As noted in the previous chapters, the applied approach can describe only the
first wave of the epidemic and does not take into account imported cases, so to
assess its accuracy e, we can use information on the accumulated number of cases
V f recorded in the day, which corresponds to t final , and formula (4.20). The corresponding values are shown in Table 6.2 and demonstrate that the accuracy of both
predictions are rather good (e = 7.8% and 15.3%), but the discrepancy of the
second prediction for China was lower (e ¼ 3:8%).
As of September 26, 2020, the number of cases in South Korea was 23,611 [52].
It means that for 4.5 months of observation of the epidemic (after the publication of
the second prediction in [75]), the revealed exceeding the forecast level was only
1.18 times. Thus, both predictions for the final sizes of the COVID-19 epidemic in
Korea were not bad, especially if we take into account that the used SIR model
supposes the constant values of its parameters (in particular, zero number of
imported cases). Later, we will discuss how to take into account changes in the SIR
model parameters and increase the accuracy of predictions.
6.3 Italy
In this section, we consider the first wave of the COVID-19 epidemic in Italy. The
results of comparison with the second prediction for mainland China and several
SIR simulations will be presented.
Dramatic situation in Italy in March–June 2020 forced to pay much attention to
the pandemic dynamics in this country. The first study is already described in
Chap. 3. It concerns the comparison of the number of cases in Italy with the number
of cases W j in China available in Table 1.2. Due to the fact that the Chinese data
were incomplete by February 10, 2020 (see [2, 42, 43, 67]), there was a need for a
new comparison of the dynamics in these two countries. After the publication of the
results of the second forecast for China [69], it became possible to compare the
resulting V(t) curve with the number of cases registered in Italy immediately after
the outbreak (available in Table 3.1).
Since the epidemics in these countries started at different times, it was necessary
to make time synchronization (see [50]). Let us suppose that the epidemic outbreak
in Italy happened on March 22, 2020 (the cumulative number of cases in this
country was 76; see Table 3.1). The time moment t s corresponding to the number of
victims V = 76 was calculated with the optimal values of parameters for the second
prediction for mainland China available in Table 6.1. The result t s = −15.82545
means that all the corresponding time moments for the data set for Italy have to be
shifted by the value 52.82545, since March 22 corresponds to the time moment
t j = 37 (see Table 1.2, where zero t j value corresponds to January 16, 2020). The
“stars” in Fig. 6.8 represent the accumulated number of confirmed cases in Italy
with the corresponding time shift. The line shows the V = I + R values corresponding to the second prediction for China (see Table 6.1 and Fig. 6.4).
46
6 SIR Simulations for the First Waves of the COVID-19 …
first wave of the epidemic and does not take into account imported cases, so to
assess its accuracy e, we can use information on the accumulated number of cases
V f recorded in the day, which corresponds to t final , and formula (4.20). The corresponding values are shown in Table 6.2 and demonstrate that the accuracy of both
predictions are rather good (e = 7.8% and 15.3%), but the discrepancy of the
second prediction for China was lower (e ¼ 3:8%).
As of September 26, 2020, the number of cases in South Korea was 23,611 [52].
It means that for 4.5 months of observation of the epidemic (after the publication of
the second prediction in [75]), the revealed exceeding the forecast level was only
1.18 times. Thus, both predictions for the final sizes of the COVID-19 epidemic in
Korea were not bad, especially if we take into account that the used SIR model
supposes the constant values of its parameters (in particular, zero number of
imported cases). Later, we will discuss how to take into account changes in the SIR
model parameters and increase the accuracy of predictions.
6.3 Italy
In this section, we consider the first wave of the COVID-19 epidemic in Italy. The
results of comparison with the second prediction for mainland China and several
SIR simulations will be presented.
Dramatic situation in Italy in March–June 2020 forced to pay much attention to
the pandemic dynamics in this country. The first study is already described in
Chap. 3. It concerns the comparison of the number of cases in Italy with the number
of cases W j in China available in Table 1.2. Due to the fact that the Chinese data
were incomplete by February 10, 2020 (see [2, 42, 43, 67]), there was a need for a
new comparison of the dynamics in these two countries. After the publication of the
results of the second forecast for China [69], it became possible to compare the
resulting V(t) curve with the number of cases registered in Italy immediately after
the outbreak (available in Table 3.1).
Since the epidemics in these countries started at different times, it was necessary
to make time synchronization (see [50]). Let us suppose that the epidemic outbreak
in Italy happened on March 22, 2020 (the cumulative number of cases in this
country was 76; see Table 3.1). The time moment t s corresponding to the number of
victims V = 76 was calculated with the optimal values of parameters for the second
prediction for mainland China available in Table 6.1. The result t s = −15.82545
means that all the corresponding time moments for the data set for Italy have to be
shifted by the value 52.82545, since March 22 corresponds to the time moment
t j = 37 (see Table 1.2, where zero t j value corresponds to January 16, 2020). The
“stars” in Fig. 6.8 represent the accumulated number of confirmed cases in Italy
with the corresponding time shift. The line shows the V = I + R values corresponding to the second prediction for China (see Table 6.1 and Fig. 6.4).
46
6 SIR Simulations for the First Waves of the COVID-19 …