**Herd Immunity revisited**

At the start of the pandemic, there was much discussion about the possibility of letting it run its course until ‘Herd Immunity’ was reached. This option was rejected as it was projected to involve perhaps 350,000 deaths and a crisis in hospital admissions. Now, with deaths probably over 50,000, and a ‘second wave’ starting, the option of aiming for herd immunity has resurfaced – more precisely, aiming for herd immunity in the younger age-groups, combined with protection for the most vulnerable sectors of the population. So it seems a good time to have another look at the question.

**Background**

Statistical models of epidemics predict that, in the absence of any control measures, after an initial exponential rise in the number of cases, the epidemic will start to slow down as the proportion of the population who have already had the disease (and are presumed to be immune) rises, and hence the proportion who are still sensitive declines. Eventually it grinds to a halt because there are no longer enough non-immune people to sustain it. This point is known (rather unfortunately) as herd immunity.

It all hinges on the value of the now infamous parameter called R. For COVID-19, R is thought to be somewhere between 3 and 4, in a wholly susceptible population, in a country like the UK. That is, one infectious individual will, on average, infect 3-4 others. The point at which herd immunity kicks in (the Herd Immunity Threshold, HIT) can be estimated from the initial value of R, so if R=3, then HIT is about 67% (or 2/3). That’s about 40 million cases.

To calculate the number of expected deaths, we need to know how many of those will die – the case fatality rate. That is commonly put at about 1% (on average). 1% of 40 million is 400,000 (which is more or less where that 350,000 figure comes from).

The value of R is not just down to the nature of the virus. It is also influenced by the probability of making an ‘effective contact’ – that is a contact between an infectious person and a non-immune one, which is in turn affected by a number of factors such as how long you remain infectious, as well as how many people you come into contact with while you are infectious. This will depend on where you live; someone living in a remote area will contact very few people compared to one in a big city. A national value of R is a very rough measure of progress as it is an average value over areas with widely different real values.

The likelihood of an effective contact will also depend on your personal behaviour, especially the extent to which you go and mix with others. This is where the lockdown measures come in. They are an attempt to alter people’s behaviour so they will contact fewer people, and hence drive down the value of R.

**So what?**

Suppose the restrictions succeed in driving down the value of R to below 1, and keeping it there, the model tells us that each infectious person is infecting less than one other person, and hence the disease will die out, even without achieving herd immunity. And we’ll suppose that at this point, say 20% of the population have been infected (and hence are assumed immune). We would now have no cases, but 80% of the population is still non-immune. Is that the end of the story?

If we were living in complete isolation from the rest of the world, it would be. But we are not. All it needs is for one infected person to enter the country from an area where the disease is still rampant and away we go again. New Zealand is in just this situation, and they are attempting to keep it out by quarantining all those entering the country (which must devastate their tourism industry). But it is unimaginable for the UK to attempt to do this.

Furthermore, although after the first wave of infections there was a very substantial drop in the number of cases (presumably due to the restrictions, or some of them anyway), the disease did not disappear completely. There were enough cases continuing to be able to re-seed the epidemic once the brakes were taken off, so the second wave was inevitable. If the new restrictions now coming in succeed in controlling the second wave, we can confidently assume the same will happen again.

What this tells us is that if we don’t achieve herd immunity, we will have to carry on with some form of lockdown indefinitely (at least until a reasonably effective vaccine is available).

So we need to look again at the herd immunity strategy, and the assumptions that led us to reject it initially. In particular, how far have we already gone in that direction – in other words how many people have actually been infected? The limitations of testing means that it doesn’t tell us that. One way to estimate it is by looking at the number of deaths. Let’s call that 60,000 (a bit higher than the data from death certificates). If the case fatality rate is 1%, that implies a total of 6 million infections so far; in other words, about 10% of the population have now been infected at some stage. If the fatality rate is lower than that (I have seen estimates from elsewhere that put it as low as 0.3%), then the number of infections could be much higher, possibly up to 30% of the population. If you were to do this calculation in earnest, you would need to allow for the number of deaths in the elderly or other highly vulnerable groups (with a much higher fatality rate).

Alternatively, a more direct way, is to assess the frequency of SARS-CoV-2 antibodies in the population. ONS do sample surveys to measure this, and the latest figures I’ve seen put it at about 6%. However, this does assume that everyone who had been infected at some stage produces enough antibody to be detected by the test.

If we take somewhere in the region of 10% as the proportion who have been infected, that is still way short of the 67% that we think is needed for herd immunity. However, we’re looking at overall figures for the whole country, while COVID has affected some places much more than others. Trying to unravel that gets complicated, especially as those places with more cases have a higher initial value of R, and hence require a higher level of herd immunity. But it is tempting to wonder why London has not seen anything like the same level of 2^{nd} wave (as yet).

However, although we may still have a way to go before getting herd immunity, is there any alternative? Of course, if a vaccine emerges (even a partially effective one), it would change the situation drastically. Without that, are we faced with having restrictions indefinitely? It may be that all that would achieve is to prolong the epidemic, but smoothing it out so that the NHS doesn’t get overwhelmed. In other words, we would get the same number of cases, and deaths, but over a longer time.

One alternative that is being canvassed is to withdraw restrictions and allow the epidemic to run its course, while, at the same time, providing better protection for those more vulnerable, especially in care homes. In that way, we could build up herd immunity in those who are very much less likely to suffer serious effects, which in turn would protect the most vulnerable. This is often caricatured as locking away all the elderly and sick people and throwing away the key. But it doesn’t have to mean that. We could, for example, provide much better support for care homes – not just PPE for the staff (important that it is) but also in installing facilities, such as screens, that would allow safe visiting. And we would need to make sure that those who were isolating at home would also receive better support, not just in providing food parcels, but again devising ways in which they could safely receive visitors.

The final verdict must be that unless and until we get a vaccine, herd immunity (however it is achieved) is the only way in which this epidemic will cease.

Herd immunity seems fine until you realise as you get older you are more likely to get kicked out of it. I would assume that would happen in large herds like buffalow ( well before we came along with our own virus ie a rifle). I can see the logic of it but Im just not quite ready to do my bit by dying for my country. But yes unless we become a totaly closed island all we are really doing is trying to keep non productive people like me alive at the expense of the many. Thank heavens I live in a civilised if confused society.

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You don’t get ‘kicked out of it’. The point about herd immunity is that it protects everyone, even those who are not immune, because when you get to that stage the disease doen’t have a chance to get a hold. While I understand why no-one will say that herd immunity is our aim, unless we get a vaccine that is the only way the epidemic will end.

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