Recent data demonstrates the UK is likely past the peak of new coronavirus infections. The lockdown has done its job.

Now the UK, and other countries, are contemplating strategies to relax lockdowns and revive economic activity. But it’s a tricky balancing act – because weakening restrictions too much risks a second peak of infections and deaths.

The progression of the virus in most countries starts with an exponential growth in cases, followed by a slower reduction as lockdown measures kick in. This can be explained by considering the infection rate (the number of people, on average, an infected person infects) before and after lockdown. If the infection rate (R0) is greater than 1 the number of cases grows exponentially. But if measures are taken to reduce it below 1, it declines. I use the model I’ve built to forecast the virus to illustrate this effect, on the graph below.

For the model I’ve assumed an initial infection rate of 3.0, and 0.91 after lockdown. Although, in reality, the infection rates are likely to be different – the graph illustrates the general pattern for a country’s experience before and after lockdown.

So, if lockdown’s relaxed won’t we end up in the same position as before – with exponential growth sweeping us to another peak?

Not quite. One crucial difference from the position at the start of the virus is that a proportion of the population has recovered. In my model I forecast that 14% of the population will have recovered from the virus by 7 May 2020.

Most of those recovered should be immune (although there’s debate over whether this is the case). The presence of a proportion of the population with immunity reduces the virus’s effectiveness – even if we removed the lockdown altogether.

If lockdown is removed, the infection rate in the population wouldn’t go back to 3.0. Instead it would be 3.0 x 0.86 = 2.58 – because 14% are now immune.

However, we don’t want to fully remove lockdown, because this still generates an overall infection rate greater than 1. But, because of immunity, lockdown restrictions could be lifted just enough so that the overall infection rate doesn’t go above 1.

For example, if lockdown is relaxed enough to increase the infection rate from 0.91 to 1.05, because 14% of the population are immune, the overall infection rate will be 1.05 x 0.86 = 0.90. So economic activity could be increased, without causing another peak – illustrated in the graph below.

This shows how established immunity can make it easier to relax lockdown. And, ironically, the fact that the UK has suffered more infections than some other countries puts it in a stronger position to relax lockdown.

But, determining how to do this in practice is complex. The government needs to make a judgement based on an assessment of:

• infection rates,
• the proportion of people recovered,
• level of immunity in people recovered.

On top of this, it will also need to decide how to relax the lockdown without the overall infection rate increasing above 1. All of this will be assessed with what’s likely to be incomplete data.

Even if the government finds a way to relax lockdown so that the overall infection rate stays below 1, restrictions need to stay in place, otherwise we’ll get another peak. Hopefully, the government can find a combination of measures that are economically acceptable until a vaccine is available. The only other way out of this is by further relaxing lockdown – causing future peaks, with a consequent increase of deaths, but establishing additional immunity (the so-called herd immunity approach).