Herd immunity is often held up as a solution to the COVID-19 crisis. Bob Hancké (LSE) argues that it is a dangerous solution, and morally rejectable – in large part because it is a special instance of Goodhart’s law, undermining the very goal it purports to achieve. Herd immunity is not only technically flawed, as many medical experts argue, but also epistemologically wrong in the case of COVID-19.
In mid-October a group of respected medical scientists issued the (somewhat pompously titled) Great Barrington Declaration (GBD), which urged, among other things, the adoption of a ‘herd immunity’ strategy to cope with COVID-19. The economic, social and physical and mental health costs of severe constraints on normal activity are now larger than they would be in a situation where the pandemic could just run its course. The GBD recommends that a sizeable share of the population build up immunity while protecting the most vulnerable, thus stopping the growth of the viral infection.
While I am not an epidemiologist or in any other way trained in matters related to health, I do teach research design and care deeply about the quality of public policy, especially in the case of a nasty epidemic like COVID-19. As the debate about herd immunity, especially after the GBD, gathered steam, a problem that has haunted many well-meant policies suddenly seemed to make a guest appearance. Made famous by LSE professor Charles Goodhart, the law with his name goes roughly like this: If an observed (statistical) regularity becomes the target of an intentional policy, it ceases to be a meaningful measure for policy making.
In what follows, I start by unpacking the concept of herd immunity in light of the ironies associated with Goodhart’s law and then develop a very simple model to assess it as a strategy for coping with COVID-19. The upshot is this: the law is alive and well in this area; if adopted, herd immunity would not only undermine its own targets, but its death toll is way beyond what modern societies should or could countenance.
The immunity of the herd
Herd immunity is – for those very, very few among us lucky enough not to have been bombarded with it since early spring 2020 – an epidemiological term referring to the level of aggregate immunity in a population that is necessary to stop an epidemic. The basic idea is that if a certain share of the population, usually held to be around 75%, is immune to a virus, its chances of spreading in the population fall to almost zero. It tries to go from patient A to B, but B has a 75% chance of being immune, so it is very likely not to make it past B; aggregate this over the entire population and the net effect is that almost all contagious jumps from A to anyone else will fail and the virus will slowly die out. While there are loads of possible qualifications (speed of transmission, the immunity rate fluctuating between high and low intensity periods, etc.), none of these would change the fundamental logic. Importantly, you do not need 100% coverage for herd immunity to kick in. Everything above 60% is a good start (in 3 cases out of 5 the disease will not be transmitted), and 75% (3 out of 4) is almost certain to do the trick entirely.
Like all ideas, the notion of herd immunity is based on a few assumptions – most of which are related to its origin in veterinary medicine, where it is a technique to counter a contagious infectious disease making its way through the relatively small local bovine population. Vaccinating a minimum threshold number will create the positive externality explained earlier, in which even non-vaccinated cows run a very low risk of infection. It is also used in mass vaccination programmes for humans, but usually in a quite tightly controlled environment where the same assumptions have to hold: you need to know everything relevant on the evolution of the contagious disease, be certain that immunity will result from the treatment, and be able to measure the number of vaccinations, the degree of immunity and the size of the risk population accurately. Sadly, thus far COVID-19 has escaped much of our understanding in all or most of these areas.
‘We know nothing’
Not only do we know relatively little about the evolution of the disease, as an excellent article in The Atlantic explains, we have no idea, really, what exactly drives the spread of the coronavirus and what the best mitigation strategies are. For example, why did a few small towns in northern Italy record more deaths than the rest of the country combined? Or why did South Korea manage to control the spread of coronavirus, with only a few hundred excess deaths after a very inauspicious start? Apparently, the R number that everybody has focused on to understand the coronavirus’s road through the population is one measure, but probably not a very helpful one. Dispersion rates – and overdispersion as a super-spreader handmaiden – are at least as important, but little is known about how to handle let alone prevent them. In short, we do not understand COVID-19 all that well. Effective vaccines that can be manufactured at scale are, if Ebola, HIV and a few other viruses are anything to go by, possibly still quite a way off. Most of the conditions for a successful herd immunity strategy, and especially the basic knowledge, are simply absent, as an open letter in The Lancet argues.
The dark side of herd immunity
But there is more. The notion of herd immunity produces a series of paradoxes that actually undermines the very idea itself. As a strategy it lacks precision; as a technique it is brutal; and dynamically it is self-destroying. Take each one of these points at a time.
Starting with the basics, let us assume, generously, that once recovered a person is fully immune. It is not certain if this is the case with COVID-19 – there are reported cases of reinfection within one cycle – but assuming immunity after surviving the infection simply stacks the cards against our argument (and if this were not true, the idea of herd immunity makes little sense), so no harm done from a logical and methodological point of view.
Then define herd immunity (H) as the ratio of living immune (R) to P, the total living population: H=R/P. For the sake of the argument, we assume that the target value for H is 75%, i.e. three people out of four need to have been infected and then become immune (or were, for a variety of unknown other reasons, naturally immune). Again, given what we know about COVID-19 in particular and highly contagious viral diseases in general this may not be a high enough value for H; but the H=0.75 assumption simply means that we stack the cards against our argument a second time, without producing a problem for our model. Methodologically these two assumptions are akin to what is known as a critical or limiting case strategy: if our argument holds under these adverse conditions for it to work, the point we make will certainly be true under more favourable circumstances.
An outcome, not a strategy
Back to the H value, now. The interesting thing about this ratio (and all others) is that it is a compound variable, with two direct variables of interest at its roots – in this case R and P – but with an indeterminate relationship. To reach the target H value, R can increase while P remains stable; P can decrease with R stable; both can move simultaneously in opposite directions, R up and P down; both can increase but R increases more than P; or both can decrease but P decreases faster than R. All these combinations will lead to a rise in H. Nothing about H tells us a priori what needs to happen: herd immunity is an outcome of two analytically and practically separate processes, both of which can, at best, only be imperfectly controlled and monitored. This raises the first problem with the concept of herd immunity: since it is a compound variable, the outcome of two complex processes, it is not obvious how it can be a clear, deliberate strategy.
Secondly, the idea has some perverse consequences as a result of this lack of conceptual clarity, as the simple model below illustrates. If A infects B and B dies, the absolute number in R remains constant, while the absolute number for P goes down by 1. That has two very different effects for the ratio R/P. The first is that as a result of B’s death, one infection did not result in a person who is immune, a gap that can only be filled by another infected-and-then-immune person (call this substitution). The second effect, however, pulls in the opposite direction: with a smaller population (Pt0-1 death), we need, in absolute terms, fewer people to be infected to get to the 75% target value for H (call this subtraction).
More, not fewer, infections
Here a subtle version of Goodhart’s law comes into play. Because the effect of the target associated with substitution (0.75) is smaller than the target associated with subtraction (1), deaths as a result of infections increase the number of people who need to be infected to get to 75% of the population. In plain English: trying to bring the infection under control means that more people have to be infected.
As if that was not enough, there’s a morbid twist to this dynamic: because infections carry with them the risk of death, herd immunity leads to a non-trivial increase in the number of additional deaths above those to be expected.
To illustrate this, let us use some actual numbers (I borrowed these from the sister post by Nick Barr): assume H to be 75% and the death rate for the infection to be 1%. In a country like the UK (population c. 65 million) reaching an H value of 75% requires that a whopping 48.75m need to be infected (note that the UK is currently estimated to have a 6% immunity rate, and even if it were double that, reaching a H value of 75% would remain a steep hill to climb). Of those 48.75m, 1% or 487,500 will die. (Interestingly, this is almost exactly the estimated number of deaths predicted by the Imperial College model as the basis of the UK’s spring 2020 lockdown, if the virus had not been countered with stringent containment measures.) If we get the death rate slightly wrong and it is 2%, 975,000 people have to die to reach a H value of 75%. Gulp.
The grim reaper’s second bite of the cherry
The story gets better (or, actually, worse). To achieve an overall infection survival rate of 75%, it is necessary to replace some of the initially infected who died, i.e. to expose more people to infection, as we said earlier. But that is not without costs. With a 1% death rate, a target H value of 75% requires an additional 0.18% exposure, in fact. Assuming a 1% death rate, the number of deaths rises to 488,722 (and over 977,000 in the case of a 2% death rate), i.e. an additional 1,222 (or 2,444) deaths over and above the already staggering baseline numbers.
In sum, there are many very serious problems with the concept of herd immunity. First, conceptually it is hard to think of herd immunity as a clear strategy, given that it consists of two imperfectly understood variables that are only partially under our control. Secondly, a sustained herd immunity strategy kills, prima facie, at least 487,000 people (I abstract here from improvements in health care, which might flatten the curve somewhat but won’t fundamentally change the dynamic unless there is widespread access to an effective vaccine). Finally, the perverse effect associated with this application of Goodhart’s law adds an additional 1,200 (or up to 2,500 if the death rate is above 1%). Such numbers are the stuff of mid-20th century horrors, dystopian movies and end-of-time sci-fi novels, not of sensible policy making.
‘Protecting’ the vulnerable
There is only one logically tight counterargument: protect, i.e. isolate, the vulnerable part of the population with known co-morbidities. That makes some logical sense, in the same way that you could theoretically imagine a single wee-free swimming pool lane. The problem with the idea is that it stumbles at the first practical hurdle: even assuming the vulnerable population is correctly identified (a big if, considering how little we know), how do you stop them from starving, shopping, talking to neighbours, family, etc. for the possibly very long time it takes to get to a 75% H value? At a rate of increase of 7% per annum, roughly the figure for 2020, we are talking about a decade of ‘protection’. And even with an effective vaccine many will still face several years of such ‘protection’. The New York Times ran an eyebrow-raising article on that particular problem with ‘mass murder’ in the title.
Bull immunity and his excrement
Carl Bergstrom and Jevin West, the authors of the highly insightful and entertaining Calling Bullshit: The Art of Skepticism in a Data-driven World refer to Goodhart’s law as a heuristic to spot BS – not unlike what I have done here. Their last chapter, ‘Refuting Bullshit’, invites all of us to point the finger at BS when we spot it. In that spirit, I hereby declare herd immunity in today’s situation a dangerous technocratic fool’s errand, without any basis in fact or science. Bullshit, in other words.
This post represents the views of the author and not those of the COVID-19 blog, nor LSE. The author wishes to thank Nick Barr, Henrike Granzow and Laurenz Mathei for helpful comments on an earlier draft.
Thank you. Interesting and helpful. I have two questions which you may have covered.
The first is that you assume the death rate at 1%. However the death rate does not appear to be even across the population. I wonder if your statement that you are stacking the assumptions still works if it is possible to build herd immunity in lower risk groups where death rates are much lower. I do not know the answer and am curious rather than argumentative.
My second point, which is argumentative, is whether there is a strategy with lower harm. Measuring this is difficult because strategies carry harm other than Covid. My mother is a high risk individual and would not be likely to survive an attack of covid. She would still like to see us at Christmas because she may not have another. I do not refute your logic but maybe what it shows is that there is an inevitable death rate to Covid regardless of the choices made. I very much hope not – by the way.
There does appear to be a problem with all modelling. Every modelling applies an exact theory with estimated data. The WHO estimate that there is a higher infection rate in the global population than your figures. I believe they estimate 10% have been infected.
Mass testing produces more actuate results.
It amazes me that still any deaths where the person tested positively in the past 28 days count as a Covid death. So they include deaths from accidents, heart attacks, cancers and other causes.
I’m not sure Herd Immunity is a strategy. It is the desired outcome. It can be achieved by vaccination or by natural exposure. A vaccination may not be effective for everyone (if one works at all) so we will rely on herd immunity to protect those who are unable to generate an immune response. Despite widespread vaccine uptake in the UK, flu-related deaths are still around 10k in a good year and have been much higher in some recent years.
Also, the numbers above are overly pessimistic – and the article ignores heterogeneity in the population. The Imperial college model used a Fatality Rate of 0.9% which was reasonable assumption in February and March when data was limited but it’s looking more likely that the true IFR is nearer to 0.4% and maybe lower, The risk for over 70s is much higher than for younger people. For under 50s flu presents a greater risk of death than Covid -19.
Finally, Herd Immunity isn’t a simple knife edge threshold. The virus spread in a new surge will be slowed considerably to a much more manageable level if 30% to 40% are immune. Some scientists are suggesting it could be much lower than that. The 6% of the population who are estimated to have antibodies is almost certainly well below the proportion who are immune. The immune system is incredibly complex and not everyone will need to produce antibodies to overcome the virus and those that do produce them don’t necessarily retain them indefinitely – but memory B cells can quickly regenerate an immune response.
The bottom line is we can continue to carry on implementing a series of lockdowns (which won’t work – See Spain , Peru, Argentina, France, UK) indefinitely in the hope that an effective vaccine becomes available or we can adopt a strategy which allows the population to develop a level of herd immunity while protecting the vulnerable.
Thanks for these comments and questions. Many of these points had crossed my (and my colleague Nick Barr’s) mind when we were discussing our joint blogs.
I recommend to Mr Finn that he reads Nick’s post alongside mine. If after that herd immunity still looks like a good idea, we just have to part intellectual ways. I am perfectly happy to accept that some of the estimates are too high (or too low — we simply don’t know and every day brings more mysteries), but they don’t change the fundamental logic of the problem, it seems to me.
In that sense, there are two points to be made here. One is that the precautionary principle dictates that we adopt a low-risk strategy in the absence of persuasive counterarguments. Given how much of a mystery Covid-19 is, with reinfections, long Covid, newly emerging high-risk groups, and now a rising mortality rate among young people, we are in the precautionary realm, which means we not only shield as much of the population as possible, we also think of ways to stop the spread. Two, assume for a moment that the mortality rate is 0.5% and that in this particular instance herd immunity kicks in at around 50% — both heroic assumptions but there you go. That would mean that instead of the almost 500,000 above we would be talking about c. 150,000 for the UK. I am not sure I would call that a victory. To be clear, I am not sure if I am right or he is; but I do know that even if Mr Finn is, we would be living through a nightmare.
Mr Kennedy puts his finger on a key problem: are the effects of a lockdown not worse than most reasonable alternatives? Perhaps — but we don’t know any reasonable alternatives beyond test and trace. That’s apparently how South Korea got Covid under control, and that has also been the WHO’s mantra since February. I have no idea why the UK government (and many others in Europe, for that matter) have not used the painful lockdown in the spring to set up a serious test and trace system (beside spending money on pointless apps and expensive inept consultants), but its glaring absence is why you’re mum is, sadly, on balance better off not enjoying Christmas with you. Such a system would probably also address the problems that Mr Finn flags: lockdowns are very blunt instruments. True but as long as the only intelligent alternative is absent, they are a blunt but realistic policy?
As to age-specific mortality rates and their possible effects, two things to bear in mind. The first, as I said above, is that we do not know enough about the profile of the virus and the disease to be confident enough to try age-specific measures. Second, we sort of tried exactly this, but without giving it that name, when we reopened schools and universities. Look what happened. Within a few weeks, these places had become super-spreaders, students were forced to remain in quarantine and, assuming they are allowed to leave, they will almost certainly carry the virus along on their Christmas break. My suspicion is that the rising infection rates throughout Europe right now are a direct result of these tacit age-specific measures: holidays (many with pre-existing conditions stayed at home shielding), and schools and universities reopening. That’s why age-specific measures are conceptually like a wee-free swimming pool lane — the colourful image I used for a tragic reality.
Finally, to Christopher: I am unclear if you mean more accurate or more actual results, but both seem to me to be the stuff that you would hope for. The more we know, the better we could handle this. In any case, the logical conclusion of your point about testing is to stop it and then the virus will go away… The current occupant of the White House seems to believe that too. But not everything is, despite what some naive Foucauldians might think, just a matter of numbers.
Some late deaths are indeed attributed to Covid-19, but others may not be. Unless we know for sure that there is a systematic mistake in recording deaths, it doesn’t seem to me to be the stuff of conspiracy theories. We have conventions when measuring, be they right or wrong. But while it is not entirely clear to me what Christopher is trying to get at, I don’t think there is indeed a massive conspiracy going on. After all, most governments would probably prefer to artificially deflate their numbers in this case.
So, some corrections in the margin might make sense (but not quite yet), though I stand by the basic problem that I identified. Herd immunity is a very bad idea.
If this is the best you can do, it seems the Declaration is onto something. You talk about 60% needing to become immune, but in any healthy under 65 year old is more likely to choke to death on a peanut than to die of covid and has a vanishingly small chance of serious illness from covid even if not immune. So all these statistical hoops you jump through, which come from the study of flu and other diseases that affect young people, are irrelevant.
A very poor and biased approach to the subject.