A mathematical case for masks

Small changes to coronavirus infection rates make a big difference to death rates. At a time when governments across the globe consider which policy tools can best reactivate economic activity – it’s worth evaluating how even small policy tweaks can help keep the death rate down.

In my blog “How to relax lockdown without a second peak”, I showed how, as a country establishes increased immunity to coronavirus (if those recovered retain immunity), the overall infection rate reduces. In the UK, based on my model, I’ve assumed that the effect of the current lockdown, together with established immunity, delivers an overall infection rate “R” of around 0.80 at the start of May.

If it carries on like this, the disease will eventually disappear. But continuing the current lockdown is probably economically and socially unacceptable. The greater the relaxation of lockdown measures, the more R increases. So, it’s likely governments are weighting up how best to proceed.

Because of the exponential nature of a virus’s infection rate, small changes make a big difference to the death rate, as illustrated on the graph below.

lockdown scenarios

Here, I’ve used my model to forecast the effect on death rates of different infection rates – ranging from 0.8 (assumed current lockdown rate) to 1.3. As can be seen, even with a small range, the outcomes are very different – with a second peak where the R rate is greater than 1.

Of course, there’s no exact link between policy and infection rate. In practice, governments will likely assess the impact of a range of measures to determine a combination that have the desired effect. However, one of the difficulties is that there is a lag between implementing policies to combat the virus and seeing their effect – through infection and death rates. And, as this is a new virus, data from other countries on policy impacts is sparse – and may not be relevant due to different local conditions.

However, the clear conclusion from reviewing the impact of different infection rates, is that – small reductions in the infection rate make a big difference to future deaths. So, after relaxing lockdown, it’s worth adopting simple and practical policies that are likely to reduce the infection rate. For example, should people wear masks or face coverings? There’s been considerable media debate in the UK about the effectiveness of masks in stopping the spread of the virus – but, even if they only reduce the infection rate by a small amount, they could save thousands of deaths.

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