6.5 Spain
In this section, we consider the first wave of the COVID-19 epidemic in Spain and
present the results of three SIR simulations.
SIR simulations for the COVID-19 epidemic dynamics in Spain were performed
with the use of V j and t j data sets presented in Tables 6.5 and 6.6 for different time
periods T c taken for calculations. The results are shown in Table 6.13 and
Fig. 6.17; some of them were published in [74, 83]. The estimations for parameters
N, m, a, t
Ã
1 and for the final day of the first epidemic wave in Spain are rather
different. The smallest value of e corresponds to the prediction 2 and is rather low.
Nevertheless, the highest value of F=F C ð1; n À 2Þ was obtained in prediction 3, and
the highest value of the correlation coefficient r corresponds to prediction 1.
Predictions 1 and 3 yield also smaller values of the saturation level V 1 and corresponding V curves deviated faster from the V j values registered in Spain after
April 10, 2020. Therefore, prediction 2 can be treated as the most reliable and
demonstrate once more that more fresh data sets yield better estimations of the
COVID-19 epidemic dynamics. The average time of spreading infection s ¼ 1=q
was estimated as 1.46 for this prediction. This value is very close to the value
obtained in the most reliable estimation for Italy (1.47, prediction 6), but it is much
higher than corresponding value in Austria (0.77, prediction 4). These results can
explain much higher numbers of cases in Spain and Italy. The SIR curves corresponding to prediction 2 are shown in Fig. 6.17.
Figure 6.17 illustrates that second prediction for Spain looks too optimistic
(“stars” deviate from the blue line more than for other European countries). The
second prediction for this country has lower value of F=F C ð1; n À 2Þ in comparison
with the predictions 1 and 3 (see Table 6.13), but for these predictions the deviations are even larger. Probably, the final size and the duration of the epidemic in
Spain have to be re-estimated with the use of fresher data sets in order to decrease
the value of relative error e.
The results for Spain are compared with the situation in other countries and
regions in Figs. 6.6 and 6.7. The SIR curves (second prediction) and markers
representing the V j values taken for calculations (“circles”), comparisons (“triangles”) and verifications of calculations (“stars”) are shown in Figs. 6.6 and 6.7 by
yellow color for Spain. It can be seen that the first cases in Spain probably occurred
in the beginning of January, 2020 (later than in USA, Italy, Germany, South Korea,
and UK), but already in May, in terms of the number of cases, this country was
second only to USA.
6.6 France
In this section, we consider the first wave of the COVID-19 epidemic in France and
present the results of three SIR simulations.
62
6 SIR Simulations for the First Waves of the COVID-19 …
In this section, we consider the first wave of the COVID-19 epidemic in Spain and
present the results of three SIR simulations.
SIR simulations for the COVID-19 epidemic dynamics in Spain were performed
with the use of V j and t j data sets presented in Tables 6.5 and 6.6 for different time
periods T c taken for calculations. The results are shown in Table 6.13 and
Fig. 6.17; some of them were published in [74, 83]. The estimations for parameters
N, m, a, t
Ã
1 and for the final day of the first epidemic wave in Spain are rather
different. The smallest value of e corresponds to the prediction 2 and is rather low.
Nevertheless, the highest value of F=F C ð1; n À 2Þ was obtained in prediction 3, and
the highest value of the correlation coefficient r corresponds to prediction 1.
Predictions 1 and 3 yield also smaller values of the saturation level V 1 and corresponding V curves deviated faster from the V j values registered in Spain after
April 10, 2020. Therefore, prediction 2 can be treated as the most reliable and
demonstrate once more that more fresh data sets yield better estimations of the
COVID-19 epidemic dynamics. The average time of spreading infection s ¼ 1=q
was estimated as 1.46 for this prediction. This value is very close to the value
obtained in the most reliable estimation for Italy (1.47, prediction 6), but it is much
higher than corresponding value in Austria (0.77, prediction 4). These results can
explain much higher numbers of cases in Spain and Italy. The SIR curves corresponding to prediction 2 are shown in Fig. 6.17.
Figure 6.17 illustrates that second prediction for Spain looks too optimistic
(“stars” deviate from the blue line more than for other European countries). The
second prediction for this country has lower value of F=F C ð1; n À 2Þ in comparison
with the predictions 1 and 3 (see Table 6.13), but for these predictions the deviations are even larger. Probably, the final size and the duration of the epidemic in
Spain have to be re-estimated with the use of fresher data sets in order to decrease
the value of relative error e.
The results for Spain are compared with the situation in other countries and
regions in Figs. 6.6 and 6.7. The SIR curves (second prediction) and markers
representing the V j values taken for calculations (“circles”), comparisons (“triangles”) and verifications of calculations (“stars”) are shown in Figs. 6.6 and 6.7 by
yellow color for Spain. It can be seen that the first cases in Spain probably occurred
in the beginning of January, 2020 (later than in USA, Italy, Germany, South Korea,
and UK), but already in May, in terms of the number of cases, this country was
second only to USA.
6.6 France
In this section, we consider the first wave of the COVID-19 epidemic in France and
present the results of three SIR simulations.
62
6 SIR Simulations for the First Waves of the COVID-19 …