The Calculus of Contagion


Adam Kucharski in Aeon (Photo by Dominique Faget/Afp/Getty):

There are several ways to estimate the reproduction number of an infection. If we know how long people are infectious for – and hence the average time between each ‘generation’ of disease cases – we can estimate the reproduction number by looking at how quickly the epidemic grows. Alternatively, we can estimate it by calculating the average age at which people experience their first infection. The more infectious a disease is, the sooner a person will become infected.

By calculating reproduction numbers, we can quantify and compare different infections. Measles is at the wildfire end of the scale. In an unvaccinated population, it has a reproduction number that lies somewhere between 12 and 18. This explains why measles has always been a childhood disease; a high reproduction number drives down the average age of infection. In contrast, the 1918 pandemic influenza strain – the infamous ‘Spanish flu’ – had a reproduction number of around 2 or 3. Because the disease came with a high fatality rate, even this relatively low reproduction number was enough to create widespread devastation. In the middle, we have infections such as polio (5 to 7) and mumps (4 to 7).

Although the reproduction number does not tell us how fast an infection will spread from person to person, it does show how much effort is required to eradicate a disease through vaccination. For a disease such as measles, we need to vaccinate a lot of the population to reduce the average number of secondary cases, and hence get the reproduction number below that crucial value of 1. But the reproduction number isn’t just useful for studying familiar infections. It can also help us deal with new disease threats.

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