Covid-19: Herd Immunity in the UK

“…’cos I wanna be… herd immunity!”

with apologies to the Pistols (00:29)

The ongoing Covid epidemic in the UK will only recede when we have achieved herd immunity, by definition. The fact that permanent or semi-permanent behaviour changes may contribute to herd immunity does’t alter this fact, because the level of immunity to achieve R<1 always depends on the social context. Some of the confusion appears to be due to the use of GCSE level concepts to deal with a PhD level problem – it is particularly egregious to suppose that everyone will inevitably be exposed to SARS-CoV2 when some individuals have orders of magnitude fewer social contacts than others. The UK should take into account the potential for its vaccination programme to reduce transmission as well as how effectively vaccines protect the recipients.

Edmunds vs Pollard

On Friday 13th March 2020, Professor John Edmunds OBE famously told a Channel 4 News special (12:30 in) that: “The only way to stop this epidemic is indeed to achieve herd immunity”.

Yet Professor Sir Andrew Pollard, Chair of the UK’s Joint Committee on Vaccination and Immunisation (the JCVI), now insists that herd immunity is “not a possibility”.

How to evaluate these claims?

Edmunds is an epidemiologist and was simply stating Epidemiology 101. There was a lot more to the debate on Channel 4, of course, but, whilst trying to present the UK’s apparent policy at the time of allowing the epidemic to run its course, while “flattening the curve”, Edmunds invoked the principle that eventually enough people would acquire immunity through infection for the virus essentially to run out of people to infect. End of epidemic.

It quickly became clear, of course, that aiming for herd immunity through infection would be a Bad Thing, because of the severity of Covid-19, but achieving herd immunity primarily by vaccination would clearly be a Good Thing. Don’t get confused!

Pollard is NOT an epidemiologist, but an immunologist, so it’s slightly concerning that as Chair of the JCVI he seems to discount the value of vaccines in preventing transmission. The Guardian quoted him expounding further:

“The Delta variant will still infect people who have been vaccinated. And that does mean that anyone who’s still unvaccinated at some point will meet the virus … and we don’t have anything that will [completely] stop that transmission.”

Note the Guardian had to add the word “completely”. This isn’t the first time I’ve heard an expert in the UK simply ignore the fact that the vaccines reduce transmission (by about 50% according to the Guardian article reporting Pollard’s comments).

And when the UK finally announced this week that 12-15 year-olds would be “offered” the vaccine, there was barely a suggestion that one reason they might want to accept the offer is that they would thereby reduce their risk of transmitting the virus, for example to family members. Actually, I tell a lie – one person stressed this point: a teenager who’d lost a grandparent to Covid.

All this is rather disturbing for those of us who want a return to normality, because Edmunds is logically correct. Case numbers either increase (R>1) or they decrease (R<1). If they’re decreasing, then “herd immunity” has been achieved. Transmission chains will fizzle out. Until then case numbers will tend to increase and, when this starts to stress the NHS, control measures will become necessary.

There’s no choice: we have to achieve herd immunity, if we want to ever return to the status quo ante Covid.

Covid in the UK

The UK has explicitly adopted a policy of “living with the virus”. This makes almost no sense, because, to labour the point, if R<1 the epidemic will peter out, so we won’t have to “live with the virus”, but if R>1 case numbers will continually increase, hospitalisations or deaths will eventually reach an intolerable level and control measures will become necessary. How is that “living with the virus” and not what’s been happening for the last 18 months? Or is a permanent state of crisis what is meant by “living with the virus”?

It’s all the more puzzling that we’re not talking about herd immunity in the UK when case numbers are not consistently increasing even though Covid restrictions have been dramatically eased. In fact, twice now, in mid-July 2021 and at present, in early September 2021, case numbers have unexpectedly declined, coincident with or shortly following spells of hot weather (~30C max daily temperatures), which maybe the virus really doesn’t like (though other factors could also be part or all of the cause):

Figure 1: UK Daily Covid cases – government data as of 16/9/21

It seems that to drive case numbers right down quite rapidly all we would have to do is tighten controls slightly from the current level. Maybe we could all wear masks in more settings, which really isn’t that big a deal. Even this wouldn’t be necessary if we could reduce transmission more by vaccination. Instead it seems we’re going to try to relax fully, whilst the NHS is already stretched.

Here’s the thing. It seems the vaccines aren’t reducing hospital admissions enough (but see footnote), especially in older age groups:

Figure 2: Vaccine protection by age, presented by Chris Whitty, Downing Street press conference 14/9/21

It looks (by eye from the graph above) like vaccinated over 80s with Covid are about 30% as likely to be hospitalised as unvaccinated infected over 80s (and those in their 70s about 25% as likely etc). Unfortunately 30% of a very big number is still a big number.

Hopefully, of course, boosters will increase above ~70% the effectiveness of the vaccines in reducing the risk of hospitalisation in the over 80s. Until they kick in, though. waning immunity suggests the risk will only increase.

If we wait for everyone to catch the virus, as proposed by Professor Sir Andrew Pollard, it’s going to take a long while to get through this thing, because, even as medics are on the radio telling of stress in the NHS, infections (as confirmed by PCR tests – actual infections may be a bit higher) are only running at a bit over 100 to 200 per 100,000 per week for the vulnerable older age groups:

Figure 3: Cases by age, government data for England as of 14/9/21

The same figure shows, though, that rates of infection in younger age groups have been running – allowing for under-reporting and more in line with ONS population infection surveys – at around 1% a week for a couple of months now (in England, at least – the Scottish curve is very different). Since someone just recovered from Covid is almost certainly immune from further infection for a period of weeks or months, that’s around 10% full immunity of younger age cohorts just from infections in the current wave.

But this rate of infection is not enough: without high levels of vaccination the current infection rate would need to be sustained for the best part of a year to result in herd immunity. This might well not work, as immunity might wear off before then, resulting in reinfections.

Vaccines are needed as well. A high level of vaccination in younger age groups would (assuming ~50% immunity from infection of those vaccinated) reduce the time needed for current infection rates to produce herd immunity to just months, at the most (the current level of immunity to infection is uncertain).

One advantage of the UK’s relatively high infection rates, though, is that, because a relatively high proportion of immunity is being gained through infection, herd immunity will kick in at a lower level of population immunity than otherwise, because of the critical point that those with the most social contacts will tend to be infected earlier. Herd immunity becomes a lot easier to achieve once the superspreaders are out of the equation!

It might also be worth pointing out that infection and vaccination aren’t exclusive. The evidence is that immunity is higher in those who have been both vaccinated and infected, in whatever order. So those most likely to be infected – because they have more contacts at work or during their leisure activities – are more likely to beome fully immune even if everyone is vaccinated.

The UK has an explicit strategy of “living with the virus”, which doesn’t seem to mean anything, since the virus will either spread exponentially or decline exponentially. The problem with the UK’s strategy is that it tends to de-emphasise the importance of measures to achieve herd immunity. So whilst care workers are obligated to be vaccinated, and health workers may follow, the same isn’t true of other groups who come into contact with many people in their work or leisure activities. A checkout worker in a shop, for example, could infect dozens of other people if infectious only for one shift. Similarly, vaccine passports for large gatherings are on hold. And whilst 12-15 year-olds are finally to be vaccinated, the idea that increasing their immunity would benefit society as a whole is almost taboo. The discourse is also self-contradictory: if care workers are to be vaccinated to protect others, why shouldn’t everyone else be as well? It should be one’s civic duty to be vaccinated!

Reviewing epidemiological concepts: R and herd immunity

But, hang about! In younger people infections are running at several times the rate in those older groups. Even if we take into account that more older people are vaccinated (infection reducing by around half the likelihood of becoming infected during contact with an infected individual), all the younger people will be infected long before all the older people. There will then not only be fewer people for the elderly to catch Covid from, but these people will be spreading the virus less readily. The younger people are more likely to catch Covid because they have more contacts (on average), but they are also more likely to spread it because they have more contacts.

If current trends continue, the epidemic will eventually peter out before all the older people (or more accurately all the people with small numbers of contacts) are exposed to the virus. Pollard is therefore simply incorrect when he says that: “anyone who’s still unvaccinated at some point will meet the virus” (though the chances of doing so are quite high). Herd immunity is possible.

The point is that if R0 (i.e. before anyone is infected) is 7 for Delta (as is often quoted), that doesn’t mean, as epidemiologists often claim, that 6/7 of the population (around 86%) must acquire full immunity for R to be <1 and herd immunity to kick in. No, no, no! This point needs to be stressed: it is always the case that <86% immunity is required, because those with more contacts will on average catch the virus sooner than those with fewer contacts.

So if you try to establish R0 by the rate of spread of the virus in a naive population (which is what is done), the standard method will always overestimate the number of people who must catch the virus (or be vaccinated) to achieve herd immunity!

It’s important to understand that R (or “R0”) depends on context. It is not a property of the virus, but a property of the virus and it’s environment. If people have more contacts, for example, greater use of public transport, then R will be higher. In fact, quoting the same R for London as for Cornwall is entirely misleading.

Behavioural changes – greater working from home, mask-wearing etc – also reduce R, of course. After all, that’s the whole point of encouraging these changes.

So where are we with R now in the UK? Here’s what a senior epidemiologist has to say:

Professor Graham Medley from the London School of Hygiene & Tropical Medicine, the Chair of the SPI-M group of expert advisors to the government, said: “It’s not an on/off process – herd immunity kicks in as immunity increases.

“People in England are approximately making contact with about half the people that we were pre-pandemic.

“We estimate that at full contact rates and no immunity the R for Delta would be about 7. At half the contact rates, we would expect R to be about 3.5.

“But we are actually seeing R about 1.4, and the difference is immunity – so immunity is reducing the R value by about 60 per cent. Without immunity we would be having a huge epidemic.”

Channel 4 FactCheck: Why hasn’t “herd immunity” stopped Covid?

There’s a lot to criticise in that passage, especially the implied uniformity across the UK. Also, R is now much closer to 1 than perhaps when Medley was writing in July. And contact rates have no doubt increased. Surely we could reach herd immunity with the retention of some infection-prevention measures combined with increased vaccination aimed at reducing transmission.

Why are we planning on “living with the virus” and not pushing for herd immunity?


So what can we conclude from all this?

1. The UK may be closer to herd immunity than is generally supposed. (At least temporary herd immunity – future epidemics are likely due to new variants and/or if population immunity declines).

2. This near herd immunity is a result not only of immunity acquired through infection and vaccination, but also to a large extent of changes in behaviour, such as working from home. However, such changes are not being entirely abandoned. In fact, working from home at least some of the time is preferred by many and likely to continue indefinitely. The UK should explicitly try to make permanent the least-cost behavioural and technological changes – such as mask-wearing in certain settings and improved ventilation – that reduce R and thereby help create herd immunity, not just to Covid, but also other respiratory diseases.

3. The UK should explicitly try to increase population not just individual immunity by vaccination, to compensate for the gradual increase in contacts likely as people gradually abandon at least some of the habits they have gained during the pandemic. Vaccination should be promoted as “doing your bit” for society, not just to protect yourself. If compulsory vaccination is seen as appropriate for care workers this should be extended to other occupations involving large numbers of contacts, or contact with vulnerable people.

4. There is hope even with current policies that the UK will soon achieve herd immunity as more younger people acquire immunity through infection. But pushing harder on vaccines would achieve the same result quicker and with fewer cases, hospitalisations and fatalities amongst the more vulnerable, principally the elderly.

Footnote (added 27/10/21): Figure 2, the graph of hospital admissions by vaccine status is inaccurate, because of problems with population estimates, e.g. see the discussion in the Observer of 19th Sept by David Spiegelhalter and Anthony Masters, Take care with claims about unvaccinated case rates. I tweeted to Spiegelhalter that this problem could easily be resolved by sampling the population, but the graph is still being used, e.g. at the Downing Street press conference on 20/10/21.