Given the names of the three groups, this is commonly known as
the ‘SIR model’. Say a single influenza case arrives in a population of
10,000 people. If we simulate a flu-like epidemic using the SIR model,
we get the following pattern:
Simulated influenza outbreak using the SIR modelThe simulated epidemic takes a while to grow because only one
person is infectious at the start, but it still peaks within fifty days. And
by eighty days, it’s all but over. Notice that at the end of the epidemic,
there are still some susceptible people left. If everyone had been
infected, then all 10,000 people would have eventually ended up in
the ‘recovered’ group. Kermack and McKendick’s model suggests
that this doesn’t happen: outbreaks can end before everyone picks up
the infection. ‘An epidemic, in general, comes to an end before the
susceptible population has been exhausted,’ as they put it.