the above formulas, so to assess the accuracy of the calculations of the first epidemic waves in different countries, we can offer the following formula:
e ¼
V f À V 1
V f
ð4:20Þ
where V f is the real accumulated number of cases registered at day corresponding to
t final .
Indeed, the presented theory only states that for the invariant characteristics of
the epidemic (N, m, a, t
Ã
1 ) during the time after T c to t final , the real number of cases at
time moment t final should be equal to the calculated value of V 1 . Therefore, we
have the right to compare V f and V 1 . Equation (4.20) is a characteristic not only of
the accuracy of the theory, but also an assessment of the fact that in the period after
T c to t final the characteristics of the epidemic changed insignificantly (e.g., the
quarantine conditions or social behavior changed little). Chapter 6 will provide
examples of the application of the SIR model and calculations of the relative error e
with the use of formula (4.20) for many countries and regions and will discuss the
reasons for small and large discrepancies between forecasts and actual observations.
As long as there are infected people in the population, there is a chance to meet
one of them. The corresponding probability can be estimated with the use of simple
formula:
p t
ð Þ ¼
I t
ð Þ
N pop
ð4:21Þ
where N pop is the volume of population. With the use of corresponding SIR curves,
it is possible to estimate p(t) for every moment of time. Formula (4.21) can be
useful for deciding which countries’ citizens are welcome guests after the
resumption of international passenger traffic. 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.
In April–July 2020, the quarantine weakening and its strengthening in
September–October 2020 have become urgent in many countries. The SIR I
(t) curves can be used to assess their feasibility. For example, number of infected
persons in Kyiv (some of them may feel completely healthy or have mild symptoms) was estimated by 100 on May 11, 2020 [73, 74]. It means that the probability
to meet such person was rather low (p % 3; 4 Â 10
À5 ). But if you have M contacts,
the probability of meeting at least one infected person increases according to the
formula:
P ¼ 1 À 1 À p
ð
Þ
M % pM
ð4:22Þ
Therefore, a person on duty in the subway or a bus driver is quite likely to meet
an infected person during, for example, 15 days of work. Meeting an infected
4 Classical SIR Model and the Exact …
29
e ¼
V f À V 1
V f
ð4:20Þ
where V f is the real accumulated number of cases registered at day corresponding to
t final .
Indeed, the presented theory only states that for the invariant characteristics of
the epidemic (N, m, a, t
Ã
1 ) during the time after T c to t final , the real number of cases at
time moment t final should be equal to the calculated value of V 1 . Therefore, we
have the right to compare V f and V 1 . Equation (4.20) is a characteristic not only of
the accuracy of the theory, but also an assessment of the fact that in the period after
T c to t final the characteristics of the epidemic changed insignificantly (e.g., the
quarantine conditions or social behavior changed little). Chapter 6 will provide
examples of the application of the SIR model and calculations of the relative error e
with the use of formula (4.20) for many countries and regions and will discuss the
reasons for small and large discrepancies between forecasts and actual observations.
As long as there are infected people in the population, there is a chance to meet
one of them. The corresponding probability can be estimated with the use of simple
formula:
p t
ð Þ ¼
I t
ð Þ
N pop
ð4:21Þ
where N pop is the volume of population. With the use of corresponding SIR curves,
it is possible to estimate p(t) for every moment of time. Formula (4.21) can be
useful for deciding which countries’ citizens are welcome guests after the
resumption of international passenger traffic. 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.
In April–July 2020, the quarantine weakening and its strengthening in
September–October 2020 have become urgent in many countries. The SIR I
(t) curves can be used to assess their feasibility. For example, number of infected
persons in Kyiv (some of them may feel completely healthy or have mild symptoms) was estimated by 100 on May 11, 2020 [73, 74]. It means that the probability
to meet such person was rather low (p % 3; 4 Â 10
À5 ). But if you have M contacts,
the probability of meeting at least one infected person increases according to the
formula:
P ¼ 1 À 1 À p
ð
Þ
M % pM
ð4:22Þ
Therefore, a person on duty in the subway or a bus driver is quite likely to meet
an infected person during, for example, 15 days of work. Meeting an infected
4 Classical SIR Model and the Exact …
29