On Wednesday I watched (via Zoom of course) a webinar by Prof Jose Jimenez: *Airborne transmission of SARS-CoV-2, and how to protect ourselves: What we know now*. You can watch it on YouTube. I learnt a lot from it. Jimenez and coworkers have repurposed a model originally developed for the transmission of TB through the air of a room, to the study of SARS-CoV-2. The model is called the Wells-Riley model, after two of its inventors. Jimenez and coworkers have even implemented it as a Google Sheets spreadsheet, so you can see what this model predicts yourself.

The Wells-Riley model is simple. It says that if you share a room* containing a total air volume *V*, for *t *hours with an infected person, then on average you are expected to breath in

*n *= *q*B*t */ *V*r* infectious doses

where *q *= the number of infectious doses the infected person breathes out per hour, *B *= the volume of air you breathe in per hour, and *r =* is the rate at which infectious virus in the air is removed, either because it is removed by air ventilation or because the delicate virus decays.

Then Wells and Riley assumed that if you breathe in one or more infectious dose, you become infected. For this probability they used the standard statistical expression (what is called Poisson statistics), and came up with the probability *P* of being infected of

*P *= 1 – exp[ – *n *]

Now Wells and Riley developed this model for TB – Wells and Riley pioneered research showing you could catch TB by breathing in air, that someone infected with TB have breathed out, even if you were metres away from the infected person. But a team of scientists including Jimenez applied it to a superspreader event that occurred during a choir rehearsal in Washington state, USA. The choir rehearsal was of about 60 people, of whom about half became infected, two of which unfortunately died. The room volume was about* V = *1000 m^{3}, and the event lasted a couple of hours. We breathe in about *B *= 1 m^{3} of air per hour. They assume** that with reasonable ventilation the elimination rate *r *of the virus is a few per hour – this is reasonable as this is what building regulations suggest is a good turnover of air due to ventilation.

Then if you assume that the infected person was breathing out about 1000 infectious doses of SARS-CoV-2 per hour, you get the observed over 50 % probability of becoming infected during the choir rehearsal.

This is pretty scary, but this is what is called a superspreader event, i.e., a rare event in which many people were infected. It is hard to prove this, but it seems likely that the infected person was someone who breathes out much more virus than average. As I talk about in an earlier post, there is huge variability in how much virus is inside an infected person. If an infected person breathes out only one tenth or one hundredth of the virus of the individual in this superspreader case, then the predicted probability of infection drops to about 5% or to 0.5 %.

But the Wells-Riley model predicts that the probability of becoming infected would then increase if you share a smaller room with an infected person, or the room is poorly ventilated. Now Wells-Riley is *very* simple model of a very complex phenomenon, and the nature of dangerous diseases such as COVID-19 makes it hard to test the model, so there is a real risk that one or more its assumptions is really quite bad. But at least it provides a starting point to think about how to estimate the probability of becoming infected with COVID-19.

* The Wells-Riley model is for transmission when you are socially distanced from the infected person. Presumably the probability of being infected will be higher, if you are close to the infected person.

** I am simplifying the paper a bit, see Miller *et al* for details.

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