To calculate the number of days from start of the epidemic outbreak which is
different for every country (see italicized values in the last column of Table 3.1), it
is necessary to compare it with the data set listed in Table 1.1. To increase the
accuracy, we let this number to be non-integer. To calculate the corresponding time
difference d t , the parabolic interpolation for the initial number of cases V in South
Korea will be used. The first three points in Table 1.1 yield the corresponding
equation:
V ¼ at
2
þ bt þ 51; a ¼ 16:5; b ¼ 36:5
ð3:1Þ
Then by putting into (3.1) the values V = V b for the number of cases at the starting
day of the epidemic outbreak (italicized in Table 3.1), the corresponding values d t
were calculated for every country with the use of formula
d t ¼
Àb þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
b 2 À 4ac
p
2a
; c ¼ 51 À V b
ð3:2Þ
which yields a solution to the quadratic Eq. (3.1). The calculated values of d t are
shown in the last row of Table 3.1. Then the time moments for Italy have to be
shifted by 0.549 days, for Germany by 6 + 0.154 days and so on.
The data sets from Tables 1.1 and 3.1 synchronized with the use of Eqs. (3.1)
and (3.2) are shown in Fig. 3.2 by “stars” for countries in Europe and by “squares”
for USA. The data for South Korea are shown by red line with “circles”. Blue
“stars” represent the sum of cases for five countries in Europe. It can be seen that in
March 2020, Italy, Spain, Germany, Switzerland, and France had no chance for
rapid stabilization of the number of cases. The situation in USA was not clear.
Unfortunately, in this country very rapid increase of the number of cases occurred
after March 15, 2020. Blue “stars” in Fig. 3.2 still followed the straight line,
therefore the number of cases in Europe increased exponentially between February
22 and March 14, 2020.
The application of the same simple procedure was illustrated for the epidemic
outbreak in Austria. The number of cases in this country was V b = 66 on March 6,
2020. Let us suppose that epidemic in this country started on this day.
Corresponding values are as follows: t ej = 13 (see Table 3.1) and d t = 0.3542
(according to Eq. (3.2)). If we want to know how the situation looked as of March
15, 2020 (ninth day of the epidemic in Austria), we may open the corresponding
WHO report (number 56) and find the number 959 for Austria. This figure has to be
compared with the number of cases from Table 1.1, corresponding to the time
moment 9 + 0.3542. To avoid any additional calculations, let us take the value
2337 for comparison. Thus, the situation in Austria did not look bad. Further
pandemic development was determined by many factors (in particular, the weakening of quarantine and changes in social behavior). As of September 26, 2020 (see
WHO weekly update report [52]), the number of cases in Austria (42,940) was
much higher than in South Korea (23,611).
18
3 Comparisons of the Early Stages of the COVID-19 …
different for every country (see italicized values in the last column of Table 3.1), it
is necessary to compare it with the data set listed in Table 1.1. To increase the
accuracy, we let this number to be non-integer. To calculate the corresponding time
difference d t , the parabolic interpolation for the initial number of cases V in South
Korea will be used. The first three points in Table 1.1 yield the corresponding
equation:
V ¼ at
2
þ bt þ 51; a ¼ 16:5; b ¼ 36:5
ð3:1Þ
Then by putting into (3.1) the values V = V b for the number of cases at the starting
day of the epidemic outbreak (italicized in Table 3.1), the corresponding values d t
were calculated for every country with the use of formula
d t ¼
Àb þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
b 2 À 4ac
p
2a
; c ¼ 51 À V b
ð3:2Þ
which yields a solution to the quadratic Eq. (3.1). The calculated values of d t are
shown in the last row of Table 3.1. Then the time moments for Italy have to be
shifted by 0.549 days, for Germany by 6 + 0.154 days and so on.
The data sets from Tables 1.1 and 3.1 synchronized with the use of Eqs. (3.1)
and (3.2) are shown in Fig. 3.2 by “stars” for countries in Europe and by “squares”
for USA. The data for South Korea are shown by red line with “circles”. Blue
“stars” represent the sum of cases for five countries in Europe. It can be seen that in
March 2020, Italy, Spain, Germany, Switzerland, and France had no chance for
rapid stabilization of the number of cases. The situation in USA was not clear.
Unfortunately, in this country very rapid increase of the number of cases occurred
after March 15, 2020. Blue “stars” in Fig. 3.2 still followed the straight line,
therefore the number of cases in Europe increased exponentially between February
22 and March 14, 2020.
The application of the same simple procedure was illustrated for the epidemic
outbreak in Austria. The number of cases in this country was V b = 66 on March 6,
2020. Let us suppose that epidemic in this country started on this day.
Corresponding values are as follows: t ej = 13 (see Table 3.1) and d t = 0.3542
(according to Eq. (3.2)). If we want to know how the situation looked as of March
15, 2020 (ninth day of the epidemic in Austria), we may open the corresponding
WHO report (number 56) and find the number 959 for Austria. This figure has to be
compared with the number of cases from Table 1.1, corresponding to the time
moment 9 + 0.3542. To avoid any additional calculations, let us take the value
2337 for comparison. Thus, the situation in Austria did not look bad. Further
pandemic development was determined by many factors (in particular, the weakening of quarantine and changes in social behavior). As of September 26, 2020 (see
WHO weekly update report [52]), the number of cases in Austria (42,940) was
much higher than in South Korea (23,611).
18
3 Comparisons of the Early Stages of the COVID-19 …