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

4 min readOct 15, 2020

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

Forecast Monitor

15/10/2020. No F-235.

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

On September 13, 2020, was published a forecast of the COVID-19 epidemic development in France (https://www.facebook.com/ab.alyokhin/posts/180502150259355). As usual, the forecast included the main 10-day and auxiliary (approximate) 30-day forecasts.

After 32 days, we publish the results of another analysis of the accuracy, this time of a 32-day forecast.

Despite the fact that the coronavirus in France continues to spread at a record pace, both the 10-day (https://www.facebook.com/ab.alyokhin/posts/183268109982759) and 21-day (https: //www.facebook. com / ab.alyokhin / posts / 186217339687836), the forecast turned out to be very accurate.

Let us see how the forecast accuracy has changed after the expiration of the next 11 days period.

The results of the analysis of the 32-day forecast presented in table. 1–2 and fig. 1–11.

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 epidemic in France for a 32-day forecast period. The absolute and relative errors of daily forecasts, as well as the average absolute MAE error and the average absolute error in percent of the MAPE forecast.

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

In both tables, the dates of the forecast period that were not included in the previous survey highlighted in purple, and the data from the previous survey hidden in order to reduce the size of the tables.

The mean absolute percentage errors (MAPE estimates *) of the forecast for the main indicators of the epidemic in France are as follows:

- total number of infected people — 0.81%;

- total number of deaths — 0.83%;

- total number of recovered — 3.41%;

- number of active cases — 1.42%.

The error in predicting the most important derived indicators of the COVID-19 epidemic in France (MAPE * estimates), as shown in Table. 2 is also low:

- mortality rate I (TC) — 1.16%;

- mortality rate I (CC) — 2.06%;

- IP progress indicator — 2.92%,

As you can see, the accuracy of forecasting the main indicators of the epidemic is somewhat reduced, but still remains very high for such a long forecast in the context of the dynamically and dramatically developing epidemiological situation in France.

The graphs (see Figure 1–11) show who is the troublemaker and the main cause of forecast error.

In fig. 1–4 are given:

- actual trajectories of the main indicators of the COVID-19 epidemic in France for the entire observation period;

- calculated trajectories of these indicators for the same period;

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

Diagrams Fig. 5–8 reflect:

- actual trajectories of changes in the daily indicators of the COVID-19 epidemic in France over the entire observation period;

- calculated trajectories of these indicators for the same period;

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

Diagrams Fig. 9–11 contain the following data:

- actual trajectories of lethality indicators I (TC), I (CC) and IP progress indicator for the entire observation period;

- calculated trajectories of the indicators for the same period, as well as a 30-day forecast period;

- actual values of these indicators at the end of the pre-forecast period.

As these graphs show, for 32 days of the forecast period only the indicator of the daily increase in recovered (Fig. 7) significantly deviated from the predicted values, which led to a deviation from the forecast of the indicator of the total number of recovered (Fig. 3) and mortality index I (CC) (Fig. ten).

Other indicators behaved strictly in accordance with the forecast, which indicates the persistence of trends in the development of the COVID-19 epidemic in France throughout the entire forecasting period. The absence of effective efforts to counter the spread of coronavirus all this time and, as a consequence, a natural increase in the total number of deaths (Fig. . 2), which, moreover, slightly exceeded the forecast level.

Sources of statistical data:

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

Our materials also:

https://www.facebook.com/MATHMODELCOVID19

https://t.me/mathmodelcovid19

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)