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

5 min readDec 10, 2020

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

Forecast Monitor

10/12/2020. No F-279.

https://www.facebook.com/ab.alyokhin/posts/214911373485099

This Forecast Monitor devoted to analyze the accuracy of the COVID-19 outbreak forecast for Italy published on November 20, 2020 (see https://www.facebook.com/ab.alyokhin/posts/200837361559167). The forecast contained medium-term main (10 days) and long-term approximate (30 days) forecasts of the most important indicators of the COVID-19 epidemic in this country, starting from October 31st.

Today we present the results of evaluating the accuracy of the 20-day component of this forecast (see Tables 1–2, and Fig. 1–11).

Table 1 shows the calculated and actual values of the main cumulative indicators of the COVID-19 epidemic in Italy for 20 days of the actual forecast period, the absolute (AE) and relative (PE) errors of daily forecasts, the average absolute MAE error, and the average absolute percentage error of the MAPE forecast in the whole.

Table 2 shows similar data for lethality rates I (TC), I (CC) and the IP progress indicator.

Regardless of the forecasts accuracy analysis of their accuracy is extremely important.

The high level of compliance of the actual data with the calculated ones indicates that the trends that have developed persist during the forecast period.

The deviation of the actual data from the calculated ones indicates either error in identifying existing trends using forecast models, or changes in the trends themselves during the forecast period. Thus, analyzing the accuracy of forecasts allows us to identify weaknesses in the models and / or to better understand the processes that determine the development of the epidemic.

That is why, adhering to the ideology of rolling forecasting, which presupposes the timely adjustment of forecasts taking into account the current situation, we from time to time analyze the forecasts accuracy after long periods.

In the analyzed forecast, it was assumed that the trends in the development of the COVID-19 epidemic in Italy would continue in the near-term outlook. Estimates of the forecast accuracy make it possible to judge the validity of this assumption.

As follows from the tables above, the average absolute percentage errors (MAPE estimates) for the main cumulative indicators of the COVID-19 epidemic in Italy over 20 days are:

- total number of infected people — 4.61%;

- total number of deaths — 0.77%;

- total number of recovered — 11.12%;

- number of active cases — 2.41%.

The average absolute percentage errors (MAPE estimates) for the main synthetic indicators of the epidemic are:

- mortality rate I (TC) — 4.98%;

- mortality rate I (CC) — 9.73%;

- IP progress indicator — 3.63%.

The errors in forecasting a number of indicators are very large. The reasons for this are clearly demonstrated by the diagrams in Fig. 1–11. In these diagrams, the observation period subdivided into the pre-forecast period (green color of the corresponding curves) and the forecast period (red color). This allows you to make the discrepancy between the actual data and the calculated ones during the forecast period more evident.

The diagrams in Fig. 1–4 indicate:

- actual trajectories of the main indicators of the COVID-19 epidemic in Italy for the entire observation period, including the 20-day forecasting period;

- calculated trajectories of these indicators for the same period.

Diagrams Fig. 5–8 characterize:

- actual trajectories of changes in the daily indicators of the COVID-19 epidemic in Italy for the entire observation period, including the 20-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.

The diagrams in Fig. 9–11 reflected:

- actual trajectories of lethality indicators I (TC), I (CC) and IP progress indicator for the entire observation period, including the 20-day forecast period;

- calculated trajectories of the indicators for the same period, as well as for a 30-day forecasting period.

As follows from the forecast accuracy estimates and the presented diagrams, starting from the 4th — 5th day of the forecast period, the effect of tightening quarantine began to manifest itself (see Table 1 and Fig. 5): the daily increase in infected people quickly went down.

This is further evidence that Italy knows how to fight the spread of coronavirus, but does not always show these skills. Recall that additional victims of the epidemic, new patients and the state itself are paying for this with their lives.

This is strikingly different from the situation in Ukraine, which, over the entire period of the COVID-19 epidemic, has never demonstrated the ability to reduce the number of new infections. The maximum that managed during all this time was to achieve a temporary exit of this indicator to a plateau several times, which is equivalent to a linear increase in the epidemic, but not to its curtailment. At the same time, in Ukraine, the true reasons for the release of this indicator to a plateau, the role of manipulation with tests and statistical data in achieving such a result remain unclear.

The patterns that determine the dynamics of the total number of deaths and daily increases in lethal outcomes practically did not change during the 20-day forecast period (Table 1, Fig. 2, Fig. 6), which ensured a high level of forecast accuracy for these indicators.

The dynamics of other epidemic indicators is a consequence of the dynamics of the number of new infected.

Thus, the daily gains in the number of recovered patients (Fig. 7) and the number of active cases (Fig. 8) decreased significantly. The consequence of these changes is a slight increase in mortality indicators (Fig. 9–10) and a decrease relative to the forecast level of the progress indicator (Fig. 11).

In general, by demonstrating possession of the tools to contain the spread of the coronavirus, Italy, like many other countries, demonstrates the lack of will to apply them firmly and consistently, paying the price for this with additional victims of COVID-19.

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)