would bring the disease under control. We can use the same logic to
work out vaccination targets for other infections. If R is 10 in a fully
susceptible population, we’d need to vaccinate at least 9 in every 10
people. If R is 20, as it can be for measles, we need to vaccinate 19
out of every 20, or over 95 per cent of the population, to stop
outbreaks. This percentage is commonly known as the ‘herd
immunity threshold’. The idea follows from Kermack and
McKendrick’s work: once this many people are immune, the infection
won’t be able to spread effectively.
Reducing the susceptibility of a population is perhaps the most
obvious way to bring down the reproduction number, but it’s not the
only one. It turns out that there are four factors that influence the
value of R. Uncovering them is the key to understanding how
contagion works.
O 19 1987 , Princess Diana opened a new treatment unit in
London’s Middlesex Hospital. While there, she did something that
surprised the accompanying media and even the hospital staff: she
shook a patient’s hand. The unit was first in the country that was
specifically built to care for people with . The handshake was
significant because despite scientific evidence the disease could not
spread through touch, there was still a common belief that it could.
[45]
The rise of / in the 1980s created an urgent need to
uncover how the epidemic was spreading. What features of the
disease were driving transmission? The month before Diana visited
Middlesex Hospital, Robert May and Roy Anderson had published a
paper that broke down the reproduction number for .[46] They
noted that R was influenced by a number of different things. First, it
depends on how long a person is infectious: the shorter an infection
is, the less time there is to give it to someone else. As well as the
duration of infection, R will depend on how many people someone
interacts with while infectious. If they have a lot of contact with others,
it will provide plenty of opportunities for the infection to spread.
Finally, it depends on the probability that the infection is passed on