Evidence-based social distancing guidelines

Early on in the pandemic, social distancing measures were introduced, with various distances. The UK went for 2 m, the USA for 1.8 m (6 feet), Hong Kong 1 m, etc. None of these were based on much evidence, but we now know a lot more. COVID-19 is an airborne disease. Although more data is badly needed, it seems likely that somewhere between most, and almost all, infections are caused by breathing in virus, that an infected person breathed out seconds or minutes earlier. The virus is carried by tiny droplets suspended in the air. And most transmission is indoors.

In a well-ventilated room, the amount of air you breathe in that is second hand is about 1 %, with the other 99% being fresh air. The figure is several % if the room is poorly ventilated, but for the moment let us assume that the room is well ventilated. If you are far from an infected person and breathing in the room then about 1%/N of the air comes from the infected person, with N the number of people in the room. Now, when air crosses a room, the droplets the virus is in dry out. We think this drying out kills perhaps 90% of the viruses, leaving about 10% still to infect us. There is very limited data here, but we will use this figure.

So, sharing a room from someone but being far from them protects you by diluting their breath by a factor of 100 N. And drying out reducing the infectious virus by another factor of 10. This means that sharing a well ventilated room with an infected person is about 1000 N times less dangerous than breathing all your air directly from their breath.

But you very rarely take a breath of air that all comes directly from another person, you have to be very close to someone to do that, and we don’t get that close to people, certainly not with work colleagues or friends. So, how far away from someone do you have to be to benefit from this risk reduction by a factor of a 1000 N?

Howard Stone at Princeton University and colleagues have looked at this, as has MIT’s Lydia Bourouiba and her colleagues*. The first thing to realise is that our breath leaves our mouth and nose as a forward facing jet of air, and that we breathe in the air immediately in front of our mouth and nose. So being within 1 or 2 m, but facing away from someone, will not typically have a much higher risk than being metres away across a room. If an infected person is behind me, and facing away from me, their breath is going away from my mouth and nose and will only be carried there via the usual air currents in any room. They can be 50 cm behind me, or 3 m behind me, it shouldn’t make much difference.

So, the riskiest position is directly facing someone and close to them, for example, when you are talking to them. But how close is close? Looking at Stone and colleague’s work, even 20 to 30 cm away from your mouth, your breath is already mixing with the room air – diluting any virus you may be breathing out, and killing some of it, as the droplets dry out. So if the risk at a distance of 0 cm is 1000** times that in a well ventilated room, it has probably dropped to at most 100 times that in the room, at a distance of 30 cm – which is closer than we usually are in social and work situations.

At distances around a metre then the breath is diluted by factors of tens, and by then most droplets should be dry. So then risk should be at least 100 times smaller than a distance of 0 cm, so probably at most ten times higher than in a well ventilated room. But at a distance of 1 m, if you are directly facing an infected person who is also facing you, the risk is several times higher, than it would be across the room. At 2 m, the risks should be approaching the background risk in the room.

In short, it looks like facing someone within a range of maybe a metre or so is a lot riskier than being across a well ventilated room. So the distances used in the original social distancing guidelines are sensible, they just did not take account of the directional nature of air flow from one person’s breath to another. Although it should be said that social distancing rules have another effect. They cap maximum occupancy, if we are to stay 2 m away from others in all directions, then the room can have a maximum capacity of one person per 4 m2. And reducing the number of people in a room reduces the risk to everyone in the room.

* The Stone group’s work is here, here, and here, while Bourouiba has a couple of good reviews that look at her work and that of others, they are here and here.

** The risk is 1000 N times the risk of breathing in air that all comes from an infected person. But if there is 1 infected person out of N people in a room then the probability that the person you are close to being infected is 1/N, so the factors of N cancel. It is also true that the arguments of this blog post – which are all fluid mechanics and viral survival – can only ever be used to estimate relative risks. Estimating absolute risks requires knowing other parameters, such as the viral load of the infected person, which can vary enormously from one infected person to another.

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