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

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

Forecast Monitor

10/11/2020. No F-258.

https://www.facebook.com/ab.alyokhin/posts/196744245301812

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

After 10, 21 and 32 days, we published the results of the analysis of the accuracy of this forecast:

https://www.facebook.com/ab.alyokhin/posts/183268109982759

https://www.facebook.com/ab.alyokhin/posts/186217339687836

https://www.facebook.com/ab.alyokhin/posts/189237982719105.

In our last assessment monitor, we concluded that over the 32 days forecast period, only the daily growth rate of the recovered significantly deviated from the forecast values, which entailed a deviation from the forecast of the total number of recovered people and the mortality index I (CC). The other indicators behaved strictly in accordance with the forecast, which indicated that the trends in the development of the COVID-19 epidemic in France continued throughout the 32-day forecast period, the lack of efforts to counter the spread of coronavirus and, as a result, a natural increase in the total number of deaths.

Today 58 days have passed since the forecast made. It is obvious that it could not maintain its relevance for such a long time. At the same time, comparing the current epidemiological situation in France with even outdated forecast calculations is important to understand how the COVID-19 epidemic is developing in this country. In this case, the forecast acts as a starting point.

Let us show this using the diagrams in Fig. A, fig. B and fig. 1–11.

Fig. A shows the forecasts trajectories the relative errors of the main cumulative indicators of the epidemic by days of the forecast perspective. The diagram clearly shows that for more than a month the accuracy of the forecast of all indicators remained very high. However, on the 33rd day of the forecast period, errors of the total number of infected and active cases began to grow rapidly. Rapid, although not so rapid, growth also demonstrated by errors in forecasting the total number of deaths and recovered.

Fig. B, shows the statistical reproductive number dynamics, which has the meaning of the growth rate of daily increase indicator of infected, shows that it was during this period (the first ten days of October 2020) that the rate of infection spread significantly accelerated.

Graphs fig. 1–11 show how this affected the main indicators of the COVID-19 epidemic in France.

Fig. 1–4 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 the IP progress indicator for the entire observation period;

- calculated trajectories of the indicated 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.

Fig. 1 and fig. 2 demonstrates the extra cost for the French disregard for the spread of infection. Exceeding the forecast for the number of infected on November 9 is more than half a million people (just think about these numbers), and in terms of the number of deaths, more than 6 thousand people. Moreover, this despite the fact that the forecasted trajectories themselves were increasing.

Diagrams Fig. 5–8, demonstrating how events unfolded in France in a daily context, turned the catastrophic first wave of the epidemic into a slight excitement on the surface of a quiet pond.

Synthetic indicators (Fig. 9–11), which are mortality rates and an indicator of progress, reacted little to the above-mentioned cataclysms due to the preservation of proportions between the basic indicators of the epidemic. In the development of the epidemic in France, now, therefore, absolute indicators set the tone. It is the increase in the number of infected that gives rise to a corresponding increase in the number of deaths, recovered and the number of active patients, which, in turn, determines the number of hospitalized people and the overall load on the medical system.

These circumstances are extremely important for understanding the development of the COVID-19 epidemic in Ukraine. In our country, there is an equally frivolous attitude towards curbing the spread of coronavirus, the possibility of providing medical assistance to sick people is incomparably less than in France, there is a tendency for an increase in the mortality rate among Covid patients. If such trends continue in the country, the payment for such an attitude towards coronavirus, at least in specific terms, may be significantly higher. Moreover, conversations alone, even from the high rostrum, cannot improve the situation.

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)