The path between herd immunity and lockdown

In four decades working as an engineer and scientist, I have rarely known a more polarised time within the scientific field. The marketplace of ideas is depressingly split down the middle: you are either for herd immunity in the shortest possible time or for a full lockdown.

There is, however, a third way: a method that will allow the coronavirus to slowly spread within the population without causing a very high death toll and overwhelming the NHS – while, at the same time, protecting the economic and social wellbeing of the country.

How can this third way be achieved? The key is to control what the epidemiologists call the 'basic reproduction number' or R0-value, which is the average number of people in a fully susceptible population someone with Covid-19 infects before recovering.

Why is this number so important? Because we all have a personal R0-value over which we have direct control; by washing our hands, staying two metres apart and wearing masks. The national R0-value then keeps the score on how well the nation overall is doing these things and this determines how fast the virus spreads.

It is a fundamental tenet of control engineering that to control something you need to measure it, whether it's the speed of a jet fighter or the temperature in a hot water tank. But measurement alone is not enough. The controller, whether a computer or a human being, needs rapid feedback without delay if the system is to work effectively.

The government is struggling to keep the epidemic under control for two very basic reasons: it is measuring the wrong thing and, in any case, its measurement process is slow and delayed.

The measurement the government is using to control the virus is called the R-rate. It is a more complex version of the R0-value which also factors in how many people haven't yet had the disease. Designing a control scheme around something over which one exerts only an indirect influence in this way is a fundamentally unsound strategy.

For instance, imagine a situation, by no means impossible, where increasing numbers of people start to give up on social distancing, and the R0-value gradually rises from where we are now (1.4) up to 1.5 by the end of November, 1.7 in the new year, and then all the way up to 3, where it was last March when no one knew about social distancing. If you were monitoring the simpler R0-value on a daily basis, you would spot the upward trend and take necessary precautions. However, in the same instance, if you were to use the government’s R-rate – which takes account of population immunity and therefore reduced chance of infection – then you would see the R-number fall, even as the number of infections increased, because the number of people able to be infected would drop.

The government's difficulties in controlling the virus do not end there, because for most of the time it does not actually know what the R-rate is. Why? Because it is only estimated retrospectively and at irregular intervals by different academic groups in the UK. So the measurement arrives with the decision-maker after a delay of at least a week.

I have now devised a way of measuring the right parameter, the R0-value, on a daily basis.

Chart 1. Measured daily R0-value from July 2020 onwards

My measurement of the R0-value in Britain shows that in July it was below 1. But it rose steadily as our society increasingly reopened following lockdown. Its current level is around 1.4. This means that the average infected person in the UK is coming into contact with either one or two people closely enough to infect them.

There have been frequent complaints about the UK's sloppy adherence to the coronavirus rules, but the graph shows that the nation is currently holding the line at half what the R0-value was before the first lockdown. Perhaps even a little praise might be in order for the considerable efforts of the British people.

So what would happen if we continued to behave in the way we did before London and other places were placed in Tier Two? And what if we kept the R0-value at 1.43 – its level before the Tiers were first introduced – until the end April 2021, and then relaxed restrictions altogether?

My modelling (Chart two) shows that new infections would rise to about 90,000 a day by the end of this year and then start falling. The predicted peak number of cases a day would be 20 times what we saw back in April. But as we are now testing around 10 times more people, it would only be roughly double in equivalent terms.

Because we now know much better how to treat the disease and we have increased capacities with the Nightingale hospitals, we would likely be able to cope with this rise.

Chart 2. Forward projection. The R0-value stays at 1.43 from 17 October 2020 to 30 April 2021, then rises to 3 as all restrictions are lifted

Would the removal of all restrictions in the spring lead to a third wave in this scenario? Yes, with a height similar to that of the second wave, attained at the beginning of July 2021. But the UK, according to my modelling, would become entirely free of the disease by the end of 2021.

If we can cope with the coronavirus epidemic, provided we keep the R0-value at the figure at roughly 1.4, what happens if we try to push it to a lower level, say 1.2? Infections and deaths in the short term would not rise much above what we are currently seeing. We would lay ourselves open, however, to the great hazard that if people get fed up with the tight restrictions by the spring, we could have a huge third spike (as seen in chart three below).

Chart 3. Forward projection. The R0-value is held at 1.2 from 17 October 2020 to 30 April 2021, then rises to 3 as all restrictions are lifted

In other words, what you gain now, you lose in spades later on.

A nation’s economy not only supplies a framework for society, it keeps us living longer, especially in a developed country like Britain. This explains why children born in some poorer, sub-Saharan states will survive to an average age of only 55, while those born in wealthier Japan can expect to live three decades more.

It explains the year-on-year rise in life expectancy in Britain as GDP per head increased over the decades before the 2007-2009 financial crash, when GDP per head fell by 6 per cent. It also accounts for the fact that the growth in UK life expectancy stalled a couple of years later. Poverty kills as surely as Covid-19.

Yet today, with the national debt rising above £2 trillion for the first time and mass unemployment on its way, the plight of our economy is many times worse than 2007 to 2009.

The result of a crippled economy is that thousands of us – now and in the future – will be condemned to a shorter, more miserable existence.

But much of this could be mitigated if we stopped trying to keep a tight rein on the R-rate and turned our focus to the R0-value, which we can rapidly monitor. It would give the government the chance to get effective control of the epidemic.

They could set the R0-value at a sensible point of their choice and institute measures, including persuasion, to get the nation to hit their target.

Using the new measurement they would be able to tell each day how close they were getting to the target and modify their measures (or not) accordingly – without the need for legally enforced tier restrictions.

An R0-value of 1.4, as we have currently, looks, to me, the best compromise we have between keeping the economy open and protecting the vulnerable. Society would be all the worse if we don’t stick with it.

Philip Thomas is professor of risk management at the University of Bristol.