example of prediction 6). To more quickly assess the quality of the forecast, it is
necessary to constantly monitor the real epidemic dynamics and refine the calculations using more recent data if there are large discrepancies between the actually
recorded number of cases and the theoretical V = I + R curves.
6.4 Austria
In this section, we consider the first wave of the COVID-19 epidemic in Austria and
present several SIR simulations.
The author is very grateful to his Austrian friend and co-author Gerhard
Demelmair who did a tremendous job of collecting and systematizing statistical
information (it is presented in numerous tables), so a lot of attention was paid to
SIR simulations of the epidemic in Austria [71, 74, 75, 77, 78]. The corresponding
data sets are presented in Tables 6.8 and 6.9. The results of two first SIR simulations with the use of different periods T c taken for calculations are shown in
Table 6.10.
To calculate the first prediction, we took only the data points for the period
March 6–18 (13 t j 25). The incredible small figure for the saturation level
V 1 % 3589 was obtained. The calculations also gave the value t final % 47:1.
According to this estimation, the local transmission in Austria could stop after April
10, 2020. The corresponding SIR curves are shown in Fig. 6.12.
The real number of cases deviated very fast from the solid line shown in
Fig. 6.12. After April 10, it was possible to calculate the error according to discrepancy according to the formula (4.20). The value e ¼ 73:5% turned to be too
large. We have used more fresh V j data (for the period March 14–29, 2020) to
calculate second prediction. The results are also presented in Table 6.10. Much
higher figures for the saturation level V 1 % 14; 251 and epidemic duration
(t final % 67:3) were obtained. The value of e was only 7.8%. These results demonstrate once more that the numbers of COVID-19 cases are not reliable immediately
after the epidemic outbreak, since many infected persons remain not detected.
It must be noted that the correlation coefficient for the first prediction is slightly
higher (see Table 6.10). Therefore, the value e is better estimation of the reliability
of prediction. If the real number of cases is much higher than the predicted saturation level V 1 , there is no need to wait until predicted moment of time t final . In
such situations, new estimations with the use of fresher data sets are necessary. We
have done this with the use of also some V j values from Table 6.11. The results of
such calculations are shown in Tables 6.10 and 6.12.
The obtained values of e are rather low, and for predictions 2 and 5 they are very
close (see Tables 6.10 and 6.12). Also close are the estimations for parameters N, m,
a, t
Ã
1 and for the final day of the first wave of the epidemic in Austria for predictions
2–5. The average time of spreading infection 1=q was estimated as 0.44–0.77 days
and is much lower than in Italy (see Table 6.7), but higher than for the first
54
6 SIR Simulations for the First Waves of the COVID-19 …
necessary to constantly monitor the real epidemic dynamics and refine the calculations using more recent data if there are large discrepancies between the actually
recorded number of cases and the theoretical V = I + R curves.
6.4 Austria
In this section, we consider the first wave of the COVID-19 epidemic in Austria and
present several SIR simulations.
The author is very grateful to his Austrian friend and co-author Gerhard
Demelmair who did a tremendous job of collecting and systematizing statistical
information (it is presented in numerous tables), so a lot of attention was paid to
SIR simulations of the epidemic in Austria [71, 74, 75, 77, 78]. The corresponding
data sets are presented in Tables 6.8 and 6.9. The results of two first SIR simulations with the use of different periods T c taken for calculations are shown in
Table 6.10.
To calculate the first prediction, we took only the data points for the period
March 6–18 (13 t j 25). The incredible small figure for the saturation level
V 1 % 3589 was obtained. The calculations also gave the value t final % 47:1.
According to this estimation, the local transmission in Austria could stop after April
10, 2020. The corresponding SIR curves are shown in Fig. 6.12.
The real number of cases deviated very fast from the solid line shown in
Fig. 6.12. After April 10, it was possible to calculate the error according to discrepancy according to the formula (4.20). The value e ¼ 73:5% turned to be too
large. We have used more fresh V j data (for the period March 14–29, 2020) to
calculate second prediction. The results are also presented in Table 6.10. Much
higher figures for the saturation level V 1 % 14; 251 and epidemic duration
(t final % 67:3) were obtained. The value of e was only 7.8%. These results demonstrate once more that the numbers of COVID-19 cases are not reliable immediately
after the epidemic outbreak, since many infected persons remain not detected.
It must be noted that the correlation coefficient for the first prediction is slightly
higher (see Table 6.10). Therefore, the value e is better estimation of the reliability
of prediction. If the real number of cases is much higher than the predicted saturation level V 1 , there is no need to wait until predicted moment of time t final . In
such situations, new estimations with the use of fresher data sets are necessary. We
have done this with the use of also some V j values from Table 6.11. The results of
such calculations are shown in Tables 6.10 and 6.12.
The obtained values of e are rather low, and for predictions 2 and 5 they are very
close (see Tables 6.10 and 6.12). Also close are the estimations for parameters N, m,
a, t
Ã
1 and for the final day of the first wave of the epidemic in Austria for predictions
2–5. The average time of spreading infection 1=q was estimated as 0.44–0.77 days
and is much lower than in Italy (see Table 6.7), but higher than for the first
54
6 SIR Simulations for the First Waves of the COVID-19 …