate in France by the end of the 30-day forecast period will be in the range from 17.28% (Fig. 11) to 27.08% (Fig. 12) with a progress indicator of 63.67% (Fig. 13), which is a very high level compared to many other countries. In this regard, it should be noting that the mortality rate I (TC) is more inertial than the mortality rate I (CC). Therefore, it should be expecting that the actual mortality rate in France would be near the lower limit of this range.

In general, characterizing the current trends in the development of the COVID-19 coronavirus epidemic in France, it should be noting that this process has slowed significantly (at best). This is clearly seen in fig. 1 (the trajectory of the total number of infected in a classic, well-controlled epidemic is described by a regular S-curve); fig. 4 (peak formation in this diagram is violated); fig. 11 (the mortality index I (TC) tends to increase towards the end of the epidemic, but this is not observed here); fig. 13 (progress indicator in France has almost stopped growing). All this, according to our observations, is a direct result of an insufficiently well-controlled weakening of quarantine.

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)