Lila Soto: Hugo, tell me you've been somewhere interesting this week, because I have been in a very specific rabbit hole and I need company.
Hugo Vance: Departmental meetings, I'm afraid. Your rabbit hole sounds considerably more appealing.
Lila Soto: Mm, okay, so — herd immunity. And the number that broke my brain a little is this: ninety-two to ninety-five percent. That's what you need for measles. That high a share of a population immune before the disease stops circulating. Seasonal flu's threshold? Below thirty percent. Same principle, I mean, the exact same underlying idea about how immunity moves through a group — and the math is almost unrecognizable.
Hugo Vance: It all comes down to the basic reproduction number — R₀. The average number of secondary infections one person causes in a fully susceptible population. Measles sits between twelve and eighteen. Seasonal influenza, at its most transmissible, barely clears two. The herd immunity threshold is literally calculated from that number: one minus one over R₀. So the formula is simple. What the formula contains is not.
Lila Soto: Wait — so the threshold is almost entirely a function of how contagious the pathogen is?
Hugo Vance: In the simplified model, yes. And here's where I'd be cautious — that model assumes populations mix uniformly, which they do not. But as a starting place, it holds. And it held well enough that the World Health Organization declared smallpox globally eradicated in 1980. That's the anchor. The one disease, the one human disease, ever fully erased through sustained vaccination leveraging this principle.
Lila Soto: And smallpox is gone, full stop — but measles was *eliminated* in the United States in 2000, and now it keeps coming back in pockets.
Hugo Vance: Indeed. Which is the distinction I think matters most here. Herd immunity is indirect protection — when enough people are immune, unimmunized individuals are shielded because transmission chains can't sustain themselves. That much is real and durable as a principle. What is *not* durable is the coverage that maintains it. Those are different things, and we tend to conflate them.
Lila Soto: So the fragility isn't in the concept — it's in us, in the institutions holding it up?
Hugo Vance: That's where I'd put it, yes. Same mechanism, wildly different requirements by disease, and the gap between reaching the threshold and *holding* it is where everything actually gets hard.
Lila Soto: And that gap is what I want to understand — what's underneath it.
Hugo Vance: That gap — it starts with understanding what the math is actually doing. Think of a chain letter. Every person who gets it is supposed to send it to several others. The chain only dies when, on average, each person sends it to fewer than one person. That's it. Herd immunity is just: what fraction of people do you need immune so that, on average, each sick person gives it to fewer than one other person.
Lila Soto: Oh. That's — yeah, that actually clicks.
Hugo Vance: When that average — the effective reproduction number, R — drops below one, the outbreak shrinks with every generation. It's not that transmission stops entirely. It's that the chain can't sustain itself.
Lila Soto: Okay, so where does ninety-five percent for measles actually come from? Like, out of that formula?
Hugo Vance: One minus one over R₀. If measles has an R₀ of, say, eighteen — worst case — then you need one minus one-eighteenth immune. Which is roughly ninety-four percent. At twelve, you still need about ninety-two. So that band, ninety-two to ninety-five, comes directly from where measles sits on the transmissibility scale.
Lila Soto: And polio is — I mean, polio's threshold is lower because its R₀ is lower?
Hugo Vance: Five to seven, roughly. So the threshold lands around eighty to eighty-five percent. Still demanding, but measles is — well, measles is in a different category entirely. Chickenpox sits near ten, Ebola near two, the 1918 flu somewhere between 1.4 and 2.8. The same formula, completely different bars.
Lila Soto: Seasonal flu — you'd think flu would be high, but its threshold can be below thirty percent?
Hugo Vance: Because at its lower estimates, seasonal influenza barely clears an R₀ of one. So the math — actually, the math almost lets you off the hook. Which is why we've never seriously attempted flu eradication. Measles, on the other hand, demands near-universal coverage, and you see it — 2019, over twelve hundred cases in the United States, concentrated in Somali communities in Minnesota, Orthodox Jewish communities in Brooklyn. Not random lapses. Pockets where coverage slipped below that threshold.
Lila Soto: So the chain-letter logic cuts both ways — low R₀ means fewer immune people can break it, but high R₀ means one unvaccinated pocket is basically handing out stamps.
Hugo Vance: Precisely. And here's where the elegance starts to strain — the formula assumes everyone mixes uniformly. They don't. A tightly networked community can have a local R that's far above the national average even when national coverage looks fine. Which is why the math is genuinely beautiful, and also why it is not sufficient.
Lila Soto: So the math is actually elegant — which makes what comes next weirder.
Hugo Vance: And that's the part that I think breaks the clean version — because we achieved something real. Measles was eliminated. Not reduced, not managed. Eliminated, in the year 2000, from the United States. And then we watched it come back.
Lila Soto: Twelve hundred cases in 2019. That number — I keep sitting with it.
Hugo Vance: Yes. And what's instructive is what didn't change. The virus didn't mutate into something more dangerous. The math didn't shift. R₀ for measles is still twelve to eighteen. What changed was coverage — in specific, reachable pockets. Somali communities in Minnesota. Orthodox Jewish communities in Brooklyn. Concentrated gaps.
Lila Soto: Which means we — I mean, we didn't lose the principle. We stopped doing the maintenance. That's a different kind of failure.
Hugo Vance: That's exactly the distinction I'd want to hold onto. The structurally uncomfortable part is that the basic HIT formula doesn't actually account for the work of holding it. It tells you the threshold. It says nothing about the dam.
Lila Soto: The dam — yeah. Is that what calling it a 'principle' kind of obscures? Like, a principle sounds permanent. This sounds like... infrastructure that needs constant budget.
Hugo Vance: And there are two cracks the formula doesn't even see. One is the uniform-mixing assumption — the math treats everyone as equally likely to encounter everyone else, which we've established is false. The other is — actually, this one I find more quietly alarming — waning immunity. Vaccine protection diminishes over time. So does protection from prior infection. The population's immune status is not static even if no one stops vaccinating.
Lila Soto: Wait — so even if coverage stays constant, the effective immunity in a population can quietly erode?
Hugo Vance: Yes. And layered on that — no vaccine is a hundred percent effective. So the proportion of people who need to be *vaccinated* to hit the threshold is actually higher than the threshold itself. You need more than ninety-five percent vaccinated to get ninety-five percent immune, because some vaccinated people simply don't mount a full response.
Lila Soto: Oh, that gap is — hm. That gap is invisible in how we talk about it.
Hugo Vance: It's invisible until a parent in an elementary school hallway gets a notice that measles appeared in the next district over. A disease that was, within their lifetime, *gone* from their community. And the protection they assumed had been banked — quietly, it had eroded.
Lila Soto: That's the moment where the math becomes — I don't know, personal in a way the formula never prepared anyone for. And the COVID version of that story is even stranger, because the threshold itself was moving. Which is kind of where I want to go next — Wyoming versus New Jersey were living inside almost completely different outbreaks.
Hugo Vance: Indeed. And immune escape adds a layer the measles story doesn't have, which makes the COVID case considerably more — well. We'll get there.
Lila Soto: Wyoming and New Jersey — same country, same virus, same year. What does it mean that they were operating under almost completely different transmission realities?
Hugo Vance: One Bayesian study put Wyoming's R₀ for SARS-CoV-2 at 2.3 and New Jersey's at 7.1. Three times higher. Which means New Jersey's herd immunity threshold was fundamentally different from Wyoming's — not because the math changed, but because density, contact rates, transit systems, all of it changed the effective number.
Lila Soto: So a single national threshold was always — I mean, it was always fiction.
Hugo Vance: A simplification, I'd say. A useful one for communication. But yes — Anthony Fauci naming a number for the country, any number, was already smoothing over enormous variation in what the actual target was district by district.
Lila Soto: And then the target started moving.
Hugo Vance: That's the part that has no clean precedent. With measles, R₀ is stable — twelve to eighteen, full stop. With SARS-CoV-2, variants kept shifting the underlying transmissibility, waning immunity kept shrinking the effective immune denominator, and suddenly the formula is — well, it's chasing a number that won't hold still.
Lila Soto: Wait — waning immunity plus new variants means the threshold itself is a moving target *while* you're trying to hit it?
Hugo Vance: Yes. The standard HIT formula has no variable for a pathogen that's actively evolving to escape prior immunity. It assumes the R₀ you started with is the R₀ you're still working against.
Lila Soto: Mm. Some researchers were arguing though — I remember this — that population heterogeneity could actually lower the naturally acquired threshold? Like, if the most socially connected people got infected first, they'd take disproportionate transmission out of the system.
Hugo Vance: They did argue that. And the heterogeneity logic isn't wrong in principle. But — here's where I'd be cautious — the way you test that claim through natural infection is by letting people get sick and die to see if it works. The mortality cost of that experiment is not theoretical.
Lila Soto: Oh. That's — yeah, that lands differently when you say it that way.
Hugo Vance: Because hesitancy doesn't let a community *avoid* the herd immunity threshold. It just determines how the community reaches it. Through vaccination, or through the disease itself — the deaths, the long-term complications, the hospitalizations. The threshold gets reached either way.
Lila Soto: And the cost gets redistributed — onto people who couldn't vaccinate in the first place. The immunocompromised, infants too young, people with allergies.
Hugo Vance: That's the mechanism underneath indirect protection. The entire point — well, one of the entire points — of herd immunity is shielding the people for whom vaccination was never an option. When coverage slips, those individuals are not protected by their own choice. They're exposed by everyone else's.
Lila Soto: That's the 'oh, THAT's why' moment, isn't it. It's not about individuals opting out. It's about where the risk lands when they do.
Hugo Vance: The cost isn't absorbed by the person who declined. It's passed — structurally, mathematically — to whoever is most vulnerable in the surrounding population. Which is what the formula, for all its elegance, never quite says out loud.
Lila Soto: And that's — I mean, that's the pattern I see across all of this. The math started in livestock pens, early 1900s, veterinary science trying to understand how disease moved through animal populations. And somehow that same principle got scaled up, applied to the 1918 flu, refined over decades, and eventually became the mechanism behind the WHO declaring smallpox eradicated in 1980. That's kind of an extraordinary arc. Livestock pens to the only human disease we've ever fully eliminated.
Hugo Vance: And polio isn't gone. Nearly a century of campaigns, and it remains endemic in a small number of countries. Which — you see, that tells you something the smallpox story alone doesn't. The structural principle is real. The math is airtight. And it is still not sufficient, on its own, to finish the job.
Lila Soto: So the question was never really whether herd immunity is a durable structural principle. It's whether we have the coordination and the will to sustain it once the threat stops feeling urgent.
Hugo Vance: That's the thing I'm still turning over, honestly. The math doesn't hold vaccination rates up. Institutions do. Communities do. And those are — well. Those are exactly the things that are fragile.
Lila Soto: Yeah. That's an uncomfortable place to land. But I think it's the honest one.
Hugo Vance: I think it is. Thank you for the rabbit hole — it was considerably better than the departmental meeting.
