# The never ending quest for herd immunity

Last week I read a news article on how the CDC are moving away from a target of controlling the covid epidemic by trying to reach herd immunity. In the words of Dr Jefferson Jones, a medical officer on the CDC’s COVID-19 Epidemiology Task Force:

The prospects for meeting a clear herd-immunity target are “very complicated,” … Thinking that we’ll be able to achieve some kind of threshold where there’ll be no more transmission of infections may not be possible,”

Well, he’s right. Herd immunity is a complex topic with many aspects to consider, including how the risks of infection and onwards-transmission might be influenced by factors such as age, vulnerability, as well as nuances such as the importance of care-homes, healthcare facilities and education centres.

But, at a fundamental level, herd immunity can be considered as being rather simple. The herd immunity threshold for a population where everyone has a similar risk of disease is set by a simple equation

*Where R0 is the virus’ basic reproduction number, ie how many people on average each infected person will pass the infection on to. (for a covid specific academic discussion about this equation and herd immunity see this paper)*

Back in early 2020 the basic reproduction number of covid (R0) was estimated to be approximately 2.5-3. Putting this value for R0 reveals an estimate of the proportion of the population needed to be vaccinated to achieve herd immunity — around 60%-66%. Thus around that time we had reports (eg, this one) saying that we’d need to have around 60% of the population either vaccinated or having been infected with covid naturally. By last May the range had increased to 70-90% vaccination, but now with no contribution from natural infection1 — I note that at the time the estimated R0 for the newer variants has risen to approximately 5-8 — giving a herd immunity threshold using the equation above of around 80%-88%.

I believe that use of the simple herd immunity equation is why the original estimate of the proportion of the population needed to be vaccinated was around 65%, and why it has since risen to around 85%, itself explaining the push to vaccinate children (vaccination levels can only reach approximately 80% by only vaccinating adults).

**However, that equation for herd immunity is incomplete — it assumes that the** **vaccine is 100% effective at stopping infection and thus onwards transmission**. This is a reasonable assumption because most important vaccines are highly effective at stopping infections (the influenza vaccine is a rare exception) and thus it is seldom necessary to correct for this. However, adding in the term for vaccine effectiveness does change the equation:

*Where the new term ε is the vaccine efficiency, or the proportion of infectious cases that are prevented compared with the unvaccinated. Note that this term only relates to infections and onwards transmission, not the impact of the vaccines on hospitalisation and death.*

Of course, back in early 2020 there was no consideration that a vaccine solution to covid would have anything other than very high effectiveness at reducing infections (and for good reasons2) so their estimate of the numbers required to have been vaccinated or infected were reasonable. However, by spring ‘21 we were beginning to understand the relatively poor performance of the vaccines at preventing infection, and should have updated our assumed ‘herd immunity threshold’; inexplicably, the advice on herd immunity thresholds continued to assume that the vaccines were highly protective.

The impact of this new term (vaccine effectiveness) in the equation cannot be understated. For example for an R0 of 5, the original equation stated that around 80% of the population would need to be vaccinated; with a vaccine effectiveness of 80% (ie, ‘high’ for the covid vaccines) this becomes 100%. **The authorities knew back in the spring that the herd immunity threshold from vaccination was far higher than their stated 80%, but didn’t inform the public that this was the case.**

Even worse, the vaccines don’t even offer this level of performance. With an R0 of 3 (ie, close to the original estimate for Wuhan strain) and 60% vaccine effectiveness (apparently, what we have now, although there is strong evidence that it is worse than this) you get an estimate of the herd immunity threshold of approximately 110%. As you can’t vaccinate more than 100% of the population, **a calculated herd immunity threshold of over 100% means that herd immunity is impossible**, at least by that means. An R0 of 6 and a vaccine effectiveness of around 33% give a calculated herd immunity threshold of around 250% — *even more impossible*.

Going back to where I started this post, Dr Jones said that herd immunity is ‘*very complicated’*. It is. There are complications such as how immunity changes with the age distribution in the population, how protection wanes over time and the influence of a minority in the population that have different responses to the vaccines (eg, the immuno-suppressed) — but it never gets any better than the threshold given by the second equation above. To be fair to Dr Jones, he at least presented the possibility that herd immunity might not be possible, but there are plenty of others at senior levels in countries around the world who still maintain that herd immunity is a valid goal — the belief that herd immunity will help us appears to be entrenched, both in society in general and in those the government select to advise them.

The authorities have known since at least spring that the vaccines would not be capable of offering us a herd immunity protection. It is inexplicable why they continued, and still continue, to push the message that we have to meet some arbitrary and unscientific vaccination threshold to ‘defeat covid’.

There was no explanation as to why natural infection was no longer considered — for the non-vulnerable the risks are low and the protection offered appears to be long-lasting, but that’s an issue for another day

There were good reasons to assume that any vaccine solution would have excellent effectiveness at preventing infection — mainly because poor vaccines introduce significant risks — see this important paper for a review of how vaccines with low effectiveness can end up making things far far worse.

Bartram, this is a splendid, very understandable piece.

In conjunction with the Roy Anderson study, everything now becomes clear for the cockupist.

They are just trying to increase the vaxx rare to reach HI and following RMA's recommendations to a T.

Besides misunderstanding HI, ignoring its complexities and often likely still equating it with elimination, they ignore that negative VE, like confirmed now in the UK, by definition/math leeds to a RISE in cases, as we can all witness now. The question then becomes: are the additional hospitalisations/deaths due to the vaxx rate push increased rise in cases lower than the ones prevented through that additional vaxxing, or lower than if vaxxing was stopped now, or if it had only been performed with those at most risk.

I think we all know the answer to that intuitively, but maybe you can throw some mathematical light on it?!

Here in NZ herd immunity was initially suggested at 70%, then retracted, then no level was high enough, then 90% was the magic double vaccinated number then experts said it was not enough. Zero talk of natural immunity. Really. I think the state is just in the business of selling vaccines at this stage. That's the only theory that makes all the insanity make sense. NZ political class and media are in PR for Pfizer and this is the best business model I've ever seen.