Last time I promised you an infection that never ends — not because anyone stays sick, but because a city is large enough that there is always someone new to hand it to.
Start with a list of islands. In 1966 Francis Black, an epidemiologist at Yale, gathered fifteen years of monthly measles reports from nineteen island communities and set each beside one number: how many new susceptible people the island produced in a year. Babies, less the ones who did not survive infancy. The Falkland Islands, population two and a half thousand, produced forty-three a year. Fiji produced thirteen thousand four hundred. Hawaii, sixteen thousand seven hundred.
Transmission broke off in every one of them except Hawaii.
Nothing keeps it
Measles is a poor candidate for permanence. It has no reservoir but us — no cattle to wait in, no soil, no water — and it does not linger in a person: you are infectious for about five days, and then you are immune for the rest of your life. Every human it touches is spent.
So it cannot persist by staying anywhere. It persists only by being handed on, and only to someone who has never had it — which, in a place that has just had an epidemic, means someone who was not yet born when the epidemic ended. Susceptibles are consumed by the virus and replaced by the maternity ward, and where those two rates match, the infection becomes a permanent feature of a town in which nobody is sick for long. No. 46 was immunity assembled inside one body in a week; this is immunity as an inventory held by a whole city, which nobody is keeping and everybody is spending.
The floor
The two rates can fail to match. In 1957 the statistician M. S. Bartlett went through case reports from British and American cities and found the chain kept breaking below roughly four to five thousand cases a year; on that basis he put the critical community size — the population at which measles is as likely as not to die out after an epidemic and have to be reintroduced from outside — at about 250,000 to 300,000 people. He knew the figure was soft: cities are not sealed, and reintroduction from outside hides a fade-out.
Black’s islands were the test, since reintroduction there is rare and countable. His answer refined Bartlett’s rather than overturning it: measles may fade out in a community as large as 350,000, he wrote, and possibly over 500,000 if closely settled, though a dispersed population might hold it below that — probably not under 200,000. Modern work quotes 300,000 to half a million for Europe and North America.
The dial is the birth rate
What is that threshold actually made of? In 2000 David Earn and colleagues pointed out something almost embarrassingly simple about the standard epidemic equations: the birth rate enters them in exactly the same place as vaccination, and both enter where the transmission rate does. Vaccinating a fraction of newborns gives dynamics identical to leaving them all unvaccinated and making the virus that much less contagious. Halving the birth rate does the same thing. One dial, three labels.
Which is why London’s epidemics came annually before 1950 and every second year from 1950 to 1968. The post-war birth rate fell, and the disease changed its rhythm without the virus changing at all. Liverpool, whose birth rate stayed above the national average until 1968, kept its annual cycle straight through. Nobody was turning this dial on purpose. The flag is that measles needs a big city. The truth is that it needs a fast one.
The number is not tidy, though, because arrivals are not the only thing with a rhythm. Niamey, in Niger, had some 750,000 people in 2001 — twice the historical threshold, in a country with close to the world’s highest birth rate — and should by rights have had relentless annual measles. Instead it gets occasional enormous outbreaks separated by years of almost nothing. Transmission in the Sahel is so fiercely seasonal, keyed to the end of the rains, that the troughs run deep enough to break the chain anyway.
About as old as cities
Black saw the implication and put it in his title. Populations of several hundred thousand are recent; they did not predate the river-valley civilisations. A virus that burns out below a quarter of a million people cannot have been endemic among bands of a few hundred — there was nowhere for it to be. So measles must be young, and he guessed it had come from something in cattle.
In 2020 a team sequenced measles from a 1912 lung specimen in a Berlin museum and ran the clock back. The split from rinderpest, the cattle plague, dates to between 1174 BCE and 165 CE, most likely the sixth century BCE — and Babylon, Athens and Rome crossed the threshold shortly after. The range is wide, and a virus diverging is not the same event as a chain of human cases beginning. But the shape of the answer is Black’s: measles is about as old as the first places big enough to hold it.
Nothing in the loop cares who is in it. It only cares how fast we arrive.
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One loop I’m watching
Next: a fire deliberately held at the exact edge of running away — each event causing precisely one more, indefinitely — and the strange accident of physics that gives the people at the controls minutes to react instead of microseconds. Next time.