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

6 min readJul 21, 2020

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

Forecast Monitor

07/21/2020. No 114.

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

This monitor is dedicated to the analysis of the forecast accuracy of the COVID-19 epidemic in Italy, published 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 from June 1.

On July 2, 2020, the results of the latest analysis of the accuracy of this forecast based on actual data for 32 forecast days (see https://www.facebook.com/ab.alyokhin/posts/158398982469672) were published, which indicated exclusively high tonnage of the forecast for such a long period.

Today we publish the results of the analysis of the same forecast; 50 days have passed since the date of its preparation. This would be beyond reason if it were not for the amazingly high forecast accuracy.

Quantitative estimates and related illustrative material are presenting in Fig. 1–13

Estimates of the forecast accuracy of the main indicators of the epidemic in Italy are giving in Tables 1 and 2 (Fig. 1, 2).

Table 1 shows the calculated and actual values of the main indicators of the COVID-19 coronavirus epidemic in Italy for 50 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 percentage of MAPE of the 50-day forecast as a whole. In this and the following table, due to its size, the rows are hiding, which are contained in the forecast monitor dedicated to the analysis of the accuracy of this forecast for 32 days (see the link above).

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

The data in these tables, including bias estimates of 1.26% (total number of infected), 0.63% (total number of deaths), and 3.42% (total number of recovered), indicate an extremely high prediction accuracy for such long (50-day) forecasting period. Note that the accuracy of the forecast has changed little over the 18 days that have passed since the previous analysis, and even surpassed the previous level in terms of the recovered rate.

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, the values of all the main indicators of the epidemic either did not deviate, or did not deviate significantly from the forecast. This speaks of highly stable trends in the development of the epidemic in Italy and visually confirms the high quality of the forecast.

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 50-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 forecast (for the period from June 1 to June 10, 2020).

As you can see, the actual values of the daily indicators varied around the model trends and indicate that the epidemic in this country continues to move towards its final state.

Diagrams Fig. 10–11 reflect such parameters of the coronavirus epidemic in Italy as:

- actual trajectories of lethality indicators I (TC) and I (CC) for the entire observation period (up to July 20, 2020 inclusive), including the 50-day forecast period;

- calculated trajectories of the indicated indicators for the same period.

They also show exceptional predictive accuracy for these generalized epidemic indicators.

The diagram in Fig. 12 shows the model trend of the reproductive number R0, which characterizes the growth potential of the epidemic. If this indicator is less than one, the epidemic begins to fade and eventually ends. The less one reproductive number, the faster the rate of decay of the epidemic.

This chart shows that in Italy the value of this indicator fell relatively quickly below 1.00 (on the chart this value was reaching on March 30, 2020).

We have repeatedly compared the development of the epidemic in Ukraine with the course of the coronavirus epidemic in other countries. Unfortunately, Ukraine cannot stand comparison with the leaders. In our country, the reproductive number fluctuates around the 1.00 mark for a long time, which constantly feeds the epidemic. Comparison with Italy in this case allows us to judge how long the life cycle of the epidemic in Ukraine can be with this level of containment, if in Italy it is still far from the end of the epidemic.

Fig. 13 for the estimated and actual trajectories of the progress bar

IP for the entire observation period (up to July 20, 2020 inclusive), including the 50-day forecast period), shows that the process of ending the epidemic usually takes on the character of an asymptotic approximation to the final state and significantly stretches over time.

Based on the results of assessing the accuracy of the forecast from June 1, 2020 for a 50-day lead period (01.06–20.07.2020), the observed deviations of the actual data from the calculated ones, it can be concluded that the epidemiological situation in Italy continues to develop steadily and predictably in the direction completion.

The graphs illustrating the course of the epidemic in this country are identical to those found in any textbook on mathematical epidemiology. Unfortunately, the price of such a “classic” is many thousands of dead and great grief that came to many Italian families.

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)