Chapter 5
Statistics-Based Procedure of Parameter
Identification for the Classical SIR
Model
The procedure of the SIR parameter identification and examples of calculations are
presented.
In the case of a new epidemic, the values of four independent parameters
N; m; a; t
Ã
1 of SIR model are unknown and must be identified with the use of
limited data sets. A statistics-based approach was developed in [35] and used in [38,
50, 66–78] to estimate the values of these unknown parameters for different
countries and regions. The essence of the method is to use observations of
the number of victims V j corresponding to the moments of time t j to calculate
F 1j ¼ F
Ã
1 ðV j ; N; mÞ for every fixed values N and m with the use of (4.14) and then to
check how the registered points fit the straight line (4.13).
Equation (4.13) can be rewritten as follows:
y F
Ã
1 ðV; N; mÞ ¼ at À at
Ã
1
ð5:1Þ
Equation (5.1) coincides with (2.3) if we assume
a ¼ c; b ¼ Àat
Ã
1
ð5:2Þ
As in Chap. 2, we can estimate the values of parameters c and b, by treating the
values y j F
Ã
1 ðV j ; N; mÞ and corresponding time moments t j as random variables
and use the observations of the accumulated number of cases (e.g., presented in
Table 5.1) and the linear regression [33] in order to calculate the coefficients c
_ and
b
_
of the regression line
y
_ ¼ c
_ t þ b
_
ð5:3Þ
using the standard formulas (2.6) and (2.7). Values c
_ and b
_
can be treated as
statistics-based estimations of parameters c and b from relationships (2.3). Then the
estimations for parameters a, t
Ã
1 can be easily recalculated using (5.2).
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
I. Nesteruk, COVID-19 Pandemic Dynamics,
https://doi.org/10.1007/978-981-33-6416-5_5
33
Statistics-Based Procedure of Parameter
Identification for the Classical SIR
Model
The procedure of the SIR parameter identification and examples of calculations are
presented.
In the case of a new epidemic, the values of four independent parameters
N; m; a; t
Ã
1 of SIR model are unknown and must be identified with the use of
limited data sets. A statistics-based approach was developed in [35] and used in [38,
50, 66–78] to estimate the values of these unknown parameters for different
countries and regions. The essence of the method is to use observations of
the number of victims V j corresponding to the moments of time t j to calculate
F 1j ¼ F
Ã
1 ðV j ; N; mÞ for every fixed values N and m with the use of (4.14) and then to
check how the registered points fit the straight line (4.13).
Equation (4.13) can be rewritten as follows:
y F
Ã
1 ðV; N; mÞ ¼ at À at
Ã
1
ð5:1Þ
Equation (5.1) coincides with (2.3) if we assume
a ¼ c; b ¼ Àat
Ã
1
ð5:2Þ
As in Chap. 2, we can estimate the values of parameters c and b, by treating the
values y j F
Ã
1 ðV j ; N; mÞ and corresponding time moments t j as random variables
and use the observations of the accumulated number of cases (e.g., presented in
Table 5.1) and the linear regression [33] in order to calculate the coefficients c
_ and
b
_
of the regression line
y
_ ¼ c
_ t þ b
_
ð5:3Þ
using the standard formulas (2.6) and (2.7). Values c
_ and b
_
can be treated as
statistics-based estimations of parameters c and b from relationships (2.3). Then the
estimations for parameters a, t
Ã
1 can be easily recalculated using (5.2).
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
I. Nesteruk, COVID-19 Pandemic Dynamics,
https://doi.org/10.1007/978-981-33-6416-5_5
33