The key to stopping the spread of a disease is to get R0 below 1. If it’s above 1 it will exponentially increase throughout the population; if it’s below 1 it will dwindle to nothing. There are complicating factors but that’s basically it.

One way to reduce R0 is to reduce the number of susceptible people in the population, for instance by vaccinating. Take measles as an example. It’s very infectious: in a susceptible population it has an R0 of about 20. You want to get that below 1. To do that with vaccination alone, you need to vaccinate at least 19 out of every 20 people. Then of the 20 people it would have infected, 19 will be resistant, so the number of infected will not increase.

It’s a simple equation. If your vaccine is perfectly effective, then you need to vaccinate 100% of the population minus (100 divided by R0). For measles, that’s 100 – (100/20) = 95; so you need 95% vaccination for herd immunity from measles.

Vaccination is not the only way of achieving immunity. For some diseases — including measles, and chicken pox — you are usually immune for life once you have it. So you could get herd immunity for measles if >95% of the population had it (and no one new was born).

That’s basically what this part of the government plan seems to be. With Covid-19, the R0 is not well known (and depends on social factors), but Imperial College puts it between 1.5 and 3.5 and the WHO at between 1.4 and 2.5. Let’s take the highest estimate, 3.5. If having the disease once makes you immune forever, then 100-(100/3.5)=71%; herd immunity would be achieved when 71% of the population has had it.

Of course, that assumes perfect immunity. If — as with flu — that’s not the case, the maths is very different. In fact, if the percentage who are still vulnerable after vaccination or exposure is greater than the percentage required for herd immunity, then it becomes impossible to achieve herd immunity, even if 100% of the population is exposed or vaccinated.

At the moment it’s not clear whether Covid-19 will become seasonal, like flu, or will be a once-in-a-lifetime illness like measles. It makes a huge difference to whether herd immunity will work or not.

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Tom Chivers is a science writer. His second book, How to Read Numbers, is out now.

TomChivers

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