A mathematical model and forecast for the coronavirus disease COVID-19 in France
By: Impeer Of The Nas Of Ukraine
Tags: Covid 19, Covid 19 Crisis, Corona

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

Forecast Monitor

03/09/2020. No F-170

https://www.facebook.com/ab.alyokhin/posts/177709390538631

On June 30, 2020, we published another forecast monitor (see https://www.facebook.com/ab.alyokhin/posts/157423242567246) dedicated to the COVID-19 coronavirus epidemic in France. As usual, the forecast included the main 10-day and auxiliary (approximate) 30-day forecasts.

On July 10, 2020, the results of the 10-day assessing component of the forecast published using the actual data that appeared over 10 days of the forecast period (https://www.facebook.com/ab.alyokhin/posts/160856195557284). Then the 10-day forecast showed outstanding accuracy.

On July 30, 2020, the results of the assessment of the already 30-day forecast using actual 30 days data published (https://www.facebook.com/ab.alyokhin/posts/167312718244965). The forecast accuracy remained very high.

On August 11, 2020, an estimate of this forecast using 42-day actual data released (https://www.facebook.com/ab.alyokhin/posts/171231191186451). In this review, despite the still formally high estimates of accuracy, we concluded that this forecast exhausted itself. Therefore, it is not able to reflect the development of the coronavirus epidemic in France in accordance with emerging new trends.

65 days have passed since this forecast. What is the point of returning to its consideration? It turns out that such a consideration makes a lot of sense, and it consists in a warning to those who can also frivolously lose all the advantages in the fight against coronavirus. Although we perfectly understand that those countries that did not have such positive experience in taming the coronavirus, like France, and (races) have nothing to lose. Nevertheless…

This time, for obvious reasons, without detailed tabular data solely for the protocol, we only note that by its 65th day this forecast came with the following accuracy indicators:

- total number of infected people — 8.49%;

- total number of deaths — 2.70%;

- total number of recovered — 3.27%.

Recall that the accuracy of forecasts with MAPE estimates up to 10% is considering high.

However, in this monitor, we will leave the formalities aside and consider the graphs with the actual and calculated trajectories of the main indicators of the COVID-19 coronavirus epidemic in France.

In fig. 1–4 are given:

- actual trajectories of the main indicators of the coronavirus epidemic in France for the entire observation period, including the 65-day forecast 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).

What we see in these diagrams?

The diagram in Fig. 1 shows that in France, in terms of the spread of the coronavirus, a new outbreak has begun, almost an exact copy of the first. You can call it the second wave, but it does not change the essence and scale of what is happening. Another outbreak was superimposed on the consequences of the first (see the graph reflecting the dynamics of the active cases number in Fig. 4), and this is the main drama of the situation. Of course, the experience of treating coronavirus patients in France is now completely different, but the burden on the medical system will have to be enormous.

Diagrams Fig. 5–6 duplicate diagrams in Fig. 1–2 with the following differences:

- these graphs indicate the actual values of the corresponding indicators at the time of the forecast;

- calculated indicators at the end of the 30-day forecast period;

- actual and calculated values of these indicators at the end of the 65-day forecast period, i.e. as of 2 September 2020

Therefore, at the forecast time (June 29, 2020), more than 164 thousand cases of infection recorded in France (Fig. 5). If the prevailing trends at that time persisted, 15 thousand more patients expected in 30 days. However, in the last days of the 30-day forecast period, the situation in the country began to change radically. The consequences of these changes are as follows. Instead of 197 thousand infected (according to the forecast, while maintaining the previously existing trends) in France today there are almost 100 thousand more infected. This is the price of conniving at the coronavirus.

The situation with the total number of deaths is not so dramatic. However, this is due to the fact of natural time lags between the flows of the infected and the dead (the length of the period of stay in hospitals for those who recovered and those who died), the second wave of the epidemic has not yet reached mortality rates (for a closed case). The lifetime of the second wave is even significantly lower than the time lags noted above.

Diagrams Fig. 7–10 reflect:

- actual trajectories of changes in the daily indicators of the coronavirus epidemic in France for the entire observation period, including the 65-day forecast 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.

These diagrams confirm what said above. Neither the daily indicator of the number of deaths (Fig. 8), nor the daily indicator of the number of those who recovered (Fig. 9) have not yet responded to the second wave and are changing in strict accordance with the trends prevailing at the time of the forecast.

In contrast, the daily increase in the number of infected (Fig. 5) and the number of active cases (Fig. 10) immediately recorded the appearance and extent of the second wave. Both of these indicators reached their peak (characteristic of the first phase of the epidemic in France) values.

When it is happening in a country that has demonstrated the ability to effective coronavirus resist, and these skills have not disappeared anywhere, the word “Shame” suggests itself, but we will save it for other cases.

Diagrams Fig. 11–13 contain:

- 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 you know, France has one of the highest mortality rates, which currently ranges from 10% to 26%. At the same time, the actual mortality rate today characterizes precisely the second indicator. This seems to be enough for careful in pursuing a policy to ease quarantine. Nevertheless, no, the progress indicator (Fig. 13) demonstrates a visually beautiful, but in reality tragic, aerobatics figure and today it is at the level that reached in France on April 8–9, 2020.

After all that has been saying, great doubts arise as to whether France will be able / willing to repeat exactly the previous path to restore the lost positions, or will take a different path. For our compatriot, the phrase “We will go the other way” means a lot. However, this is France. We can only forecast and observe of which path this country will choose.

The new forecast being prepared during these hours and will show where the preservation of the current trends can lead France.

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)

https://www.facebook.com/ab.alyokhin/posts/152284093081161 (South Korea)

Publications on case fatality rates and progress indicator

https://www.facebook.com/ab.alyokhin/posts/105684827741088

https://www.facebook.com/ab.alyokhin/posts/106831140959790

https://www.facebook.com/ab.alyokhin/posts/107444734231764