COVID-19), the values of a are higher than for AIDS, for example. Parameter a
accumulates also the frequency of contacts and the way of contacting. Epidemics
used to start at large cities where the average contact rate is much higher than in
small villages. So the COVID-19 epidemic outbreak in densely populated regions
of Italy is not surprising. In order to decrease the value of a, we have to minimize
the number of our contacts and change our contacting habits. For example, we have
to avoid the public places and use masks there, minimize or cancel traveling. We
have to change our contact habits: to avoid handshakes and kisses. First, all these
simple things are very useful to protect yourself. In addition, if the majority of
people will do this jointly, we have chance to diminish the value of parameter a and
reduce the negative effects of the pandemic.
Usually, the parameter q is called the immunization rate. This name is reasonable when there is no isolation and all the sick persons recover. Since the removed
persons number R is the sum of isolated, recovered and dead people, Eq. (4.3)
demonstrates the increase rate for R. So we will call this parameter removing rate.
The inverse value
s ¼
1
q
ð4:4Þ
is the estimation of the average time of spreading the infection. It is not the average
time of the sickness duration. Many people are and will be isolated. They could
remain sick and dangerous, but they cannot spread the infection.
So, we are interested in increasing the value of parameter q and decreasing the
time of spreading the infection 1=q. Public authorities should work on this and
organize immediate isolation of suspicious cases. People with problems do not need
to go to the hospitals themselves and spread the infection on their way. They have
to do their best to minimize spreading the infection. All the people must know how
to contact hot lines, and special brigades have to come and isolate suspicious and
contact persons.
Since the derivative d S þ I þ R
ð
Þ =dt is equal to zero (it follows from summarizing Eqs. (4.1)–(4.3)), the sum
N ¼ S þ I þ R
ð4:5Þ
must be constant for all moments of time and can be treated as the amount of
susceptible persons before the moment t
Ã
1 of the epidemic outbreak, since I ¼ R ¼ 0
at t\t
Ã
1 . It must be noted that the constant N is not the volume of population N pop ,
but only the initial number of persons who are sensitive and not protected to some
specific disease.
Unfortunately, the ratio N
N pop may be very large for the COVID-19 pandemic.
We can see this from the situation with the liner Diamond Princess. The total initial
number of persons on board was 3711; the final cumulative number of confirmed
cases was 741, [52]. It means that the percentage of susceptible can be estimated by
24
4 Classical SIR Model and the Exact …
accumulates also the frequency of contacts and the way of contacting. Epidemics
used to start at large cities where the average contact rate is much higher than in
small villages. So the COVID-19 epidemic outbreak in densely populated regions
of Italy is not surprising. In order to decrease the value of a, we have to minimize
the number of our contacts and change our contacting habits. For example, we have
to avoid the public places and use masks there, minimize or cancel traveling. We
have to change our contact habits: to avoid handshakes and kisses. First, all these
simple things are very useful to protect yourself. In addition, if the majority of
people will do this jointly, we have chance to diminish the value of parameter a and
reduce the negative effects of the pandemic.
Usually, the parameter q is called the immunization rate. This name is reasonable when there is no isolation and all the sick persons recover. Since the removed
persons number R is the sum of isolated, recovered and dead people, Eq. (4.3)
demonstrates the increase rate for R. So we will call this parameter removing rate.
The inverse value
s ¼
1
q
ð4:4Þ
is the estimation of the average time of spreading the infection. It is not the average
time of the sickness duration. Many people are and will be isolated. They could
remain sick and dangerous, but they cannot spread the infection.
So, we are interested in increasing the value of parameter q and decreasing the
time of spreading the infection 1=q. Public authorities should work on this and
organize immediate isolation of suspicious cases. People with problems do not need
to go to the hospitals themselves and spread the infection on their way. They have
to do their best to minimize spreading the infection. All the people must know how
to contact hot lines, and special brigades have to come and isolate suspicious and
contact persons.
Since the derivative d S þ I þ R
ð
Þ =dt is equal to zero (it follows from summarizing Eqs. (4.1)–(4.3)), the sum
N ¼ S þ I þ R
ð4:5Þ
must be constant for all moments of time and can be treated as the amount of
susceptible persons before the moment t
Ã
1 of the epidemic outbreak, since I ¼ R ¼ 0
at t\t
Ã
1 . It must be noted that the constant N is not the volume of population N pop ,
but only the initial number of persons who are sensitive and not protected to some
specific disease.
Unfortunately, the ratio N
N pop may be very large for the COVID-19 pandemic.
We can see this from the situation with the liner Diamond Princess. The total initial
number of persons on board was 3711; the final cumulative number of confirmed
cases was 741, [52]. It means that the percentage of susceptible can be estimated by
24
4 Classical SIR Model and the Exact …