conclude that the beginning of the second wave of the epidemic in the UK occurred
in late April, but the corresponding values of the first derivative dV/dt (“triangles”
in Fig. 8.3) were quite high, which reduced the accuracy of SIR simulation. The
corresponding value of relative error e = 33.4% (see Table 6.16) is lower than for
Ukraine, but much higher than for the EU countries. The next epidemic waves in
the UK probably started in early August, September, and October.
The number of accumulated cases in USA (reported to WHO on May 8) was
lower than on May 9. The same incorrectness occurred between May 18 and 19. For
dates: July 17–18 and July 24–25, the numbers of cases was the same (no increase).
All these irregularities are visible in Fig. 8.4 (in particular, there are very high
values of the second derivative (“stars”). Neglecting them, we can conclude that the
beginning of the second epidemic wave in USA occurred on April 21, with the very
high values of the first derivative dV/dt (in comparison with the highest level in
early April, see “triangles” in Fig. 8.4). The period taken for SIR simulations (T c :
April 9–29, 2020, see Table 6.17) covers days from both the first and second
waves.
These facts have reduced the accuracy of the simulation (e = 78.2%). The final
day of the first pandemic wave in USA was estimated to occur on September 23,
2020 (later than in the EU countries, see Table 7.6). Between April 21 and this date,
at least six changes in epidemic dynamics are visible in Fig. 8.4. This fact also
reduced the accuracy of prediction presented in Table 6.17 which is valid for the
first wave only. Unfortunately, a new severe wave has started in USA in
mid-October (see last “star” in Fig. 8.4).
The number of accumulated cases in Spain (reported to WHO) was very
irregular in periods April 24–May 5; May 24–25; July 3–5: July 10–12; July 31–
August 2 and August 7–10 (there were no monotonic increase). These irregularities
are visible in Fig. 8.5 (in particular, there are some negative values of the first
derivative (“triangles”)). Neglecting them, we can conclude that the beginning of a
weak second wave of the epidemic in Spain occurred in mid-April, with not very
high values of the first derivative dV/dt (in comparison with the highest level in late
March, see “triangles” in Fig. 8.5). In June, the values of the first derivative were
much closer to zero which testifies to the successful overcoming of the first severe
epidemic wave in Spain. Nevertheless in July, the first derivative (and the daily
increase in the number of cases) began to increase very fast, and Spain was the first
EU country to cross the 1 million registered cases.
We have used the period T c : March 29–April 18 (which corresponds to the first
wave), to calculate the second prediction for Spain and have obtained very high
accuracy e = 12.2% (see Table 6.13). The predicted value of t final (corresponding to
July 7) agrees with the nature of the epidemic dynamics, which is characterized by
very low values of the new daily number of cases (first derivative dV/dt) until early
July 2020 (see “triangles in Fig. 8.5). As of July 7, the average value of dV/dt can
be estimated with the use of accumulated numbers of cases 249271 (June 30) and
255953 (July 13). The result is 514 new cases per day. According to (4.11) and
(4.17):
8 Identification of the New Waves of the COVID-19 Pandemic
119
in late April, but the corresponding values of the first derivative dV/dt (“triangles”
in Fig. 8.3) were quite high, which reduced the accuracy of SIR simulation. The
corresponding value of relative error e = 33.4% (see Table 6.16) is lower than for
Ukraine, but much higher than for the EU countries. The next epidemic waves in
the UK probably started in early August, September, and October.
The number of accumulated cases in USA (reported to WHO on May 8) was
lower than on May 9. The same incorrectness occurred between May 18 and 19. For
dates: July 17–18 and July 24–25, the numbers of cases was the same (no increase).
All these irregularities are visible in Fig. 8.4 (in particular, there are very high
values of the second derivative (“stars”). Neglecting them, we can conclude that the
beginning of the second epidemic wave in USA occurred on April 21, with the very
high values of the first derivative dV/dt (in comparison with the highest level in
early April, see “triangles” in Fig. 8.4). The period taken for SIR simulations (T c :
April 9–29, 2020, see Table 6.17) covers days from both the first and second
waves.
These facts have reduced the accuracy of the simulation (e = 78.2%). The final
day of the first pandemic wave in USA was estimated to occur on September 23,
2020 (later than in the EU countries, see Table 7.6). Between April 21 and this date,
at least six changes in epidemic dynamics are visible in Fig. 8.4. This fact also
reduced the accuracy of prediction presented in Table 6.17 which is valid for the
first wave only. Unfortunately, a new severe wave has started in USA in
mid-October (see last “star” in Fig. 8.4).
The number of accumulated cases in Spain (reported to WHO) was very
irregular in periods April 24–May 5; May 24–25; July 3–5: July 10–12; July 31–
August 2 and August 7–10 (there were no monotonic increase). These irregularities
are visible in Fig. 8.5 (in particular, there are some negative values of the first
derivative (“triangles”)). Neglecting them, we can conclude that the beginning of a
weak second wave of the epidemic in Spain occurred in mid-April, with not very
high values of the first derivative dV/dt (in comparison with the highest level in late
March, see “triangles” in Fig. 8.5). In June, the values of the first derivative were
much closer to zero which testifies to the successful overcoming of the first severe
epidemic wave in Spain. Nevertheless in July, the first derivative (and the daily
increase in the number of cases) began to increase very fast, and Spain was the first
EU country to cross the 1 million registered cases.
We have used the period T c : March 29–April 18 (which corresponds to the first
wave), to calculate the second prediction for Spain and have obtained very high
accuracy e = 12.2% (see Table 6.13). The predicted value of t final (corresponding to
July 7) agrees with the nature of the epidemic dynamics, which is characterized by
very low values of the new daily number of cases (first derivative dV/dt) until early
July 2020 (see “triangles in Fig. 8.5). As of July 7, the average value of dV/dt can
be estimated with the use of accumulated numbers of cases 249271 (June 30) and
255953 (July 13). The result is 514 new cases per day. According to (4.11) and
(4.17):
8 Identification of the New Waves of the COVID-19 Pandemic
119