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

5 min readAug 31, 2020

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

Forecast Monitor

31/08/2020. No F-165

https://www.facebook.com/ab.alyokhin/posts/176911327285104

This monitor is dedicated to the final analysis of the coronavirus epidemic COVID-19 in Italy forecast accuracy, published 91 days ago on June 1st (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 regularly published estimates of the accuracy of this forecast due to its outstanding predictive qualities:

https://www.facebook.com/ab.alyokhin/posts/150095069966730

https://www.facebook.com/ab.alyokhin/posts/155491646093739

https://www.facebook.com/ab.alyokhin/posts/158398982469672

https://www.facebook.com/ab.alyokhin/posts/164456381863932

https://www.facebook.com/ab.alyokhin/posts/167607534882150

https://www.facebook.com/ab.alyokhin/posts/170984117877825

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

Now the time has come to update the forecast calculations in connection with a significant change in the patterns development of the epidemic in this country. However, first we present the final estimates of the accuracy of this forecast for today (see Tables 1–2).

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Italy for 91 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 MAPE of the 91-day forecast as a whole. In this and the following tables, due to their size, the rows that are contained in the last forecast monitor devoted to the analysis of the accuracy of hidden (see the link above).

Table 2 shows similar data on case fatality rates I (TC), I (CC) and IP progress indicator.

As can be seeing from the data table. 1, the accuracy of the 91-day forecast is still very high. Average absolute percentage errors (MAPE * estimates) for the main indicators of the epidemic fixed at the following level:

- total number of infected — 3.42%;

- total number of deaths — 1.19%;

- total number of recovered — 2.42%.

The forecasting accuracy of the derived indicators of the coronavirus epidemic in Italy (MAPE * estimates) is also high (Table 2):

- mortality rate I (TC) — 2.46%;

- mortality rate I (CC) — 2.46%;

- IP progress indicator — 5.03%,

The new forecast developed based on statistical data for the entire observation period until August 30, 2020 inclusive for a forecast period of 10 and 30 days, starting from August 31, 2020.

The main parameters of this forecast are showing in Fig. 1–13.

The diagrams in Fig. 1–4 indicate:

- actual trajectories of the main indicators of the coronavirus epidemic in Italy for the entire observation period, as well as a 10-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 (for the period from August 31 to September 9) with a significance level of p = 0.01).

As follows from these charts, the forecast extrapolates to the near future the trends that have formed recently, indicating a new wave of the coronavirus epidemic in the country.

Diagrams Fig. 5–6 differ from the diagrams in Fig. 1–2 in that they show a 30-day forecast without confidence intervals, as well as the current and forecast values of the corresponding indicators at the end of the forecasting period.

The diagrams in Fig. 7–10 characterize:

- actual trajectories of changes in the daily indicators of the coronavirus epidemic in Italy for the entire observation period, including the 91-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.

As you can see, only the daily growth rate of the infected (Fig. 7) and the indicator of the number of active cases dependent on it (Fig. 10) are the troublemakers. The effect of the second wave has not yet reached the indices of the daily increase of the deceased (Fig. 8) of the recovered Fig. 9), therefore they demonstrate stability, including the forecast period.

Diagrams Fig. 11–13 reflect the following:

- actual trajectories of lethality indicators I (TC), I (CC) and the IP progress indicator for the entire observation period, including the 91-day forecast period;

- calculated trajectories of the indicated indicators for a 10-day forecast period.

These diagrams indicate that the synthetic indicators of the epidemic, directly dependent on the number of infected (this is the mortality index (Fig. 11) and the indicator of progress (Fig. 13)) under the influence of the latter and in the forecast perspective will show a negative downward trend.

Thus, we forced to state that the long period of consistent controlled approach of the COVID-19 coronavirus epidemic in Italy to its final state, which means a complete victory over the coronavirus stopped. The coronavirus is confidently gaining its ground in terms of the number of cases. Fortunately, this has not yet affect the positive trends in mortality rates, but will inevitably lead to an increase in the number of deaths.

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)