possible to estimate p(t) for every moment of time. For example, on July 19, 2020,
these probabilities can be estimated as 1:04 Â 10
À4 and 9:28 Â 10
À5 for Ukraine
and the world, respectively. It means that Ukraine was 12% more dangerous in
comparison with the average situation in the world.
Formula (4.21) can be useful for deciding which countries’ citizens are welcome
guests. If p A ðtÞ [ p B ðtÞ for countries A and B, citizens of A are not welcome guests
in country B at the moment of time t. Since such decisions are very important, we
will propose some simple method of estimating p(t) without calculations of SIR
parameters for epidemic waves in a country. According to (9.11):
I ¼
1
a i S
dV
dt
ð12:1Þ
Since function S(t) changes not very sufficient during a wave (compare initial
S i = N i – I i – R i and final S i1 values of this function in Tables 12.1 and 12.2 and in
corresponding Tables in Chaps. 10 and 11), we can use the constant value S i instead
of S(t). To estimate dV/dt, it is possible to use Eqs. (8.2) or (8.4). Finally, with the
use of (12.1), Eq. (4.21) can be written as follows:
pðtÞ % k p
dV
dt
;
ð12:2Þ
k p ¼
1
S i a i N pop
ð12:3Þ
The results of calculations for different countries and regions are presented in
Table 12.3. It can be seen that coefficient k p changes not very fast (compare values
on different days for Ukraine and the world). It means that values of this coefficient
can be used during rather long period of time before new exact estimations of I
(t) will be available. According to Eq. (12.2), the probability of meeting an infected
person mostly depends on the daily increase in the number of cases. The values
p are estimated for July 19, 2020, and presented in Table 12.3.
The p value for the fourth wave in Ukraine is 20% lower than the exact estimation 1:04 Â 10
À4 calculated before with the use of Eq. (4.21). In the case of the
world fifth wave, the difference between the exact estimation (4.21) and the
approximate formulas (12.2) and (12.3) is only 8%. It can be seen that the most
infected country was USA. The average global figure was approximately 4 times
less. The probabilities p in Kyiv, Moldova and Ukraine were around the world
average value. Lower figures were calculated for Spain and the UK. As of July 19,
2020, the safest counties were Italy, France, Austria, and Germany.
The effective reproduction number R ti (t) can be estimated using Eq. (11.1)
and constant value S i = N i – I i – R i instead of S(t). The results are shown in the last
column of Table 12.3. It can be seen that France, Italy, Germany, and Austria had
the lowest values of R ti which are close to the world figure (wave 5). Not much
higher values were calculated for USA and Ukraine (wave 4). Spain, the UK,
150
12 Global Waves of the COVID-19 Pandemic
these probabilities can be estimated as 1:04 Â 10
À4 and 9:28 Â 10
À5 for Ukraine
and the world, respectively. It means that Ukraine was 12% more dangerous in
comparison with the average situation in the world.
Formula (4.21) can be useful for deciding which countries’ citizens are welcome
guests. If p A ðtÞ [ p B ðtÞ for countries A and B, citizens of A are not welcome guests
in country B at the moment of time t. Since such decisions are very important, we
will propose some simple method of estimating p(t) without calculations of SIR
parameters for epidemic waves in a country. According to (9.11):
I ¼
1
a i S
dV
dt
ð12:1Þ
Since function S(t) changes not very sufficient during a wave (compare initial
S i = N i – I i – R i and final S i1 values of this function in Tables 12.1 and 12.2 and in
corresponding Tables in Chaps. 10 and 11), we can use the constant value S i instead
of S(t). To estimate dV/dt, it is possible to use Eqs. (8.2) or (8.4). Finally, with the
use of (12.1), Eq. (4.21) can be written as follows:
pðtÞ % k p
dV
dt
;
ð12:2Þ
k p ¼
1
S i a i N pop
ð12:3Þ
The results of calculations for different countries and regions are presented in
Table 12.3. It can be seen that coefficient k p changes not very fast (compare values
on different days for Ukraine and the world). It means that values of this coefficient
can be used during rather long period of time before new exact estimations of I
(t) will be available. According to Eq. (12.2), the probability of meeting an infected
person mostly depends on the daily increase in the number of cases. The values
p are estimated for July 19, 2020, and presented in Table 12.3.
The p value for the fourth wave in Ukraine is 20% lower than the exact estimation 1:04 Â 10
À4 calculated before with the use of Eq. (4.21). In the case of the
world fifth wave, the difference between the exact estimation (4.21) and the
approximate formulas (12.2) and (12.3) is only 8%. It can be seen that the most
infected country was USA. The average global figure was approximately 4 times
less. The probabilities p in Kyiv, Moldova and Ukraine were around the world
average value. Lower figures were calculated for Spain and the UK. As of July 19,
2020, the safest counties were Italy, France, Austria, and Germany.
The effective reproduction number R ti (t) can be estimated using Eq. (11.1)
and constant value S i = N i – I i – R i instead of S(t). The results are shown in the last
column of Table 12.3. It can be seen that France, Italy, Germany, and Austria had
the lowest values of R ti which are close to the world figure (wave 5). Not much
higher values were calculated for USA and Ukraine (wave 4). Spain, the UK,
150
12 Global Waves of the COVID-19 Pandemic