approximately 4.3 h and in mainland China—2.5 days (see Sects. 6.1 and 6.2). By
mid-April 2020, there were more than thousand people spreading the infection in
Italy (see dashed line in Fig. 6.9). The calculated value t
Ã
1 , solid line and “triangles”
in Fig. 6.9 demonstrate that the first cases of COVID-19 have not been identified in
Italy and sick people overspread it rather long time.
After the saturation level V 1 % 111; 548 of the first prediction was exceeded, 3
new predictions for Italy have been performed with the use of the official WHO
data, listed in Tables 6.5 and 6.6. To investigate the influence of the number of
observations n and the period used for calculations t j1 T c t j2 , different values of
initial t j1 and final t j2 moments of time were used. The results of calculations are
shown in Table 6.4 (predictions 2, 3 and 4). The SIR curves corresponding to the
prediction 4 are shown in Fig. 6.10. Markers represent the V j values taken for
calculations (“circles”), for a comparison (“triangles”) and a verification of predictions (“star”).
Figure 6.10 illustrates that the real epidemic outbreak could start even in January
2020. Probably, first cases of the COVID-19 infection were not identified and sick
people were not isolated. It could be a reason of the high saturation level of the
epidemic (approximately 148,000–153,000 according to the predictions 3 and 4).
The finish of the first wave of the epidemic in Italy was predicted to happen on May
25–31, 2020. The average time of spreading infection 1=q could be estimated as
0.7–0.75 days (according to predictions 3 and 4, see Table 6.4).
The discrepancies e shown in the last row of the Table 6.4 are much higher then
we have obtained for China (second prediction) and South Korea (see last row in
Tables 6.1 and 6.2). Observations of the epidemic in Italy showed that the
Fig. 6.9 First wave of pandemic in Italy, prediction 1. Results of SIR simulations. Numbers of
infected I (dashed line), removed R (dotted line) and the number of victims V = I + R (solid line);
“circles” correspond to the confirmed accumulated number of cases taken for calculations;
“triangles” correspond to the cases during initial stage of the epidemic; “stars”—two data points
used only for a verification of the prediction
48
6 SIR Simulations for the First Waves of the COVID-19 …
mid-April 2020, there were more than thousand people spreading the infection in
Italy (see dashed line in Fig. 6.9). The calculated value t
Ã
1 , solid line and “triangles”
in Fig. 6.9 demonstrate that the first cases of COVID-19 have not been identified in
Italy and sick people overspread it rather long time.
After the saturation level V 1 % 111; 548 of the first prediction was exceeded, 3
new predictions for Italy have been performed with the use of the official WHO
data, listed in Tables 6.5 and 6.6. To investigate the influence of the number of
observations n and the period used for calculations t j1 T c t j2 , different values of
initial t j1 and final t j2 moments of time were used. The results of calculations are
shown in Table 6.4 (predictions 2, 3 and 4). The SIR curves corresponding to the
prediction 4 are shown in Fig. 6.10. Markers represent the V j values taken for
calculations (“circles”), for a comparison (“triangles”) and a verification of predictions (“star”).
Figure 6.10 illustrates that the real epidemic outbreak could start even in January
2020. Probably, first cases of the COVID-19 infection were not identified and sick
people were not isolated. It could be a reason of the high saturation level of the
epidemic (approximately 148,000–153,000 according to the predictions 3 and 4).
The finish of the first wave of the epidemic in Italy was predicted to happen on May
25–31, 2020. The average time of spreading infection 1=q could be estimated as
0.7–0.75 days (according to predictions 3 and 4, see Table 6.4).
The discrepancies e shown in the last row of the Table 6.4 are much higher then
we have obtained for China (second prediction) and South Korea (see last row in
Tables 6.1 and 6.2). Observations of the epidemic in Italy showed that the
Fig. 6.9 First wave of pandemic in Italy, prediction 1. Results of SIR simulations. Numbers of
infected I (dashed line), removed R (dotted line) and the number of victims V = I + R (solid line);
“circles” correspond to the confirmed accumulated number of cases taken for calculations;
“triangles” correspond to the cases during initial stage of the epidemic; “stars”—two data points
used only for a verification of the prediction
48
6 SIR Simulations for the First Waves of the COVID-19 …