This is the most important number of the epidemic: the R – or, the reproduction number. It’s what governments around the world are keeping a close eye on to understand how the crisis is developing, and whether it’s time to loosen up measures.
If you need a refresher, Professor Merkel will be happy to update you.
The R stands for the average number of people that one sick person infects. For example, if R equals 2, that means that one person on average infects two people. These in turn each infect two people, making a total of four. So the number of new infections doubles per cycle: 1, 2, 4, 8, 16, 32 ...
This is what you call exponential growth – a development that is not linear, but that is growing ever faster.
If the R equals 1, there is no more increase in new patients, but also no decrease: 1, 1, 1, 1, 1, 1, 1, ... Then the disease is "endemic", the number of new infections remains fairly constant.
Governments worldwide are aiming for an R below 1, which means that, on average, each infected person would infect fewer than one person. Suppose the R is 0.8 and we have 10,000 infectious people walking around today (this is a fictitious number). Then the sequence becomes this: 10,000, 8,000, 6,400, 5,120, 4,096 ...
So the disease gradually dies out. That’s why it’s so important that the R falls below 1.
How is R affected by the measures?
The R is influenced by three factors:
- The chance that someone infects someone else upon contact (p)
- The number of contacts per unit of time (c)
- The period of contagiousness (when the infection can be passed from person to person) (d)
If you multiply those three, you get the R:
The beauty of the formula is that you can see exactly which knobs you can turn if you want to change the R. If you reduce one of the parts, you also reduce the R.
Let’s take the chance of someone infecting someone else (p). You can reduce that chance by washing your hands, by keeping your distance and – hopefully one day – by vaccinating people against the disease.
You can reduce the number of contacts per unit of time (c) by working from home, by cancelling events and by closing cafes and restaurants. Shutting down schools also follows this line of reasoning, although there is more and more evidence that children are not as contagious as adults.
Finally, the duration of contagiousness (d) can be shortened, for example, by quickly tracing and isolating cases of the disease. That’s why some governments are working on an app, although it’s still unclear how effective such an app will be (leaving aside whether you should want it at all).
How to calculate R?
The R is easy to calculate if you know exactly who infected whom. Per patient you just find out how many others that person has infected, take the average and – voilà – you have your R.
But that method has become unworkable in most countries. There are simply too many cases to find out exactly how the disease spread from an individual. That’s why you need a statistical method that tries to calculate that reproduction number in a different way.
In the Netherlands, the model is based on records of hospital admissions and, more specifically, intensive care. Hospitals register when someone became ill. Then later, that first day of illness is used by the modellers to calculate the reproduction rate.
(For enthusiasts: the Dutch model is based on an article published in 2007 by Jacco Wallinga, head modeller of the National Institute for Public Health and the Environment, with Harvard epidemiologist Marc Lipsitch.)
An important note: such a model assumes that the data is representative of the entire population. If certain groups do not come to the hospital – as is sometimes the case for the elderly in the Netherlands – they cannot influence this number. If there are outbreaks in nursing homes, then the actual R will be higher.
Also, the R is only an average. If 20 people don’t infect anyone and one person infects 14 people, then the R is below 1 (14/21=2/3). Yet you see that outbreaks can occur, because such a "super-spreader" can suddenly infect a lot of people.
The past week I’ve been binging The Good Place. If you’ve got Netflix, go see it. It’s a philosophical comedy show about a woman who accidentally ends up in heaven. Or, well, in "the good place", a kind of heaven. Because as you go on to find out, we humans don’t seem to have guessed right when it comes to the afterlife.
I’m almost done with the last season. Next, I have After Life (with Ricky Gervais) on my to-watch list (just to stick with the theme I’ve got going).
Before you go ...
My colleague Lynn Berger wrote a beautiful essay on the concept of home. "It seems to me that ‘home’ is only truly a ‘home’ when you have the option to leave it; when it’s a place to return to, rather than a place where you have to stay. But we are all less free to go now – and if you can’t go out, you can’t come home either."