estimate the lower and upper limits for the final size of a new wave and its duration
after prediction T s :
1:69 Á V s V i1 2:79 Á V s
ð13:5Þ
2:84
V s
d s
T s 4:39
V s
d s
ð13:6Þ
Estimations (13.5) and (13.6) were applied for new epidemic waves in different
countries and regions. The results of calculations are shown in Table 13.3. To
calculate the values V s and d s , the weekly WHO data for accumulated number of
cases w i were used [1], according to the formulas:
V s %
w i þ w iÀ1
2
;
ð13:7Þ
d s %
w i À w iÀ1
7
ð13:8Þ
The days corresponding w i and w i − 1 were chosen with the use of Figs. 8.1–8.11,
8.13, 8.14 which allows us to detect the beginning of new pandemic waves (sharp
increase in the second derivative of the accumulated number of cases shown by
“stars”). In many countries, we can see the beginning of the new wave in early
October 2020 that is why the days October 4 and October 11 were used in (13.7) and
(13.8). In some countries, the new waves have started earlier. The corresponding days
for South Korea, Spain, Moldova, and Ukraine are shown in Table 13.3. To have a
more recent forecast for Kyiv, we have used the period October 12–17 (corresponding to the beginning of the new wave seen in Fig. 8.14), the daily data set from
Table 8.2 and formulae (13.1) and (13.2). The predicted lower and upper limits of the
final sizes V i1 were compared with the real figures for accumulated numbers of cases
V j as of October 31, 2020 [1] (November 9, 2020, was used for Kyiv [95, 96]).
The results of calculations are presented in Table 13.3. It can be seen that V j
values exceed the upper limit of V i1 only in the case of Spain, but the period of
observations was 9 weeks for this country (in comparison with 3–5 weeks for other
countries and regions). It must be noted that V j number in South Korea did not
exceed even the lower limit of V i1 after 10 weeks of observations. The results of
the calculations allow us to conclude that formula (13.5) yields adequate forecasts
of the number of cases for a fairly long period, provided that the nature of the
pandemic will be as at the beginning of the corresponding wave. Some European
countries have tightened quarantines in November 2020, so we hope that the
numbers of cases will not exceed the upper limits shown in Table 13.3 for a long
time. Otherwise, new estimates should be made using the simulations proposed in
Chaps. 9 and 10 or formulas (13.5) and (13.6).
The pandemic duration projections presented in Table 13.3 are unfortunately not
optimistic. None of the countries will overcome the current wave of the epidemic in
2020. In Germany and Italy, it can last until the autumn of 2021, and in USA until
158
13 Long-Time Predictions for the Pandemic Dynamics
after prediction T s :
1:69 Á V s V i1 2:79 Á V s
ð13:5Þ
2:84
V s
d s
T s 4:39
V s
d s
ð13:6Þ
Estimations (13.5) and (13.6) were applied for new epidemic waves in different
countries and regions. The results of calculations are shown in Table 13.3. To
calculate the values V s and d s , the weekly WHO data for accumulated number of
cases w i were used [1], according to the formulas:
V s %
w i þ w iÀ1
2
;
ð13:7Þ
d s %
w i À w iÀ1
7
ð13:8Þ
The days corresponding w i and w i − 1 were chosen with the use of Figs. 8.1–8.11,
8.13, 8.14 which allows us to detect the beginning of new pandemic waves (sharp
increase in the second derivative of the accumulated number of cases shown by
“stars”). In many countries, we can see the beginning of the new wave in early
October 2020 that is why the days October 4 and October 11 were used in (13.7) and
(13.8). In some countries, the new waves have started earlier. The corresponding days
for South Korea, Spain, Moldova, and Ukraine are shown in Table 13.3. To have a
more recent forecast for Kyiv, we have used the period October 12–17 (corresponding to the beginning of the new wave seen in Fig. 8.14), the daily data set from
Table 8.2 and formulae (13.1) and (13.2). The predicted lower and upper limits of the
final sizes V i1 were compared with the real figures for accumulated numbers of cases
V j as of October 31, 2020 [1] (November 9, 2020, was used for Kyiv [95, 96]).
The results of calculations are presented in Table 13.3. It can be seen that V j
values exceed the upper limit of V i1 only in the case of Spain, but the period of
observations was 9 weeks for this country (in comparison with 3–5 weeks for other
countries and regions). It must be noted that V j number in South Korea did not
exceed even the lower limit of V i1 after 10 weeks of observations. The results of
the calculations allow us to conclude that formula (13.5) yields adequate forecasts
of the number of cases for a fairly long period, provided that the nature of the
pandemic will be as at the beginning of the corresponding wave. Some European
countries have tightened quarantines in November 2020, so we hope that the
numbers of cases will not exceed the upper limits shown in Table 13.3 for a long
time. Otherwise, new estimates should be made using the simulations proposed in
Chaps. 9 and 10 or formulas (13.5) and (13.6).
The pandemic duration projections presented in Table 13.3 are unfortunately not
optimistic. None of the countries will overcome the current wave of the epidemic in
2020. In Germany and Italy, it can last until the autumn of 2021, and in USA until
158
13 Long-Time Predictions for the Pandemic Dynamics