Herd Immunity, Facts and Numbers

Today, I have a few words to say about herd immunity because there’s very little science in the discussion about it. I also want to briefly comment on the Great Barrington Declaration and on the conversation about it that we are not having.


First things first, herd immunity refers to that stage in the spread of a disease when a sufficient fraction of the population has become immune to the pathogen so that transmission will be suppressed. It does not mean that transmission stops, it means that on the average one infected person gives the disease to less than one new person, so outbreaks die out, instead of increasing.

It’s called “herd immunity” because it was first observed about a century ago in herds of sheep and, in some ways we’re not all that different from sheep.

Now, herd immunity is the only way a disease that is not contained will stop spreading. It can be achieved either by exposure to the live pathogen or by vaccination. However, in the current debate about the pursuit of herd immunity in response to the ongoing COVID outbreak, the term “herd immunity” has specifically been used to refer to herd immunity achieved by exposure to the virus, instead of waiting for a vaccine.

Second things second, when does a population reach herd immunity? The brief answer is, it’s complicated. This should not surprise you because whenever someone claims the answer to a scientific question is simple they either don’t know what they’re talking about, or they’re lying. There is a simple answer to the question when a population reaches herd immunity. But it does not tell the whole story.

This simple answer is that one can calculate the fraction of people who must be immune for herd immunity from the basic reproduction number R_0 as 1- 1/R_0.

Why is that? It’s because, R_0 tells you how many new people one infected person infects on the average. But the ones who will get ill are only those which are not immune. So if 1-1/R_0 is the fraction of people who are immune, then the fraction of people who are not immune is 1/R_0.

This then means that average number of susceptible people that one infected person reaches is R_0 * 1/R_0 which is 1. So, if the fraction of immune people has reached 1 – 1/R_0, then one infected person will on the average only pass on the disease to one other person, meaning at any level of immunity above 1 – 1/R_0, outbreaks will die out.

R_0 for COVID has been estimated with 2 to 3, meaning that the fraction of people who must have had the disease for herd immunity would be around 50 to 70 percent. For comparison, R_0 of the 1918 Spanish influenza has been estimated with 1.4 to 2.8, so that’s comparable to COVID, and R_0 of measles is roughly 12 to 18, with a herd immunity threshold of about 92-95%. Measles is pretty much the most contagious disease known to mankind.

That was the easy answer.

Here’s the more complicated but also more accurate answer. R_0 is not simply a property of the disease. It’s a number that quantifies successful transmission, and therefore depends on what measures people take to protect themselves from infection, such as social distancing, wearing masks, and washing hands. This is why epidemiologists use in their models instead an “effective R” coefficient that can change with time and with people’s habits. Roughly speaking this means that if we would all be very careful and very reasonable, then herd immunity would be easier to achieve.

But that R can change is not the biggest problem with estimating herd immunity. The biggest problem is that the simple estimate I just talked about assumes that everybody is equally likely to meet other people, which is just not the case in reality.

In realistic populations under normal circumstances, some people will have an above average number of contacts, and others below average. Now, people who have many contacts are likely to contribute a lot to the spread of the disease, but they are also likely to be among the first ones to contract the disease, and therefore become immune early on.

This means, if you use information about the mobility patterns, social networks, and population heterogeneity, the herd immunity threshold is lower because the biggest spreaders are the first to stop spreading. Taking this into account, some researchers have estimated the COVID herd immunity threshold to be more like 40% or in some optimistic cases even below 20%.

How reliable are these estimates? To me it looks like these estimates are based on more or less plausible models with little empirical data to back them up. And plausible models are the ones one should be especially careful with.

So what do the data say? Unfortunately, so far not much. The best data on herd immunity so far come from an antibody study in the Brazilian city of Manaus. That’s one of the largest cities in Brazil, with an estimated population of two point one million.

According to data from the state government, there have been about fifty five thousand COVID cases and two thousand seven hundred COVID fatalities in Manaus. These numbers likely underestimate the true number of infected and deceased people because the Brazilians have not been testing a lot. Then again, most countries did not have sufficient testing during the first wave.

If you go by the reported numbers, then about two point seven percent of the population in Manaus tested positive for COVID at some point during the outbreak. But the study which used blood donations collected during this time found that about forty-four percent of the population developed antibodies in the first three months of the outbreak.

After that, the infections tapered off without interventions. The researchers estimate the total number of people who eventually developed antibodies with sixty-six percent. The researchers claim that’s a sign for herd immunity. Please check the information below the video for references.

The number from this Brazilian study, about 44 to 66 percent seems consistent with the more pessimistic estimates for the COVID herd immunity threshold. But what it took to get there is not pretty.

2700 dead of about two million that’s more than one in a thousand. Hospitals run out of intensive care units, people were dying in the corridors, the city was scrambling to find ways to bury the dead quickly enough. And that’s even though the population of Manaus is pretty young; just six percent are older than sixty years. For comparison, in the United States, about 20% are above sixty years of age, and older people are more likely to die from the disease.

There are other reasons one cannot really compare Manaus with North America or Europe. Their health care system was working at almost full capacity even before the outbreak, and according to data from the world bank, in the Brazilian state which Manaus belongs to, the state of Amazonas, about 17% of people live below the poverty line. Also, most of the population in Manaus did not follow social distancing rules and few of them wore masks. These factors likely contributed to the rapid spread of the disease.

And I should add that the paper with the antibody study in Manaus has not yet been peer reviewed. There are various reasons why the people who donated blood may not be representative for the population. The authors write they corrected for this, but it remains to be seen what the reviewers think.

You probably want to know now how close we are to reaching herd immunity. The answer is, for all can tell, no one knows. That’s because, even leaving aside that we have no reliable estimates on the herd immunity threshold, we do not how many people have developed immunity to COVID.

In Manaus, the number of people who developed antibodies was more than twenty times higher than the number of those who tested positive. As of date in the United States about eight point five million people tested positive for COVID. The total population is about 330 Million.

This means about 2.5% of Americans have demonstrably contracted the disease, a rate that just by number is similar to the rate in Manaus, though Manaus got there faster with devastating consequences. However, the Americans are almost certainly better at testing and one cannot compare a sparsely populated country, like the United States, with one densely populated city in another country. So, again, it’s complicated.

For the Germans here, in Germany so far about 400,000 people have tested positive. That’s about 0.5 percent of the population.

And then, I should not forget to mention that antibodies are not the only way one can develop immunity. There is also T-cell immunity, that is basically a different defense mechanism of the body. The most relevant difference for the question of herd immunity is that it’s much more difficult to test for T-cell immunity. Which is why there are basically no data on it. But there are pretty reliable data by now showing that immunity to COVID is only temporary, antibody levels fall after a few months, and reinfections are possible, though it remains unclear how common they will be.

So, in summary: Estimates for the COVID herd immunity threshold range from roughly twenty percent to seventy percent, there are pretty much no data to make these estimates more accurate, we have no good data on how many people are presently immune, but we know reinfection is possible after a couple of months.

Let us then talk about the Great Barrington Declaration. The Great Barrington Declaration is not actually Great, it was merely written in place called Great Barrington. The declaration was formulated by three epidemiologists, and according to claims on the website, it has since been signed by more than eleven thousand medical and public health scientists.

The supporters of the declaration disapprove of lockdown measures and instead argue for an approach they call Focused Protection. In their own words:

“The most compassionate approach that balances the risks and benefits of reaching herd immunity, is to allow those who are at minimal risk of death to live their lives normally to build up immunity to the virus through natural infection, while better protecting those who are at highest risk. We call this Focused Protection.”

The reaction by other scientists and the media has been swift and negative. The Guardian called the Barrington Declaration “half baked” “bad science” and “a folly”. A group of scientists writing for The Lancet called it a “dangerous fallacy unsupported by scientific evidence”, the US American infectious disease expert Fauci called it “total nonsense,” and John Barry, writing for the New York Times, went so far to suggest it be called “mass murder” instead of herd immunity. Though they later changed the headline.

Some of the criticism focused on the people who wrote the declaration, or who they might have been supported by. These are ad hominem attacks that just distract from the science, so I don’t want to get into this.

The central element of the criticism is that the Barrington Declaration is vague on how the “Focused Protection” is supposed to work. This is a valid criticism. The declaration left it unclear just to how identify those at risk and how to keep them efficiently apart from the rest of the population, which is certainly difficult to achieve. But of course if no one is thinking about how to do it, there will be no plan for how to do it.

Why am I telling you this? Because I think all these commentators missed the point of the Barrington Declaration. Let us take this quote from an opinion piece in the Guardian in which three public health scientists commented on the idea of focused protection:

“It’s time to stop asking the question “is this sound science?” We know it is not.”

It’s right that arguing for focused protection is not sound science, but that is not because it’s not sound, it’s because it’s not science. It’s a value decision.

The authors of the Great Barrington Declaration point out, entirely correctly, that we are in a situation where we have only bad options. Lockdown measures are bad, pursuing natural herd immunity is also bad.

The question is, which is worse, and just what do you mean by “worse”. This is the decision that politicians are facing now and it is not obvious what is the best strategy. This decision must be supported by data for the consequences of each possible path of action. So we need to discuss not only how many people die from COVID and what the long-term health problems may be, but also how lockdowns, social distancing, and economic distress affect health and health care. We need proper risk estimates with uncertainties. We do not need scientists who proclaim that science tells us what’s the right thing to do.

I hope that this brief survey of the literature on herd immunity was helpful for you.

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I have a video upcoming later today with astrophysicist (!) Niayesh Afshordi from Perimeter Institute about his new pandemic model (!!), so stay tuned. He will also join the Thursday chat at 5pm CET. Note that this is the awkward week of the year when the NYC-Berlin time shift is only 5 hours, so that's noon Eastern Time.