The Aerosol Conundrum, and What It Might Tell Us About Herd Immunity

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Chicagoans have one thing in common: we do not, in the balmy days of mid-summer, feel nostalgic for February. So chalk up another tally on the register of ways 2020 has changed everything: we’d all merrily transport ourselves back to that naïve era when the coronavirus was a thing in China but not a scourge that would turn our lives upside down.

When the mayhem in Milan opened our eyes to the severity of the threat, we scrambled to learn how to protect ourselves. Back then, medical experts told us the virus spread primarily by airborne droplets which travel less than six feet and fall quickly to the ground. We were safe as long as we remained at least six feet away from other people, regardless of our surroundings or the length of time we were in contact.

Naturally, as scientists have studied the virus since then, knowledge improved and many of the early recommendations have changed. For example, the World Health Organization first claimed only sick people were infectious. That, unfortunately, proved false: now we know asymptomatic spreaders cause many new infections. Among the most important changes has been the growing belief that aerosols, in addition to droplets, represent a significant source of transmission.

This is frightening. Aerosols drift long distances and stay in the air for hours. It’s at least theoretically possible to breathe in a virus shed long ago by someone no longer present. How can we ever feel safe? Outdoors is better: the aerosols are dispersed by wind and waft over a wide expanse, so you’re unlikely to breathe in enough virus to cause illness.

Now, just as we’re getting used to the idea of protecting ourselves from aerosols by wearing masks and avoiding rooms with poor circulation, the Journal of the American Medical Association publishes an article on July 13 that basically says they had it right the first time: SARS-CoV-2 is spread primarily by droplets, and we probably don’t need to worry too much about aerosols. Since this runs counter to everything I’d recently read, I was eager to see their evidence. And, as we all need whatever good news we can get these days, I hoped the article would be persuasive.

It begins by admitting that experimental data shows that infected people do produce aerosols that can travel far longer than 6 feet, and that the virus can remain in the air and viable for hours. It also admits that there is anecdotal evidence of clusters of infections, in restaurants, offices, and choir groups, citing a number of the famous case studies which appear to be evidence of aerosol transmission.

Isn’t all that proof that aerosols are a threat?

Not so fast, the authors argue. We know two things about how this disease spreads, and both are inconsistent with aerosols as an important source of transmission. First, the Reproduction Rate has been estimated at approximately 2.5. As most of us have learned by now, that means that an infected person, on average, transmits the virus to 2.5 additional people. A disease spread by aerosols should have a much higher Reproduction Rate. Measles, for example, has a Reproduction Rate estimated around 18.

Second, this virus does not transmit easily. Contacts between an infected person and a susceptible person rarely result in a new infection. The article cites a variety of examples of measured “secondary attack rates.” A few samples: sharing a meal with an infected person causes infection 7% of the time, a health care worker without PPE, caring for a COVID-19 patient, is infected 3% of the time. Even living with an infected person only results in transmission 10–40% of the time. If the virus did regularly spread via aerosols, these rates would should be much higher.

Essentially, the article claims that aerosols are too efficient at spreading disease for the level of transmission we’re experiencing. If it were easy to catch COVID-19 via aerosols, many more people would have been sickened faster.

So we are left with a conundrum: infected people are producing aerosols, those aerosols are drifting around in the air, but most of the people breathing them in don’t seem to be getting sick, at least not at the rates that medical experts would expect. Why not? And does that mean that we don’t, after all, need to be overly worried about aerosols?

I’ve been contemplating this for the last few days, and I think maybe I have an answer, or at least a theory. But before I propose it, I need to explain my reasoning, and for that we’ll need to take a brief detour into the world of epidemiological forecasting.

As I was puzzling over this question, I was forwarded a paper, not yet peer reviewed, written by a team of scientists at Oxford University. This paper makes an intriguing claim, one every one of us would desperately hope to be true. The authors believe that the world is much closer to achieving herd immunity than anyone realizes. In fact, they argue that in certain localities herd immunity already exists, and that the risk of a second wave in those areas is substantially overblown.

To understand their argument, we’re going to need to take a shallow dive into some math. The generally accepted formula for reaching herd immunity is defined by the equation 1- 1/R. (R is the Reproduction Rate). So, if the Reproduction Rate is 2.5 (as claimed by the AMA article discussed above), the formula is 1- 1/2.5 = .6.

This basic formula is the reason we so often hear epidemiologists — and the journalists who quote them — say that we need 60% of the population infected before we reach herd immunity. The formula answers the following question: how many people have to be immune in order for the average infected person to infect exactly one person? If someone with COVID-19 would normally infect 2.5 people, once 60% of the population is immune, they will only infect one person on average. (2.5 x (1-.6) = 1)

The Oxford scientists, however, think this formula is lacking something. What it’s lacking is a way of addressing the possibility that some percentage of the population has a natural resistance to the virus.

The idea that some people are naturally resistant to SARS-CoV-2 is not something we hear a lot about. But the Oxford scientists cite evidence suggesting that such resistance could have come about through prior exposure to other coronavirus, such as the viruses that cause the common cold, or even perhaps from exposure to influenza viruses. Also, they speculate that biological variation in people’s immune systems or ACE2 receptors could account for natural resistance. Whatever the cause, they claim that a meaningful percentage of the population may be naturally immune, and that the formula for calculating herd immunity must be modified to account for these people.

The modification they propose is quite simple. It adds a variable, p, which represents the percentage of the population with pre-existing immunity. The new formula is 1–1/R — p. If 20% of the population is naturally immune, the threshold for herd immunity drops from 60% to 40%. And if 50% of the population had pre-existing immunity, the threshold for herd immunity drops all the way to 10%.

I’m not really in a position to evaluate their claim that many people are naturally resistant. I think, however, that the absence of a significant second wave of infections in any of the geographies that had severe first waves (Wuhan, Italy, France, UK, northeastern U.S.) provides some circumstantial evidence that considerable immunity may now exist within those populations, more than would be accounted for by serology tests.

Perhaps the Oxford scientists are right, and as bad as things appear in the U.S. today, maybe we are on the verge of vanquishing this virus once and for all. Maybe we will wake up one day in the not too distant future and this will all be over.

Too good to be true, right?

Well, right.

Here’s the problem with this approach to calculating herd immunity: the Reproduction Rate is not something anyone knows a priori. It must be empirically estimated based upon the rate of infection growth. A population in which many people have pre-existing immunity will appear to have a Reproduction Rate much lower than a population of wholly susceptible individuals. So if it were true that half the population had pre-existing immunity, the correct Reproduction Rate for the rest of the population would be 5 instead of 2.5.

And that’s what I find really interesting. What if the Reproduction Rate is really higher than anyone realizes? Could this help explain the aerosol conundrum posed by the AMA article?

Remember the problem: lots of evidence appears to point to aerosols as a source of spread, but the Reproduction Rate is too low. Not enough people are getting sick.

Unless they’re not getting sick because they’re already immune. Maybe the Reproduction Rate would be 5 if we didn’t begin with half the population having a pre-existing immunity. Maybe the secondary attack rates would be twice as high for the same reason.

If this explanation is correct, it’s kind of a bad news/good news outcome.

The bad news first: aerosols would be, in fact, an important source of transmission, and we would need to take the precautions necessary to prevent exposure to them. I certainly don’t presume to know more than the authors of the AMA article, but I’m going to continue to wear masks to keep from releasing aerosols into the air and possibly infecting other people, and I’m going to avoid spending time in enclosed, poorly ventilated spaces.

But there’s some real good news, too. Let’s turn back to the Oxford model, which claims that herd immunity threshold is equal to 1–1/R-p. If we calculate herd immunity with the very optimistic assumption that R=5 and p=.5, the result is .3 (1–1/5-.5) In this case, herd immunity is reached when 30% of the population has been infected. Three weeks ago, Dr. Scott Gottlieb, former commissioner of the FDA, said he thought New York City might be at 25% infected. As a region closes is on herd immunity, transmission naturally slows, even though the disease continues to spread. Even if the percentage of naturally immune is actually only 20 or 30% instead of 50%, we’d still be a lot closer to herd immunity than most people think. This implies that New York and the other hard-hit regions may not see a major second wave this fall or winter. And if that’s the case, this February may be just like the last one.

Let’s hope so.

Author, novelist, investor.

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