In contrast to the rates and thresholds used by Kermack and
McKendrick, R is a more intuitive – and general – way to think about
contagion. It simply asks: how many people would we expect a case
to pass the infection on to? As we shall see in later chapters, it’s an
idea that we can apply to a wide range of outbreaks, from gun
violence to online memes.
R is particularly useful because it tells us whether to expect a large
outbreak or not. If R is below one, each infectious person will on
average generate less than one additional infection. We’d therefore
expect the number of cases to decline over time. However, if R is
above one, the level of infection will rise on average, creating the
potential for a large epidemic.
Some diseases have a relatively low R. For pandemic flu, R is
generally around 1–2, which is about the same as Ebola during the
early stages of the 2013–16 West Africa epidemic. On average, each
Ebola case passed the virus onto a couple of other people. Other
infections can spread more easily. The virus, which caused
outbreaks in Asia in early 2003, had an R of 2–3. Smallpox, which is
still the only human infection that’s been eradicated, had an R of 4–6
in an entirely susceptible population. Chickenpox is slightly higher,
with an R around 6–8 if everyone is susceptible. Yet these numbers
are low in comparison to what measles is capable of. In a fully
susceptible community, a single measles case can generate more
than 20 new infections on average.[42] Much of this is down to the
incredible lingering power of the measles virus: if you sneeze in a
room when you have the infection, there could still be virus floating
around in the air a couple of hours later.[43]
As well as measuring transmission from a single infectious person,
R can give clues about how quickly the epidemic will grow. Recall
how the number of people in a pyramid scheme increased with each
step. Using R, we can apply the same logic to disease outbreaks. If R
is 2, an initial infected person will generate two cases on average.
These two new cases will on average generate two more each, and
so on. Carrying on doubling and by the fifth generation of the
outbreak, we’d expect 32 new cases to appear; by the tenth, there
would be 1,024 on average.