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

(A.B. Alyokhin, B.V. Burkynskyi, A.B. Brutman, A.N. Grabovoi, V.A, Dilenko, O.I. Laiko, Z.N. Sokolovska)

Forecast monitor

01.06.2020. No 86.


Today’s issue of forecast monitor is devoted to the analysis of accuracy of the 21-day forecast of the COVID-19 outbreak in Italy, which was compiled according to statistics until May 10th, 2020, inclusive, with 10-day and 30-day forecasting horizon and published on May 11th (see https://www.facebook.com/ab.alyokhin/posts/138610261115211).

Despite the fact that we rely on the principles of continuous rolling forecasting in our forecasting activities, the volunteer nature of our work makes it impossible to update the forecasts with the necessary frequency for each of the countries that we are interested in. However, on the positive side, this provides the opportunity to assess the accuracy of the forecasts for longer forecast period based on their comparison with the actual data, which appeared since the preparation of the forecasts. That is the opportunity we are implementing in this issue of the forecast monitor, in assessing the forecast of the COVID-19 outbreak in Italy, drawn up on May 11th, 2020, according to the statistics until May 10th, 2020, inclusive.

Table and graphs, Fig. 1–15, illustrate the forecast results and degree of conformity with statistics.

Assessment of forecast accuracy is given in table.1 and 2 (Fig. 1, 2).

In table. 1 the calculated and actual values of the main indicators of the COVID-19 outbreak in Italy for 21-day forecast period, absolute and relative errors of daily forecasts and mean absolute error MAE and mean absolute percentage error MAPE for 21-day forecast as a whole.

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

Data contained in these tables, including estimates of error, indicate a high level of forecast accuracy for such a long-term (21-day) forecast period.

Fig. 3–6 indicate as follows:

– actual trajectories of the main indicators of the coronavirus outbreak in Italy;

– calculated trajectory of these indicators;

– confidence intervals limits (ranges of possible deviations of the 10-day point forecast (for the period May 11–20, 2020) with a significance level of p=0.15).

As can be seen from graphs Fig. 3–6, all indicators of the outbreak slightly deviated from forecasted values, indicating a fairly stable trend of the outbreak in this country and the high level of forecast accuracy.

Graphs Fig. 7–8, which display calculated trajectory for the longer term along with the actual trajectories, show that with this level of 21-day forecast’s accuracy, a sufficiently high accuracy of long-term forecast should be expected too, including the forecasted final values of cumulative reported cases and deaths’ indicators.

The graphs in Fig. 9–12 reflect as follows:

– actual trajectories of the indicators’ daily changes of the coronavirus outbreak in Italy;

– calculated trajectory of these indicators throughout the entire period of observation, including the forecast and post-forecast periods;

– confidence intervals limits (p=0,3), corresponding to the 10 — day forecast (for the period of May 11–20, 2020).

Let’s note, that the daily indicators are extremely difficult objects for forecasts, because of their great variability, due to the complexity of the forecasted processes. This explains the wide confidence intervals of the forecasts of these indicators, and a relatively high probability of error of the forecasts.

As can be seen, the actual values of daily indicators with a large margin remained within the confidence intervals and fluctuated near the model trends.

Fig.13–15 reflect the following parameters of the coronavirus outbreak in Italy:

- actual trajectory of the fatality rates I(TC) and I(CC) and IP progress indicator for the entire observed period (until May 31st, 2020 inclusive), including 21-day forecast period;

  • calculated trajectories of the indicators for this period.

It follows from graphs fig.13–15 that the accuracy of the reproduction actual rates of fatality and the progress indicator by the model as well as forecast accuracy of these indicators is also very high.

Based on the accuracy assessment’s results of the forecast as of May 11th, 2020 for the 21-day forecast period (May 11–31, 2020), the observed deviations of the actual data from the calculated data, it can be concluded that epidemiological situation in Italy is stable and predictable, is developing towards completion, and a mathematical model of the coronavirus outbreak accurately identified and extrapolates these patterns for sufficiently long period of time.

However, the transition of the COVID-19 outbreak to the phase of gradual easing of quarantine requires updating the forecasts, and in addition, performing scenario calculations for the assessment of possible consequences of the measures.

Source of statistics:


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Our publications on case fatality rates and indicator of progress:




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