The medical authorities rightly took a safety-first approach to the disease, but the outcome may be less apocalyptic than first feared

After a week in which it looked as if medical calamity was about to be heaped upon financial pandemic, yesterday brought heartening news that the "swine flu" outbreak now infecting 16 countries may not be as bad as initially feared. Dozens of test samples have come back negative from laboratories, enabling Mexico to cut the number of suspected deaths from the virus from 176 to 101. There were no new deaths overnight Friday, fewer patients with severe symptoms are checking into hospitals, and very few, if any, cases in the rest of the world are showing signs of serious illness.

But significant voices were quick to declare that a definitive sigh of global relief would be premature. Dr Steve Waterman, heading a team from the US Centers for Disease Control (CDC) now working in Mexico, said they should soon learn whether the epidemic is really stabilising there. He also warned against taking false comfort from the fact that only one person has died outside Mexico, saying more deaths are likely as the epidemic evolves.

But he conceded that the virus does not appear to match the ferocity of past pandemics, and a colleague of his, CDC epidemiologist Marc-Alain Widdowson, added: "The virus has been circulating for over a month in a city of 20 million of high population density. It could have been much worse."

The World Health Organisation said that 18 countries have now reported 766 infections. The confirmed cases include 443 in Mexico, 184 in the US, 85 in Canada, 15 in Spain, 15 in Britain, six in Germany, and smaller numbers in 12 other countries. Italy reported its first known case yesterday, a man in the Tuscany region who returned from Mexico on 24 April. He has since recovered. Almost all infections outside Mexico have been mild. In Britain, where two new cases were confirmed – one being the husband of a woman who was confirmed the day before – some 632 possibles are under investigation.

In Hong Kong, an extraordinary situation developed at a hotel where 350 guests and staff have been sealed in, while officials search for anyone who had contact with an infected Mexican tourist. The man landed first in Shanghai before continuing to Hong Kong, where he checked into the Metropark Hotel. Health workers in white bodysuits patrolled the lobby of the Metropark in Hong Kong's Wan Chai bar and office district. About a dozen police officers wearing masks guarded the cordoned-off building, which was ordered to be quarantined for seven days starting on Friday.

A masked hotel guest inside flashed a handwritten sign through the lobby window to journalists swarming outside. It read, "We will exchange information for beer and food and cigarettes."

Singapore, which hasn't reported any confirmed cases of swine flu, also took tough precautions. Its Ministry of Health announced that, starting on Monday, it will quarantine for seven days any visitors and returning citizens who have been in Mexico in the past week. And in Panama, police detained an American who ran away from a hospital that was testing him for swine flu.

In Mexico, where most people were spending a second weekend stuck indoors, public hospitals have noted a steady drop in patients turning up with fevers, suggesting the infection rate may be declining as the nation dons face masks and uses hand gel. And, in New York, officials said that, after a week of monitoring, the city's outbreak shows little sign of spreading. Mayor Michael Bloomberg said that the illness had, as yet, proved to be "a relatively minor annoyance".

So far, then, so hopeful. But for much of the last week, the world seemed on an inexorable lurch towards a pandemic of possibly unusual deadliness. Sunday's casualty reports of 81 Mexicans suspected to have died from the flu, plus 1,324 possibly infected by it, and the US's 20 confirmed cases duly grew over the next few days.

On Monday came the first European case – in Spain. Later that day came the first British suspects, a honeymoon couple from near Falkirk in Scotland. The Government's Cobra committee met, doctors were dispatched to Heathrow to board incoming flights from Mexico City and ask if anyone felt unwell, the WHO's panel of flu experts teleconferenced, and the US government announced that incoming travellers would be checked at ports and borders for signs of fever.

As the WHO moved to 4 on a 1-6 scale of alert (which it did on Monday), travel restrictions began to be enforced, with the UK holiday carrier Thomson cancelling two flights to Cancun, and then Cuba being the first country to order a ban on all flights to Mexico. China followed yesterday. And, even before the WHO went to "phase 5" on Wednesday evening, countries were announcing other initiatives, not all of them based on what you might call science.

Russia, Serbia, China and Ukraine banned imports of pigs or pork from Mexico and North America; Australian officials advised people to stockpile food; Egypt ordered a mass cull of all the country's 300,000 pigs; and Iraq slaughtered the wild boars in Baghdad Zoo. In the face of this, every so often a WHO official, UN food safety expert, or some other specialist would patiently explain the flu could not be caught by eating pork. They would also point out that no pigs had yet been found with the new virus, a statement that was true until late last night, when it was found in a pig herd in Alberta, Canada.

Some governments felt obliged to share with their populace their plans for what news channel presenters kept referring to as "nightmare scenarios". US predictions were that a full-scale pandemic, if it ever came, could infect 90 million Americans, claim the lives of about two million, and leave perhaps as many as 10 million needing hospitalisation. Draft Whitehall guidance said that 750,000 might die here, and up to 30 million be infected. Alarming, even risible, though some of these forecasts might seem, not to prepare them would have been an act of spectacular neglect.

America was the first (and remains the only) place outside Mexico to record a death from the A (H1N1) virus. The identity of the victim, and his location, was not a surprise. He was a Mexican toddler who had been taken by his family to Brownsville, Texas, a town where some 7,255 Mexicans cross via a bridge to work every day. Elsewhere in the US, suspected cases built up through the hundreds, many of whom were high school students who had taken their spring breaks in Mexico. Schools closed, teams with strong disinfectants moved in to swab down classrooms, and parents worried, but only a few patients were sick enough to be in hospital. Just to be on the safe side, on Friday Washington began sending 12 million Tamiflu doses to each state.

The situation in Mexico was changing, too. Last Sunday, the city's streets fell largely silent as public gatherings, sports events and religious services were abandoned, or took place behind closed doors. Schools closed, businesses encouraged working from home, troops distributed more than six million face masks (spawning a new artform of mask decoration). On Friday, the country began a five-day shut-down, with people asked to spend as much time as possible indoors. Only stores selling essentials were kept open. Mexico City was a place where, if people began to muster on the pavements, a patrol car was liable to roll up and bark at them through a loud-hailer the words: "Disperse! It is dangerous to gather in groups. Disperse!"

But the country that looked at the start of the week as if it would be the centre of a deadly worldwide illness ended it as something of an enigma. Why were there no deaths from the virus anywhere else in the world? Why were the dead only Mexicans? Were they people who had failed to get help in time and whose illness had not been diagnosed in time? Or was there something special about conditions – and a far higher rate of infection – in Mexico that would explain it?

The CDC's Dr Waterman, when asked why the swine flu death rate is so high in Mexico while only one person is known to have died elsewhere, said this is a key question his team is trying to answer. One of the main reasons, they believe, is that there are a lot more people in Mexico who are sick than in other countries. "The reason they haven't had any deaths, if the mortality rate is 1 per cent and you only have 20 cases, you haven't had time to see that mortality yet," he said. Many infected Mexicans may also have sought help too late to be treated successfully, he said.

But the big issue for all of us is this: will A (H1N1)'s highly selective and mild mortality (certainly compared to bird flu's 60 per cent death rate) continue to be the case? And that, for all the reassuring nature of the data emerging yesterday, remains a question to which we must still wait for the answer. Possibly until the autumn.

The threat in numbers

17 Confirmed global swine flu death toll: 16 in Mexico and one confirmed in the US.

38,500 People die each week around the world from the Aids virus.

15 The number of swine flu (H1N1) infections confirmed in the UK so far.

1,288 The number of British people who die from strokes in an average week.