amount of people who are on the housing ladder by a certain age, or
the chance your bus has arrived after a certain time waiting, we’ll get
a similar picture.
Independent happenings are a natural starting point, but things get
more interesting when events are contagious. Ross called these
types of events ‘dependent happenings’, because what happens to
one person depends on how many others are currently affected. The
simplest type of outbreak is one where affected people pass the
condition on to others, and once affected, people remain so. In this
situation, the happening will gradually permeate through the
population. Ross noted that such epidemics would follow the shape of
a ‘long-drawn-out letter S’. The number of people affected grows
exponentially at first, with the number of new cases rising faster and
faster over time. Eventually, this growth slows down and levels off.
Illustrative example of the S-shaped growth of a dependent
happening, based on Ross’s model. The plot shows the growth of a
more contagious and less contagious happeningThe assumption that people remain affected indefinitely doesn’t
usually apply to infectious diseases, because people may recover,
receive treatment, or die from the infection. But it can capture other
kinds of spread. The S-shaped curve would later become popular in
sociology, after Everett Rogers featured it in his 1962 book Diffusion