We can try to find the best fitting lines for dependences
a ¼ rN
v
ð7:15Þ
V 1 ¼ dN
g
ð7:16Þ
which correspond to the straight lines in the logarithmic scale. For this purpose, we
can use the method presented in Chap. 2, if we substitute in (2.3) y by ln a and
ln V 1 for (7.15) and (7.16), respectively. Accordingly, the variable t has to be
substituted by ln N ; parameter c—by v and g for (7.15) and (7.16), respectively;
parameter b—by ln r and ln d for (7.15) and (7.16), respectively. Then we can
calculate the values y j and t j with the use of data set presented in Table 7.1 and the
linear regression (formulas (2.6)–(2.9)). The results of calculations are shown in
Table 7.3 for different amount of elements in the data sets (n = 13 for complete data
set and n = 11 for the data set without figures for China and Korea). Corresponding
straight lines are shown in Fig. 7.2 (solid for n = 11 and dashed for n = 13).
Table 7.3 and Fig. 7.2 demonstrate that both complete (n = 13) and incomplete
(n = 11) data sets from Table 7.1 support the hypotheses about functional connections (7.15) and (7.16). In comparison with Table 7.2, the values of parameters
r, F, v, g, r and d are very close and figures for r
j j and F=F C are higher The
difference in best fitting lines for complete (n = 13, dashed) and incomplete
(n = 11, solid) is almost invisible in Fig. 7.2. The best approximations (corresponding to the highest values of F=F C ratio) for the parameter a and V 1 (in
thousands) can be approximated by the following relationships:
Fig. 7.2 Values of parameters a (in (day)
−1
) and V 1 (in thousands) versus values of SIR
parameter N. The data points from Table 7.1 for different countries and regions are shown by
“stars” and “circles” for a and V 1 , respectively: “Triangles” represent data for mainland China and
the Republic of Korea. The best fitting lines are dashed for complete data sets and solid for the data
sets without China and Korea.
94
7 Comparison of the First Waves of the COVID-19 …
a ¼ rN
v
ð7:15Þ
V 1 ¼ dN
g
ð7:16Þ
which correspond to the straight lines in the logarithmic scale. For this purpose, we
can use the method presented in Chap. 2, if we substitute in (2.3) y by ln a and
ln V 1 for (7.15) and (7.16), respectively. Accordingly, the variable t has to be
substituted by ln N ; parameter c—by v and g for (7.15) and (7.16), respectively;
parameter b—by ln r and ln d for (7.15) and (7.16), respectively. Then we can
calculate the values y j and t j with the use of data set presented in Table 7.1 and the
linear regression (formulas (2.6)–(2.9)). The results of calculations are shown in
Table 7.3 for different amount of elements in the data sets (n = 13 for complete data
set and n = 11 for the data set without figures for China and Korea). Corresponding
straight lines are shown in Fig. 7.2 (solid for n = 11 and dashed for n = 13).
Table 7.3 and Fig. 7.2 demonstrate that both complete (n = 13) and incomplete
(n = 11) data sets from Table 7.1 support the hypotheses about functional connections (7.15) and (7.16). In comparison with Table 7.2, the values of parameters
r, F, v, g, r and d are very close and figures for r
j j and F=F C are higher The
difference in best fitting lines for complete (n = 13, dashed) and incomplete
(n = 11, solid) is almost invisible in Fig. 7.2. The best approximations (corresponding to the highest values of F=F C ratio) for the parameter a and V 1 (in
thousands) can be approximated by the following relationships:
Fig. 7.2 Values of parameters a (in (day)
−1
) and V 1 (in thousands) versus values of SIR
parameter N. The data points from Table 7.1 for different countries and regions are shown by
“stars” and “circles” for a and V 1 , respectively: “Triangles” represent data for mainland China and
the Republic of Korea. The best fitting lines are dashed for complete data sets and solid for the data
sets without China and Korea.
94
7 Comparison of the First Waves of the COVID-19 …