We have also calculated the duration of the epidemic wave T s in days after
moment of time t
Ã
s according to the equation:
T s ¼ t if À t
Ã
s
ð13:3Þ
and corresponding dimensionless characteristics:
D p ¼
T s d s
V s
ð13:4Þ
These values and characteristics d s =V s and V i1 =V s are also presented in
Table 13.2.
Figure 13.2 illustrates the results of calculations versus time. The values of
characteristics are shown at the moments of time t
Ã
s for Ukraine (small markers) and
the world (large markers). It can be seen that the values of parameters: D p
(“squares”), V i1 =V s (“crosses”) and d s =V s (“stars”) are rather close for the epidemic
waves which occurred after July 1, 2020. The same picture we can see in Fig. 13.3
showing the values of the dimensionless final size of the ith wave V i1 =V s
(“circles”) and duration after prediction T s (Eq. (13.3), “stars”) versus dimensionless parameter D p calculated for pandemic waves in Ukraine (small markers) and
the world (large markers).
If we are interested in long-term forecasts of the pandemic dynamics after
September 2020, it is worth taking into account the values of the parameters
obtained after July 1, 2020. Then, Table 13.2 and Figs. 13.2 and 13.3 allow us to
determine the limits for the dimensionless parameters V i1 =V s and D p and to
Table 13.2 Characteristics of the COVID-19 pandemic waves in Ukraine and the world
Country or
region, number of
wave (prediction)
Day used
for
calculations
t
Ã
s
V s ,
Eq. (13.1)
d s ,
Eq. (13.2)
d s =V s
V i1 =V s T s (days),
Eq. (13.3)
D p ,
Eq. (13.4)
Ukraine, wave 1
(prediction 8)
May 7
14,194
474.5 0.0334 2.00
156.9
5.25
Ukraine, wave 2
May 21
20,110
381.2 0.0190 3.03
409.9
7.77
Ukraine, wave 3
June 13
31,143
703.3 0.0226 2.28
193.5
4.37
Ukraine, wave 4
July 7
50,505
737.6 0.0146 1.84
252.7
3.69
Ukraine, wave 5
July 24
63,811
929.4 0.0146 2.02
195
2.84
Ukraine, wave 6
August 13
87,939
1,584.6 0.0180 2.79
237.5
4.28
Ukraine, wave 7
October 5
235,459
4,773.0 0.0203 1.69
173
3.51
World, wave 1
(prediction 2)
May 2
3,346,376
8,2258.1 0.0246 2.08
312.5
7.68
World, wave 2
May 16
4,525,359
90,255.6 0.0120 4.51
632.5
12.61
World, wave 3
June 1
6,177,809 119,995.4 0.0194 2.50
519.3
10.09
World, wave 4
June 17
8,241,160 146,738.7 0.0178 2.77
451
8.03
World, wave 5
July 9
12,112,797 207,501.7 0.0171 1.72
256.2
4.39
156
13 Long-Time Predictions for the Pandemic Dynamics
moment of time t
Ã
s according to the equation:
T s ¼ t if À t
Ã
s
ð13:3Þ
and corresponding dimensionless characteristics:
D p ¼
T s d s
V s
ð13:4Þ
These values and characteristics d s =V s and V i1 =V s are also presented in
Table 13.2.
Figure 13.2 illustrates the results of calculations versus time. The values of
characteristics are shown at the moments of time t
Ã
s for Ukraine (small markers) and
the world (large markers). It can be seen that the values of parameters: D p
(“squares”), V i1 =V s (“crosses”) and d s =V s (“stars”) are rather close for the epidemic
waves which occurred after July 1, 2020. The same picture we can see in Fig. 13.3
showing the values of the dimensionless final size of the ith wave V i1 =V s
(“circles”) and duration after prediction T s (Eq. (13.3), “stars”) versus dimensionless parameter D p calculated for pandemic waves in Ukraine (small markers) and
the world (large markers).
If we are interested in long-term forecasts of the pandemic dynamics after
September 2020, it is worth taking into account the values of the parameters
obtained after July 1, 2020. Then, Table 13.2 and Figs. 13.2 and 13.3 allow us to
determine the limits for the dimensionless parameters V i1 =V s and D p and to
Table 13.2 Characteristics of the COVID-19 pandemic waves in Ukraine and the world
Country or
region, number of
wave (prediction)
Day used
for
calculations
t
Ã
s
V s ,
Eq. (13.1)
d s ,
Eq. (13.2)
d s =V s
V i1 =V s T s (days),
Eq. (13.3)
D p ,
Eq. (13.4)
Ukraine, wave 1
(prediction 8)
May 7
14,194
474.5 0.0334 2.00
156.9
5.25
Ukraine, wave 2
May 21
20,110
381.2 0.0190 3.03
409.9
7.77
Ukraine, wave 3
June 13
31,143
703.3 0.0226 2.28
193.5
4.37
Ukraine, wave 4
July 7
50,505
737.6 0.0146 1.84
252.7
3.69
Ukraine, wave 5
July 24
63,811
929.4 0.0146 2.02
195
2.84
Ukraine, wave 6
August 13
87,939
1,584.6 0.0180 2.79
237.5
4.28
Ukraine, wave 7
October 5
235,459
4,773.0 0.0203 1.69
173
3.51
World, wave 1
(prediction 2)
May 2
3,346,376
8,2258.1 0.0246 2.08
312.5
7.68
World, wave 2
May 16
4,525,359
90,255.6 0.0120 4.51
632.5
12.61
World, wave 3
June 1
6,177,809 119,995.4 0.0194 2.50
519.3
10.09
World, wave 4
June 17
8,241,160 146,738.7 0.0178 2.77
451
8.03
World, wave 5
July 9
12,112,797 207,501.7 0.0171 1.72
256.2
4.39
156
13 Long-Time Predictions for the Pandemic Dynamics