When we talk about online contagion, it’s tempting to focus only on
things that have become popular. However, this ignores the fact that
the vast majority of things do not take off. The Microsoft team found
that around 95 per cent of Twitter cascades consisted of a single
tweet that nobody else shared. Of the remaining cascades, most
didn’t go any further than one additional step in terms of sharing. The
same is true of other online platforms: it’s extremely rare to get
something that spreads, and even when it does, it doesn’t spread
beyond a few generations of transmission. Most content just isn’t that
contagious.[41]
I , we looked at outbreaks of shootings in
Chicago, where transmission generally ended after a small number of
events. Several diseases also stumble and stutter in human
populations like this. For example, strains of bird flu like H5N1 and
H7N9 have caused large outbreaks in poultry, but don’t spread well
among people (at least, not for the moment).
What sort of outbreaks should we expect if something doesn’t
spread very effectively? We’ve already looked at how we can use the
reproduction number, R, to assess whether an infectious disease has
the potential to spread or not; if R is above the critical value of one,
there is potential for a large epidemic to occur. But even if R is below
one, there’s still a chance an infected person will pass the disease on
to someone else. It might be unlikely, but it’s possible. Unless the
reproduction number is zero, we should therefore expect to get some
secondary cases occasionally. These new cases may generate
further generations of infection before the outbreak eventually stutters
to an end.
If we know the reproduction number of a stuttering infection, can
we predict how big an outbreak will be on average? It turns out that
we can, thanks to a handy piece of mathematics. As well as
becoming a crucial part of outbreak analysis, it’s an idea that would
shape how Jonah Peretti and Duncan Watts approached viral
marketing in the early days of Buzzfeed.[42]
Suppose an outbreak starts with one infectious person. By
definition, this first case will generate R secondary cases on average.