Anderson quickly applied the idea to other problems, encouraging
others to join them.
It soon became clear the reproduction number could vary a lot
between different populations. For example, diseases like measles
can spread to a lot of people if it hits a community with limited
immunity, but we rarely see outbreaks in countries with high levels of
vaccination. The R of measles can be 20 in populations where
everyone is at risk, but in highly vaccinated populations, each
infected person generates less than one secondary case on average.
In other words, R is below one in these places.
We can therefore use the reproduction number to work out how
many people we need to vaccinate to control an infection. Suppose
an infection has an R of 5 in a fully susceptible population, as
smallpox did, but we then vaccinate four out of every five people.
Before vaccination, we’d have expected a typical infectious person to
infect five other people. If the vaccine is 100 per cent effective, four of
these people will now be immune on average. So each infectious
person would be expected to generate only one additional case.
Comparison of transmission with and without 80 per cent vaccination,
when R is 5 in a fully susceptible populationIf we instead vaccinate more than four fifths of the population, the
average number of secondary cases will drop below one. We’d
therefore expect the number of infections to decline over time, which