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What It Takes to Get to Herd Immunity

Justin Fox
·12 min read

(Bloomberg Opinion) -- The term “herd immunity” appears to have first been used in its modern sense in a December 1916 article in the Journal of the American Veterinary Medical Association with the curious title, “The Present Status of the Abortion Question.”(2)

The abortion in question was an infection causing cattle to give birth prematurely to stillborn or ailing calves. U.S. Department of Agriculture researchers Adolph Eichhorn and George Potter observed “there is a constant tendency for the disease to die in an infected herd,” which they attributed to acquired immunity.(1) To take advantage of this “herd immunity,” they advised, cows that contracted the disease should be returned to the herd after an isolation period because in most cases they were able to give birth successfully the next time around, and “the animals which have required a resistance are more valuable, in an infected herd, than newly introduced, susceptible animals.”

Over the next few years, as described in an educational (and paywall-free) article published last month in medical journal The Lancet, the term made its way into human medicine, usually but not exclusively in the context of vaccination. What percentage of a population needed to be immune to an infectious disease, epidemiologists struggled to determine, to cause it to begin to die out?

The answer delivered by the susceptible-infectious-recovered mathematical model first outlined in 1927, and developed into something like its present form in the 1980s, is simple. The key is the basic reproduction number, or R0 (with the zero usually spoken aloud as “naught”), which represents how many other people the average person with the disease is likely to infect, in a fully susceptible, fully mixed population going about its business in normal fashion. In this model, herd immunity is reached when the share of the population immune to the infection equals 1 minus 1/R0.

Which brings us to Covid-19. It is impossible to know yet how complete and long-lasting the immunity conferred by infection with the new coronavirus, or vaccination against it, will be. It does not appear to be universal, given that there have been several documented cases of reinfection. And it’s almost certainly not eternal, possibly falling somewhere between the several months of immunity that seem to follow infections with the four coronaviruses that cause common colds and the two or more years that follow infections with the more-severe and also-coronavirus-caused Sudden Acute Respiratory Syndrome and Middle East Respiratory Syndrome.

Still, that’s not nothing, and the hope that enough people could soon become immune to Covid-19 to thwart its spread has been broached by optimistic sorts since early in the pandemic. This month, three outside-the-mainstream (at least on this issue) epidemiologists issued a declaration urging an approach to managing the disease that “balances the risks and benefits of reaching herd immunity,” and the White House appeared to embrace it.

The simple herd-immunity model

How many people would have to develop immunity to Covid-19 for us reach herd immunity? There’s the simple answer — the model-derived immunity percentage described above — and at least three more-complicated ones.

First, the simple model: Estimates of the R0 of Covid-19 vary, but I’ll go with the range of 3.3 to 3.8 estimated by the Robert Koch Institute, Germany’s equivalent of the U.S. Centers for Disease Control and Prevention. Plug those numbers into the 1 minus 1/R0 formula described above, and what comes out is that 70% and 74% of a population would have to be immune to Covid-19 to keep it from spreading.

This explains the Covid-19 herd-immunity thresholds of two-thirds, 70% or more that one often sees cited in the media. These are a lot higher than the threshold for the disease with which Covid is most often compared, influenza. Even the pandemic H1N1 influenza of 2009 had an R0 estimated at 1.5 or less, and ended up infecting about 20% of the U.S. population from April 2009 through April 2010, according to the CDC. There was, to be sure, a vaccine that came out in autumn 2009, but cases had begun to decline in the U.S. even before it was widely available.

There’s no reliable tally of how many Americans have been infected so far with Covid-19. The number of confirmed cases amounts to only 2.5% of the U.S. population, but that is universally acknowledged to represent a major undercount. Guesstimates based on antibody surveys and informed extrapolation have put it somewhere between 10% and 17% of the population. So far the disease has killed 221,083 people in the U.S., according to the Johns Hopkins University Covid-19 dashboard, and nearly 300,000 if you go by the CDC’s excess-deaths estimates. Bringing the infection percentage up to 70% of the population would, if the fatality rate remains the same, lead to more than 700,000 additional deaths.

The resulting total would still be significantly less than the 2.2 million U.S. deaths researchers at Imperial College London famously forecast in March if Covid-19 were allowed to spread unchecked. That’s mainly because, while early in the pandemic the U.S. fatality rate seems to have been right around the 0.8% of infections the Imperial College team assumed, it appears to have fallen since then. Going by data scientist Youyang Gu’s sadly just-discontinued Covid-19 Projections infections tracker, the source of the 17% infection-rate estimate cited in the preceding paragraph, the fatality rate has been 0.42% overall. Still, it would have to fall by quite a bit more for reaching the 70% threshold via infection in the U.S. not to result in hundreds of thousands more deaths.

The risk of overshoot

That’s the simple and not-very-encouraging answer to the question of what it will take to reach herd immunity. The first of the more-complicated answers is even less encouraging. “The herd immunity threshold is kind of like the low-fuel light on your car. It’s not the empty-tank light,” says Georgetown University biologist Shweta Bansal. “It’s not the maximum number of individuals that will be infected. It’s the point where the epidemic begins to slow down.”

If a population reaches the herd immunity threshold via vaccination, then the disease may not spread much beyond that. If it gets there by way of a raging epidemic in which, say, 15% of the population is still infectious when the threshold is reached, then it’s a different story.

Here’s what happened when I created a simulated epidemic with an R0 of 3.5 on the Covid-19 Scenarios site created by scientists at the University of Basel in Switzerland and the Karolinska Institute in Sweden. According to the 1-1/R0 formula the herd immunity threshold is 71%, and in my simulation new infections peaked even before then, but 97% of the population still got the disease:

The benefits of heterogeneity

The other two complications at least have the potential to drive the threshold down instead of up. One is that an average measure such as R0 hides a lot of differences in how a disease spreads and who spreads it. Such heterogeneity is usually much less important for respiratory ailments than for sexually transmitted diseases and those spread by “vectors” such as mosquitoes. But Covid-19 seems to share some characteristics of the latter. Most people who get it don’t infect anyone, but some infect dozens via super-spreading events.

If people with a high propensity to spread the disease hang out with one another, and those with a low propensity do the same, then a population could reach herd immunity at a lower threshold than if everyone were the same. If the people with a high propensity to spread are also less susceptible to dying from the disease than those with a low propensity to spread, then that threshold could be reached with far less misery and death than in the scenario I outlined above.

A simple illustration: At an R0 of 2, 500 people in a population of 1,000 would need to be immune to reach herd immunity. Split that 1,000 into 500 people with an R0 of 1.5 and 500 with an R0 of 2.5 — still an average R0 of 2 — and you get to herd immunity with 167 people in the first group and 300 in the second, which adds up to 467.

The bigger the differences between the groups, the bigger the effects: If the R0s are 1.1 and 2.9, then herd immunity is reached at 373 of the 1,000. Scientists with much more complex models than that have come up with theoretical Covid-19 herd-immunity thresholds lower than 20%.

Cool, no? “I will not disagree with you that theoretically it’s a cool idea — I have built my career on it,” says Bansal, who studies how social behavior and population structure shape infectious disease transmission. “But in the absence of having really high confidence in that threshold, I don’t know how we could build policy around that.”

The role of T-cells

Meanwhile, several studies published this summer reported that as many as half of people not infected with the new coronavirus had infection-fighting T-cells that react to it, probably because of past coronavirus-caused colds. This led some to argue that 50% of the population might have already been immune to Covid-19 before the pandemic, implying we could be much closer to the herd immunity threshold than previously thought. That may have been mostly wishful thinking, though.

For one thing, if Covid-19 spread as fast as it did early this year in populations of which half were already immune, then its R0 must be twice what it was thought to be, meaning one would have to subtract that 50% from a higher herd immunity threshold of 85% to 87%. More important, subsequent studies on the role of pre-existing T-cells in fighting Covid-19 indicate they reduce the severity of infections rather than prevent them outright, and may misfire in older people. The contribution T-cells are making is probably “baked in,” researchers from the Harvard T.H. Chan School of Public Health and La Jolla Institute for Immunology wrote in Nature Reviews Immunology this month, meaning it’s “already accounted for by the empirical observational data available and factored into epidemiological models of spread and herd immunity.”

Real-world herd immunity

Looking at the actual trajectories of Covid-19 epidemics around the world, there doesn’t seem to be enough evidence yet to make confident pronouncements about what the real-world herd immunity threshold is, other than that it’s almost certainly not below 20%.

In London and Madrid, where antibody surveys indicated 18% and 11% of the population, respectively, were infected with the new coronavirus during the first wave earlier this year, that clearly wasn’t enough to prevent big new outbreaks this fall. In Manaus, a Brazilian city on the Amazon River, the epidemic seemed to fade at an infection rate that estimates based on antibody surveys put at 66% of the population, but has sparked up again recently. In Iquitos, a Peruvian city farther up the Amazon, a government-sponsored survey this summer found that 71% of the population had antibodies suggesting they had been infected, while news reports at the time indicated another 22% of the city’s residents still had the disease.

“Probably, once you get perhaps 30%, 40% of your population immune, you’re going to see a very different dynamic,” says Adam Kucharski, an epidemiologist at the London School of Hygiene and Tropical Medicine. But that dynamic will depend on other things besides just the immunity percentage. A disease’s effective reproduction number is the product of four variables that Kucharski dubs DOTS, for:

the duration of time someone is infectious the opportunities for transmission during this period (such as social interactions) the transmission probability during each opportunity (such as whether someone coughs or sneezes) the probability that the person on the other end of the interaction is susceptible to that infection.

A higher proportion of immune people reduces the S in DOTS. Individual behavior changes and government mandates can reduce 0 and perhaps T (a mask reduces the probability of transmitting the disease when you cough). Pre-existing differences in social structure also affect O — for example, people living alone make up more than 40% of households in the Nordic countries and Germany, but just 12% in Brazil and 13% in Peru. Weather appears to affect O, T and probably S as well. Having more people with immunity can definitely slow the spread of Covid-19, but given all the other things that are going on, herd immunity is something of a moving target.

(1) The term was previously used in the Report of the Committee on Animal Food to the annual convention of the U.S. Veterinary Medical Association in 1893 but was said to be brought on by "hygienic surroundings, proper exercise, proper food, and by practising the principles of breeding." So ... not the same idea.

(2) Eichhorn and Potter, who both left the USDA around the time the article was published (Eichhorn for Lederle Labs in suburban New York, Potter for the Kansas Cooperative Extension Service), attributed the disease to the brucella abortus bacteria. Subsequent research has found that many cattle abortions are also caused by the infectious bovine rhinotracheitis virus.

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.

Justin Fox is a Bloomberg Opinion columnist covering business. He was the editorial director of Harvard Business Review and wrote for Time, Fortune and American Banker. He is the author of “The Myth of the Rational Market.”

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