Absent a treatment or vaccine, the coronavirus won’t stop spreading until we reach herd immunity. On this episode of the podcast Social Distance, James Hamblin details what we know and don’t know about how to get there.

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What follows is an edited and condensed transcript of their conversation.

Katherine Wells: Hey Jim, what have you been thinking about?

James Hamblin: Something I don’t know much about, which is complex mathematics—specifically chaos theory.

Wells: Why have you been looking into chaos theory?

Hamblin: I’m trying to understand why there is so much variation in what we’re seeing with COVID-19 and, I guess, how this all ends.

Wells: My understanding from our conversations is that, at first, we thought there was going to be a vaccine and we were going to have to hang tight until that. Now it seems like we don’t really have a way to suppress the virus—we failed at a coordinated national strategy to keep things in check until we have a vaccine. My understanding is that where this is headed in the U.S. is herd immunity. Is that right?

Hamblin: Yeah, but what do you know about what herd immunity is?

Wells: Herd immunity is the idea that enough people in a particular community get the virus and develop antibodies. With antibodies, we assume they are immune for some period of time—although we haven’t totally proven that, but it’s a widespread assumption. If enough people become immune, then people who are not immune are very unlikely to get the virus. The rate of transmission goes down because there are fewer people who can possibly get it. It’s not like everyone in a community has to get it. I think I’ve heard 40 percent to 70 percent of people need to get antibodies in order to slow the spread enough that the virus might die out or be at a really, really low level. Is that correct?

Hamblin: Well, mostly. And that’s how I would have described the term before I started looking into it more. Back in February, I wrote an article called “You’re Likely to Get the Coronavirus.” In it, Marc Lipsitch, who’s a really smart and well-respected epidemiologist at Harvard, said the number was somewhere between 40 percent and 70 percent. Back then, the U.S. had like five cases and he was making a qualitative point. He was basically saying, Listen, this is going to spread really widely. It’s probably much further spread than we know about. He has since changed the estimate a little bit. He now puts it at 20 percent to 60 percent.

Wells: That is a wide range.

Hamblin: Yeah, that’s what I said, and the range matters. If you have a case-fatality rate of 1 percent, which is about where we are, that’s a difference of, like, 30 million people globally.

Wells: Thirty million deaths?

Hamblin: Yeah.

Wells: Got it. So whether we get to herd immunity at 20 percent or 60 percent is a hugely consequential thing.

Hamblin: Exactly.

Wells: I think I understand the basic premise, but I don’t understand how 20 percent could be possible.

Hamblin: It doesn’t immediately make sense that it could be so low, just from a biological and medical perspective, which is why it gets into these complex mathematical phenomena. I think it clicked for me when I talked to Gabriella Gomez. Gabriella is a mathematician who has collaborated with Lipsitch in the past and she’s currently leading this international coalition of researchers to try to model where this pandemic is headed. She said she’s very confident that the threshold for herd immunity seems to be 10 percent to 20 percent.

Wells: Ten percent to 20 percent?!

Hamblin: That’s based on models of multiple countries in Europe, so it’s not necessarily extrapolatable—and again, I should say that no one else that I spoke with thinks it’s that low. But everyone agrees that it’s theoretically within the realm of possibility. Her theory is that a lot of other models are underestimating the idea of heterogeneity.

Wells: What does that mean?

Hamblin: She thinks that this is not a model where we really see predictable outcomes. You might have a sick person go onto a plane and infect dozens of others, and you might have a sick person and fly and create no more cases. Those events start to seem sort of random.

Wells: And why would that be? Do we have theories?

Hamblin: We don’t know. These are things we’ll find out later. But one of the researchers mentioned that it could be something like the density of people’s nose hairs.

Wells: The case for nose hairs. [Laughs]

Hamblin: That’s just one of many variables. There are at least some physiological differences that will make one person more likely to become infected and have the virus thrive and spread within them.

Wells: Right. Does that mean there’s some percentage of people that just aren’t susceptible for some reason?

Hamblin: No, everyone is susceptible. But even a small variation in how susceptible you are to a given exposure makes broader prediction difficult. And that’s just one thing that makes prediction difficult. You also have these super-spreaders, who are shedding a ton, while some people might be shedding very little. Some people come in contact with tons of other people, and some people totally isolate. Once you start trying to make models about what the level of herd immunity would be, you have to factor in all these variables that are different than if you were just vaccinating everyone.

Wells: Is this what chaos theory helps explain?

Hamblin: Well, chaos theory comes into play when you’re looking at these outcomes that don’t seem possible. Mathematicians like Gomez try to find order and make predictions within that system even when things seem random. The field of chaos theory grew out of findings from applying mathematics to try to predict weather, which is very complicated. It should be really predictable, but it’s extremely difficult to predict because a slight change in one circumstance has huge downstream effects.

Wells: Is that like “A butterfly flaps its wings and a year later there’s a tsunami”?

Hamblin: Exactly. It is called the butterfly effect. Whenever someone made a decision to get on the first international flight, that wasn’t just one act. It had massive consequences. And when effects of single actions compound like that, and also when you have these many variables for potential outcomes, models vary really dramatically. That’s not to explain exactly why 20 percent is right, but it explains why it’s possible.

Wells: This is so frustrating because it’s like there could be an extremely hopeful thing but no guarantees so we can’t really do anything about it.

Hamblin: I think this is helpful—it’s information about how this is working. And I actually think it is actionable, because it tells us that we have the capacity to change this threshold. It depends, in large part, on us. There is a sort of fatalism in advocating, Oh, just let it run wild because we’re going to hit the same number of deaths no matter what.

Wells: Not that we don’t want to protect the most vulnerable people, but it did seem as though the number of deaths was essentially going to be the same whether it went fast or slow.

Hamblin: Yeah, but herd immunity is effectively like social distancing. It means you’re taking people out of the equation. It means that when you’re in a crowded restaurant where 80 percent of people are immune, then, functionally, only 20 percent of the people are in the restaurant.

Wells: If we can find ways to live this way until there is a vaccine, then the vaccine becomes quite relevant again.

Hamblin: Right. I think it will vary from place to place, but if we keep social-distancing measures in place, we won’t see a big spike. It’s not 100 percent, but it seems unlikely.

I guess if there’s a main takeaway, it’s that herd immunity is not this magical number. Herd immunity is a concept and we create it in different ways. It’s a concept that reminds us we’re all in this together and you are effectively serving as a number in the immune group when you behave responsibly.

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