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)

Forecast Monitor

09/06/2020. No 94.

Today’s forecast monitor is somewhat unusual and contains an analysis of the accuracy of the COVID-19 coronavirus epidemic development forecast in Italy published on May 11 (see https://www facebook.com/ab.alyokhin/posts/138610261115211), as well as the latest forecast published June 1, 2020 (see https://www.facebook.com/ab.alyokhin/posts/146917610284476).

Each of these forecasts contains medium-term (10 days) and long-term (30 days) forecasts of the main indicators of the COVID-19 coronavirus epidemic from May 11 and June 1, 2020. Thus, the forecasts were analyzed with a lead time of 29 and 8 days respectively. Assessing the accuracy of a forecast with such a long forecast period was due to its high accuracy and is of independent scientific interest, aimed at clarifying the potential of this forecast, as well as the models and forecasting techniques used in its development.

The reasons for updating the forecast of May 11, 2020 was substantiated in the forecast monitor devoted to the analysis of its accuracy for the period from May 11 to May 31, 2020 (see https://www.facebook.com/ab.alyokhin/posts/146725200303717) and will not be repeated here.

At the same time, after 8 days, there is every reason to analyze the accuracy and the latest forecast of June 1, 2020.

The results of forecast calculations of May 11, 2020 and the degree of their compliance with statistical data characterize the tables and graphs of Fig. 1–14.

Estimates of the accuracy of the forecast are given in Tables 1 and 2 (Fig. 1, 2).
In the table. Figure 1 shows the calculated and actual values ​​of the main indicators of the COVID-19 coronavirus epidemic in Italy for 29 days of the forecast period, the absolute and relative errors of daily forecasts, as well as the average absolute error MAE and the average absolute error in percent MAPE of the 29-day forecast as a whole.

In the table. Figure 2 shows the same data on mortality rates I (TC), I (CC) and the IP progress indicator.

The data contained in these tables, including error estimates (within 2.72% -3.38% for the main indicators of the epidemic), indicate a very high level of forecast accuracy for such a long (29-day) forecast period.

In fig. 3–5 are indicated:
- Actual trajectories of the main indicators of the coronavirus epidemic in Italy;
- calculated trajectories of these indicators;
- the boundaries of confidence intervals (ranges of possible deviations of the point 10-day forecast (for the period from May 11 to 20) with a significance level of p = 0.15).

As follows from the graphs of Fig. 3–5, all indicators of the epidemic did not deviate significantly from the forecast values, which indicates relatively stable trends in the development of the epidemic in Italy and visually confirms the high quality of the forecast.

Graphs fig. 6, 7, which, along with the actual trajectories, show the calculated trajectories for a longer perspective, show that with this level of accuracy of the 29-day forecast, a fairly high accuracy of long-term forecasts and the predicted final values ​​of the number of patients and deaths should be expected.

The diagrams in fig. 8–11 are characterized by:
- Actual trajectories of changes in daily indicators of the coronavirus epidemic in Italy;
- calculated trajectories of these indicators for the entire observation period, including forecast and post-forecast periods;
- boundaries of confidence intervals (p = 0.3) corresponding to the forecast for 10 days (for the period from May 11 to May 20, 2020).

As you can see, the actual values ​​of daily indicators did not go beyond confidence intervals, fluctuated near model trends and indicate the confident progress of the epidemic in this country towards its logical conclusion.

Diagrams fig. 12–14 reflect the parameters of the coronavirus epidemic in Italy, such as:
- the actual trajectories of the mortality rates I (TC) and I (CC) and the IP progress indicator for the entire observation period (June 8, 2020 inclusive), including a 29-day forecast period;
- calculated trajectories of these indicators for this period.

From these graphs it follows that the accuracy of the model reproducing the actual values ​​of mortality and progress indicators, as well as the accuracy of the forecast of these indicators are also very high.

Based on the results of assessing the accuracy of the forecast from May 11, 2020 to the 29-day lead-time (May 11 — June 8, 2020), the observed deviations of the actual data from the calculated ones, we can conclude that the epidemiological situation in Italy is steadily and predictably developing in the direction completion. At the same time, the gradual accumulation of errors made it advisable to update the forecasts for the development of the coronavirus epidemic in this country, which was done by us on June 1, 2020.

The results of the analysis of the accuracy of the current forecast and the corresponding illustrative material are presented in Fig. 15–29. Moreover, the structure of the analysis of this forecast is the same as the structure of the analysis of the forecast of May 11, 2020.

The main results of evaluating the accuracy of the 8-day forecast are given in the tables in Fig. 15, 16.

As you can see, the estimates (MAPE *) of the prognosis of the total number of infected and dead are extremely high (0.14% and 0.31%, respectively), and the accuracy rating of the total number of people recovered is very high (3.38%). Nevertheless, the fact that the level of this assessment (the assessment of the 8-day forecast) is almost the same as the corresponding assessment of the 29-day forecast (see Fig. 1) suggests that forecasting this indicator remains a bottleneck and this time. (Note that the reasons for such deviations have been analyzed by specialists of the working group and, if possible, will be taken into account when developing the following forecasts for both Italy and other countries.)

Diagrams fig. 17–20 allow you to visualize the degree of coincidence and / or mismatch of the actual and calculated trajectories of the values ​​of the indicators of the total number of infected and dead, recovered and active cases (current patients). As you can see, the actual values ​​slightly deviated from model trends and are within confidence intervals with a large margin.

The almost complete coincidence of the actual and calculated curves of the first two of the above indicators (see Fig. 21 and Fig. 22) allows us to hope that the final indicators of the epidemic development will be reached by the end of the forecast period of the calculated values ​​or will be close to them.

The behavior of daily indicators of the coronavirus epidemic in Italy (see Fig. 23–26) strictly corresponds to model trends, which also indicates a high predictive power of the model developed by the WG specialists.

The above fully applies to the degree of correspondence between the actual and estimated values ​​of the mortality indices I (TC), I (CC) and the progress indicator IP.

The results of the extremely long coronavirus epidemic life cycle analysis of the previous forecast and the medium-term actual forecast of the coronavirus epidemic in Italy indicate the stability of its development trends and the high quality of their reproduction by the model. The first is largely due to the high level of control over the development of the epidemic in this country, the second is due to the accumulated by the developers of the WG forecasts at IPREI NAS of Ukraine for 3 months of daily practical forecasting by experience.

Sources of statistics:
https://www.worldometers.info/coronavirus/#countries

Our materials also:
https://www.facebook.com/MATHMODELCOVID19
https://t.me/mathmodelcovid19

Our initiative group and mission:
https://www.facebook.com/ab.alyokhin/posts/117804769862427

Publications on Mortality and Progress Indicators
https://www.facebook.com/ab.alyokhin/posts/105684827741088
https://www.facebook.com/ab.alyokhin/posts/106831140959790
https://www.facebook.com/ab.alyokhin/posts/107444734231764