In the twentieth century, smallpox killed an estimated 300 million people.

Today it kills no one. Nobody has caught it anywhere in the world since 1977.

Smallpox spread from person to person, through the air and through touch, and took about twelve days to show itself.

With nobody protected, each case passed it on to between three and six others, and each of them did the same.

About three in every ten people who caught this form of it died.

People who survived smallpox never caught it again. Their bodies remembered it.

Long before anyone knew why, people in China and the Ottoman Empire used this. They took a little matter from a mild case and scratched it into a healthy person, hoping for a mild dose of the disease instead of catching it by chance. This was called variolation, and it usually worked, though a small number of people still died of it.

During a smallpox epidemic in Boston in 1721, an enslaved man named Onesimus persuaded a local minister to try variolation, a method he had learned in Africa. That same year in London, Lady Mary Wortley Montagu, who had seen variolation in the Ottoman Empire, had her own children inoculated.

In Gloucestershire, a doctor called Edward Jenner noticed that milkmaids who had caught cowpox, a mild disease from cattle, never seemed to catch smallpox.

In May 1796 he took matter from a cowpox sore on a milkmaid named Sarah Nelmes, who had caught it from a cow called Blossom, and scratched it into the arm of eight-year-old James Phipps. Phipps had a mild illness, then recovered, and never caught smallpox.

Jenner called the method vaccination, from vacca, the Latin word for cow. It was safer than variolation, because cowpox itself was mild and could not spread from person to person.

Vaccinate somebody and they are protected. Vaccinate enough people, and something else happens too: the disease runs out of people to spread to, even the ones who aren't protected. This is herd immunity.

Every vaccinated person is a gap in the chain. The more gaps there are, the harder it is for the disease to get from one person to the next.

Below a certain share of people vaccinated, an outbreak still takes hold. Above it, outbreaks fizzle out. That share is the herd immunity threshold.

By 1967, vaccination had already cleared smallpox from most of the world. Britain's last outbreak was years behind it.

But in 31 countries across South America, Africa and Asia, it was still endemic, meaning it never really stopped, all year round. Together they had an estimated 10 to 15 million cases a year.

That year, the World Health Organization began a ten-year push to find every last case.

Vaccinating eight in ten people takes huge amounts of vaccine, money and time. During the campaign there often wasn't enough of any of them. In eastern Nigeria in December 1966, William Foege's team ran short during an outbreak. Tipped off by a fellow missionary, Hector Ottemiller, they vaccinated only the people around each known case, in a ring, instead of everyone. It worked, using a fraction of the vaccine. This is ring vaccination.

The idea had older roots too. In Leicester in the 1880s, doctors controlled outbreaks not by vaccinating the whole town but by finding every case fast and watching everyone it had been near.

A ring only works because smallpox is slow. After catching it, a person carries it silently for about twelve days before falling ill, and a vaccine given in the days right after exposure can still stop it taking hold, or make it far milder. Find a case fast enough, and there's still time to protect everyone it has been near.

So the speed of reporting decides whether a ring holds. Report a case too late, or miss the first one altogether, and the outbreak can get ahead of the vaccine.

Ring vaccination only works if you find the cases. Health workers carried a card showing what the rash looked like, so anyone could recognise it and report it, even if they couldn't read. Some countries also paid a cash reward for reporting a confirmed case, which brought many hidden cases into the open.

New tools helped: a freeze-dried vaccine that survived weeks without a fridge, and a bifurcated needle, with two prongs that held just enough vaccine in a droplet and used a quarter of what the old method needed.

National health workers led the search in every country: teams under Mahendra Dutta went from village to village across India, while the World Health Organization's own staff, including Nicole Grasset and Zdeno Ježek, worked alongside them.

Between 1967 and 1977, one country after another was cleared of smallpox.

Rahima Banu, Bhola Island, Bangladesh, October 1975. A young girl became the last person in the world known to catch variola major, the deadlier of the two forms of smallpox. She recovered, and health workers ringed her village with vaccine so it stopped there.

Ali Maow Maalin, Merca, Somalia, 26 October 1977. A hospital cook who had worked on the local vaccination campaign became the last person in the world to catch smallpox naturally. He recovered, and later spent years helping vaccinate children against polio.

Janet Parker, Birmingham, England, 1978. A medical photographer working above a research laboratory was infected by smallpox virus that had escaped from it. She died that September, the last person smallpox ever killed.

Three years after the last case, and after teams had checked every country for any sign of it, the World Health Assembly made its declaration.

"The world and all its peoples have won freedom from smallpox." On 8 May 1980, smallpox became the first, and so far the only, human disease ever declared eradicated: wiped out everywhere, for good.

Smallpox could be wiped out for reasons that don't apply to every disease. It had no animal host: it only ever lived in people, so there was no hidden population to catch it from again. And its rash made every case visible; there were no silent carriers spreading it unnoticed.

Survive it, or get vaccinated against it, and you were protected for life. Find every case and ring it, and eventually there was nowhere left for it to go.

Measles and polio don't share all of those advantages, so they need far higher vaccination levels to stop them spreading, as the chart shows. Both are still being chased today: wild polio remains in two countries, and measles still circulates in many more, including the UK.

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