or
a aN pop ¼ 0:0002401N
À0:2049
pop
ð7:4Þ
The relative final size of the first epidemic wave V 1 can be approximated by
following equations:
V 1
V 1
N pop
¼ 0:0018546N
À0:11
pop
ð7:5Þ
V 1
V 1
N pop
¼ 0:0013101N
0:0778
pop
ð7:6Þ
for complete (n = 13) and incomplete (n = 11) data sets, respectively.
The proposed relative values are very weakly dependent on the size of the
population (see (7.3)–(7.6)), so they can be used in the system of differential
Eqs. (4.1)–(4.3), which takes the following form:
d S
dt
¼ À a S I
ð7:7Þ
d I
dt
¼ a S I À q I
ð7:8Þ
d
R
dt
¼ q I
ð7:9Þ
Table 7.2 Optimal values of parameters in Eqs. (7.1) and (7.2), correlation coefficients (2.7) and
the results of Fisher test application
No. No. of
Eq.
n
Correlation
coefficient
r, Eq. (2.8)
Optimal
values of
parameters
v or η in
(7.1) or
(7.2)
Optimal
values of
parameters
a or d in
(7.1) or
(7.2)
Experimental
value of the
Fisher
function F,
Eq. (2.9),
m = 2
Critical
value of
Fisher
Function
F c (1,
n − 2) for
the
confidence
level
0.001, [34]
F/
F c
1.
(7.2)
13
0.8368
0.8900
1.8546
25.6897
20.3
1.27
2.
(7.1)
13 −0.8240
−0.9625
0.0001466
23.2684
20.3
1.15
3.
(7.2)
11
0.9532
1.0778
1.3101
89.5132
22.9
3.91
4.
(7.1)
11 −0.9692
−1.2049
0.0002401
139.1859
22.9
6.08
92
7 Comparison of the First Waves of the COVID-19 …