Biology Reference
In-Depth Information
Summary. Before we examine another epidemic model, let us
summarize our results with the SIS model:
1. The average lifetime of an infection is
1
b
:
b
a
>
2. When N
0, the disease remains endemic in the
population.
b
3. When N
a
0, there is no epidemic.
C. The SIR Model
1. Description of the SIR Model
One of the assumptions we made for the SIS model was that, once
recovered, an infective immediately becomes susceptible to the disease.
Although there are certain diseases for which this is nearly true (e.g.,
gonorrhea and syphilis), there are others, such as chicken pox and
measles, for which this assumption is not justified. For these diseases,
individuals who have recovered from the infection have gained
immunity, and the SIS model will not describe such infections
accurately.
The SIR model, on the other hand, assumes that, once recovered, the
person is immune to the disease and is no longer susceptible.
This assumption necessitates a new group being added to the
population—the group of recovered, R. The assumptions for the SIR
model are:
1. The population is fixed. There are no births or deaths, and no one
migrates into or out of the population.
2. There is no incubation period for the disease.
3. As in the SIS model, we assume that the susceptibles and infectives
are uniformly mixed.
4. Once a person has recovered, he or she is permanently immune.
Again, these assumptions describe an idealized situation. As with
the SIS model, we assume that a small number of members of a
population have become sick with an infectious disease. We have three
groups:
S(t)
¼
the number of susceptibles at time t;
I(t)
¼
the number of infectives at time t;
R(t)
¼
the number of recovered at time t.
