The Rules of Contagion: Why Things Spread - and Why They Stop

by Adam Kucharski

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.