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

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

Forecast Monitor

25.08.2020. No F-154.

https://www.facebook.com/ab.alyokhin/posts/175215454121358

This monitor is dedicated to the final analysis of the forecast of the coronavirus epidemic COVID-19 accuracy in Italy, published 85 days ago on June 1 (see https://www.facebook.com/ab.alyokhin/posts/146917610284476). The forecast contained medium-term (10 days) and long-term (30 days) forecasts of the main indicators of the COVID-19 coronavirus epidemic in this country, starting from June 1.

We have regularly published estimates of the accuracy of this forecast due to its outstanding forecast qualities. Now, however, the time has come to say goodbye to him, to say goodbye because Italy and the coronavirus decided so. In addition, here we are powerless.

Before proceeding to consider the estimates of the accuracy of this forecast, we note that in fact these are estimates of the stability, now of the former, patterns of the COVID-19 coronavirus epidemic development in Italy. Indeed, such a long-term compliance of the forecast with statistical data is a clear confirmation of the invariability of the patterns development epidemiological situation in this country, which is a great merit of the government and citizens of Italy. The mathematical model only correctly identified, recorded these trends at the time of the forecast and extrapolated them to the future.

We must also pay tribute fact that many countries whose have successfully overcome the first, most acute, phase of the epidemic have long caved in under the second onslaught of the coronavirus. This was clearly visible to us by how long our forecasts remain relevant.

Therefore, earlier, France, Germany left the race (they moved away from the forecast tendencies), South Korea held out for a long time. There are now all the signs that Italy is also failing to withstand the second onslaught of the coronavirus.

We will show this using tables and diagrams in Fig. 1–12.

Estimates of the forecast accuracy of the main indicators of the coronavirus epidemic in Italy given in Table. 1–2 (see Figure 1–2).

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Italy for 85 days of the actual 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 percent of MAPE of the 85-day forecast as a whole. In this and the following table, due to its size, the rows are hidden, which are contained in the forecast monitor dedicated to the analysis of the accuracy of this forecast for 70 days (https://www.facebook.com/ab.alyokhin/posts/170984117877825 ).

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

As can see from the data table. 1 the accuracy of the 85-day forecast is still very high. Average absolute percentage errors (MAPE estimates *) for the main indicators of the epidemic are at the following level:

- total number of infected — 2.93%;

- total number of deaths — 1.11%;

- total number of recovered — 2.44%.

The forecasting accuracy of the derived indicators of the coronavirus epidemic in Italy (MAPE * estimates) is as follows (Table 2, Fig. 2):

- mortality rate I (TC) — 2.01%;

- mortality rate I (CC) — 2.61%;

- IP progress indicator — 4.75%,

It is interesting to note that in the 15 days that have passed since the publication of data on the accuracy of this forecast after 70 days, not all indicators have deteriorated.

In fig. 3–5 are indicating:

- actual trajectories of the main indicators of the coronavirus epidemic in Italy 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 (for the period from 1 to 10 June) with a significance level of p = 0.01).

As follows from the graphs in Fig. 3–5, markedly deviated from the calculated values only for the indicator of the total number of infected (Fig. 3) due to the still small second wave of new infections that arose at the end of the forecast period.

Over the past two weeks, this process has intensified, which allows us to say that the forecast is losing its power, since it does not consider this circumstance.

The diagrams in Fig. 6–9 characterize:

- actual trajectories of changes in the daily indicators of the coronavirus epidemic in Italy for the entire observation period, including the 85-day forecast period;

- calculated trajectories of these indicators for the same period;

- boundaries of the confidence intervals (p = 0.3) corresponding to the forecast for 10 days (for the period from June 1 to 10, 2020).

As you can see, among the daily indicators of the epidemic, only the growth rate of new infected people significantly deviates from the trend set in the model (Fig. 6).

Diagrams Fig. 10–12 reflect such parameters of the coronavirus epidemic in Italy as:

- actual trajectories of lethality indicators I (TC), I (CC) and IP progress indicator for the entire observation period (up to 24 August 2020 inclusive), including the 85-day forecast period;

- calculated trajectories of the indicators for the same period.

These charts show the still high forecast accuracy of the generalized epidemic indicators and their apparent negative reaction to the growing number of new infections in recent weeks (Fig. 11 and Fig. 12).

In general, provided tabular and graphic materials show that under the pressure of the coronavirus (or rather, due to the weakening of opposition from the Italian government and the citizens of this country), a long period of stable development of the COVID-19 coronavirus epidemic in Italy has ended. The country is gradually being drawing into in the second phase, which is characterizing by another rise in the number of infected.

This process is not developing as rapidly as, for example, in Israel, France and South Korea, but we know how quickly the situation can get out of control. Let us, however, hope that the citizens of Italy who have drank coronavirus grief know it even better.

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

Official page of the state scientific institution Institute of Market Problems and Economic-Ecological Research of the National Academy of Sciences of Ukraine