# When masks work, and when they don’t

With billions wearing face coverings, the question we want answered is: How effective are they at reducing the probability of you becoming infected with COVID-19? This question is very hard to answer. We can split it up into two questions: If you wear a mask, how much does this reduce the dose of virus you breathe in? And how does the chance of you becoming infected decrease, when the dose of virus you breathe in is reduced? Colleagues and I have had a go at answering the first question — preprint here. Here I will just assume that mask wearing reduces the dose by a factor of one half. This does not mean that the probability that you will become infected is reduced by one half. It is not that simple, unfortunately.

Presumably the more virus you inhale, the more likely it is that you will become infected. But we have essentially no direct data on this. One model developed for TB (which spreads in a similar way to COVID-19) predicts that the probability of infection increases as one minus the exponential of the dose, this is the Wells-Riley model. But although we have no data for SARS-CoV-2, we do have some data for norovirus, and the results for transmission of the norovirus are not consistent with the Wells-Riley model – I looked at infection with norovirus in a previous post.

You can see the difference between the predictions of the Wells-Riley model and those you get by assuming a norovirus-like dependence on dose, in the plot at the top of the post. In this plot the x-axis scale measures the concentration of virus in the air you breathe. The scale and so the actual numbers are arbitrary but note that the x-scale is a log scale — the plot covers a huge range (it increases by a factor of ten million) of concentrations of virus in the air. The y-axis is the percentage reduction in probability of becoming infected, if wearing a mask reduces the viral dose by a factor of one half.

As the Wells-Riley model has an exponential dependence of infection probability on dose, the probability of infection goes from almost zero to almost 100% over about two decades in viral dose (from 101 to 103 above). Within those two decades, wearing a mask and so reducing the dose significantly reduces the probability of becoming infected — you can see the blue dashed curved is sharply peaked and reaches an almost 25% * reduction in probability of infection. But outside these two decades of dose, the prediction is that wearing a mask has little effect. If there is a lot of virus in the air, then even halving the dose is not enough to significantly reduce the chance of you becoming infected. And if there is very little virus, then you are unlikely to become infected, with or without a mask.

If infection is more norovirus-like, then the behaviour (orange curve) is different. The prediction is that masks never reduce the probability of infection by more than about 12% *, but that over a wide range of viral concentrations, mask wearing does reduce the probability of becoming infected. One interpretation of this is that if COVID-19 transmission is like that of norovirus, it may be that some of us are more resistant to COVID-19 infection than others. This means that the window of ambient dose over which a mask is of most benefit would be different for different people. This smears out the region of doses where masks benefit, resulting in smaller benefits but over larger ranges of conditions**.

The plot at the top is just speculative, we really need more data here. But maybe it is useful, it says one very obvious thing which is that wearing a mask when the air has very little virus achieves little – if you are alone on top of a mountain then you can take the mask off. The other thing it shows is a bit less obvious, and this is that as masks are not 100% effective filters, they cease to work at very high viral concentrations. If you are stuck for hours in a small poorly ventilated room with someone who is breathing out a lot of virus, then expecting a simple cloth or surgical mask to predict you, is too optimistic. There is a reason that medical staff on COVID-19 don’t just wear a simple surgical mask, but full PPE, and this is that they need to reduce the viral dose by a lot more than half.

* These numbers increase if wearing a mask reduces the dose by more than a factor of half, for example if it is factor of three quarters, they approximately double to approximately 50% and 20%.

** The distribution for the norovirus-like case effectively averages over many different people with different susceptibilities, which would be appropriate for you if you don’t whether you are more or less susceptible than average.