Particularly in the early stages of the COVID-19 pandemic, there were still medics who thought that because the virus was confined to some sort of mythical fast dropping, droplets, the virus could only be transmitted over distances of a metre or two. The virus could not go further. This can’t be true as it conflicts with basic aerosol physics. And there is pretty strong, pretty direct, evidence for transmission of COVID-19 across large rooms. But what I had not appreciated until this week was that people studying transmission of the virus that causes foot-and-mouth disease*, have pretty good evidence that the virus can carry over tens of kilometres. For example, from northern France across the English Channel to the Isle of Wight. The distance from the Isle of Wight to France is of course a lot more than two metres.
When considering transmission of COVID-19, often the advice is that meeting outdoors is safer than indoors, because outside the virus is diluted by the atmosphere. Again this must be true, the atmosphere is a lot bigger than room. This dilution must be happening for fot-and-mouth but apparently under some conditions animals infected with foot-and-mouth disease produce enough virus to infect at least one animal in another herd ten or more kilometres downwind. By then it must be heavily diluted, we can try and estimate by how much.
A human breathes out maybe a million (106) aerosol (so too small to be seen by the naked eye) droplets an hour. Cows are bigger so if say a few tens of cows are infected they should be breathing about 108 aerosol particles an hour, between them. We don’t know what fraction contain infectious virus, presumably most don’t so let’s guess that one in a hundred contain viral particles, giving us that a infected herd of cows with ten or so infected are breathing out 106 infectious aerosol particles per hour.
Wind speeds are often around 10 km/h, so if say a barn with the infected cows in it is venting virus-containing particles at a rate of 106 infectious aerosol particles per hour, then after an hour the wind will have blown them about 10 km downwind. During this time, the air from the barn will have been mixed with a large volume of the Earth’s atmosphere. I don’t know how large a volume this will be, I can easily imagine that it could spread over an area of square kilometre but I don’t know how high above ground the air will have mixed with. If I guesstimate that the height too is one kilometre, then the 106 infectious aerosol particles are now in a volume of atmosphere of one cubic kilometre, or 109 cubic metres. Then, even if all virus survives the trip and is infectious, this dilutes the concentration of infectious aerosol particles to 10-3 per cubic metre.
We breathe in about a cubic metre of air an hour but cows are bigger so breathe in more, so say large herd of a few hundred cows breathes in a thousand cubic metres of air per hour. With a concentration of infectious aerosol particles to 10-3 per cubic metre, this means that the herd breathes in very roughly one virus-containing particle per hour.
This is a very rough estimate indeed (could easily be out by a factor of a hundred either way). Infection probabilities must be quite low, the volume may be bigger or smaller than a billion cubic metres but it is certainly much larger than the volume of a cow shed, which is presumably around a million times smaller, at of order a thousand cubic metres. So the viral concentration in the same shed could be a million times higher than in a herd 10 km downwind.
But to infect a new herd only one cow needs to become infected, and transmission does seem to occur over these huge distances, for foot and mouth, in animals. Question is: Can this long-range transmission occur in humans? As far as I know there are no recorded instances of this, but I could have missed one. Of course we gather into groups much larger than cow herds (towns and cities) and if many of the people are infected, collectively they will pump a lot of virus into the air, where the wind will carry it. For this not to occur in us humans we would need our viruses to be somehow less infectious and/or less able to survive in the environment. I don’t know why either would be true but we have a poor understanding both of why some viruses are more infectious than others, and especially of how they survive, or don’t survive, being blown 10 km in the wind.
* Foot-and-mouth disease is a viral disease that infects animals such as cows and pigs. An outbreak in the UK in 2001 was only ended after 6 million cows and sheep were slaughtered.
** This does not mean that the probability of infection is a million times lower, although at low doses the infection probability should probably be linear in dose. If you go from say a 1% probability of a cow inhaling an infectious particle to a 2% probability of inhaling one, the infection probability should double, but the probability must saturate at some point (probability of infection can’t exceed one, however high the dose.
Chance & Necessity 