The only serious case among Canada's 165 swine-flu diagnoses was showing signs of improvement Tuesday, as was life in the country where it all began - a muted Cinco de Mayo holiday marking the start of Mexico's long struggle to rebuild its shattered economy.

Before a colourless, cancelled version of its most famous national celebration, Mexico predicted a bold comeback from a devastating viral outbreak that kneecapped its critically important tourism industry and carved some US$2.2 billion out of its economy.

Mexican Finance Secretary Augustin Carstens unveiled his plan to stimulate key industries and fight unwarranted bans on Mexican pork products, promising to lure back the lucrative tourist trade and "immediately rebuild confidence in our country."

Meanwhile, in an Edmonton hospital bed, another recovery was underway: an anonymous young girl, Canada's only severe case of a condition that has killed at least 30 people and sickened thousands around the world, was breathing on her own.

"I can tell you today that she's recovering well," said Dr. Andre Corriveau, Alberta's chief medical officer of health. "Her condition is improving."

That condition, which was worse than the vast majority of outbreak cases beyond Mexico's borders, had more to do with underlying conditions than it did with the virus itself, he suggested.

"The prime reason (she was in the hospital) was the swine flu," Corriveau said. "But the other thing we're saying is there may be other factors that were part of the overall picture."

It remained unclear how the girl, whose precise age was not released, became infected.

Canada added 25 cases to its confirmed case list Tuesday - 10 new cases in Nova Scotia, seven in British Columbia, five in Ontario, two in Alberta and one in Quebec.

In the U.S., where the confirmed caseload has surpassed 650, officials confirmed the death of a resident of Texas, the second swine-flu death to occur outside of Mexico, where 29 people have already succumbed to the virus.

Canada is third on the list of countries with the most cases, followed by Spain, with 57; 27 in Britain; nine in Germany; six in New Zealand; five in Italy; four in Israel and France; two each in El Salvador and South Korea and one each in Austria, Costa Rica, Colombia, Denmark, Hong Kong, Ireland, the Netherlands, Portugal and Switzerland.

In Mexico, traffic was picking up in the capital, surgical masks were less apparent and some cafes reopened ahead of time Tuesday, the final day of a nationwide shutdown meant to reduce the spread of virus.

Flu experts said the tough measures have helped - but some were worried about a potential rebound as crowds gather again.

"The scientists are saying that we really need to evaluate more," said Dr. Ethel Palacios, the deputy director of the swine flu monitoring effort in Mexico.

"In terms of how the virus is going to behave, we are keeping every possibility in mind ... we can't make a prediction of what's going to happen."

In the U.S., the Centers for Disease Control and Prevention, which had been recommending schools where the virus was detected should close for two weeks, rescinded that advice Tuesday.

Health and Human Services Secretary Kathleen Sebelius said the virus had turned out to be milder than initially feared, and that keeping sick children home for seven days would suffice.

Mexico's cancelled holiday celebrations included the country's largest re-enactment of Cinco de Mayo's defining event: the May 5, 1862, victory over invading French troops in the central state of Puebla.

President Felipe Calderon used the occasion to foreshadow what he predicted would be another bold Mexican triumph.

"Almost a century and a half later, Mexico is facing a new threat, this time of a very different kind," he said in a speech to the nation. "An unusual threat, specifically the appearance and spread of an epidemic that has put at risk the lives and health of Mexico's families."

Carstens announced a US$1.3-billion stimulus package, mostly for small businesses and tourism, the sectors hardest hit by the outbreak. The government will temporarily cut health insurance payments for small businesses and reduce taxes for airlines and cruise ships.

Universities and high schools were being scrubbed down before students return Thursday, and younger schoolchildren are to report back to school May 11 - creating potential pools of contagion that experts worry could make the virus come back.

The schools will reopen even as experts asked restaurants to keep their customers nearly two metres apart, and Mexico's soccer federation announced that attendance would not be allowed at this weekend's season-ending games.

Calderon called it a return to "normalcy." But flu experts warned that Mexico, like the rest of the world, needs to remain on guard, and said severe cases could surface in the U.S. as well with the virus spreading in a growing number of states.

"We are by no means out of the woods," said Dr. Richard Besser, acting director of the Centers for Disease Control and Prevention.

The World Health Organization was shipping 2.4 million treatments of antiflu drugs to the 72 countries "most in need." The countries include Mexico, hardest hit by the outbreak. Others include those countries unable to afford stockpiles of the drugs.

As of Tuesday, Mexico had 942 confirmed cases, and U.S. cases grew to at least 650 in 36 states. Globally, the virus has infected nearly 1,900 in 21 countries, according to the World Health Organization and other health bodies. South Korea, Italy and Germany all reported new cases Tuesday. Experts said the known cases were almost certainly only a fraction of the real total.

Canada was reporting 165 cases Tuesday afternoon.

World health officials have said a pandemic could be declared in the days to come - a reflection of the swine flu's geographic spread, not its severity. Health Secretary Jose Cordova said those infected appeared to pass the virus on to an average of 1.4 other people, near the normal flu rate of around 1.3.

WHO was studying whether to raise the pandemic alert to 6, its highest level, which would mean a global outbreak had begun. WHO uses the term pandemic to refer only to geographic spread and not to the severity of an illness. The two most recent pandemics - in 1957 and 1968 - were relatively mild.

Margaret Chan, WHO director general, said the level will be raised if swine flu is found in another region outside North America, showing "very clear evidence of community-level transmission."

The Southern Hemisphere is particularly at risk. While Africa still hasn't reported any swine flu infections and New Zealand is the only country south of the equator with confirmed cases, winter is only weeks away. Experts worry that typical winter flus could combine with swine flu, creating a new strain that is more contagious or dangerous.

"You have this risk of an additional virus that could essentially cause two outbreaks at once," Dr. Jon Andrus said at the Pan American Health Organization's headquarters in Washington.

Still, the UN health agency urged governments to avoid unproven actions to contain the disease, including group quarantines of travellers from Mexico and bans on pork imports.

China, Argentina and Cuba are among the nations banning regular flights to and from Mexico, marooning passengers at both ends.

Two separate groups of Canadian travellers are also under "preventative" quarantine in China, although none of them have shown any flu-like symptoms.

Mexico and China both sent chartered flights to each other's countries to collect their citizens, with the chartered Mexican plane hopscotching China Tuesday to retrieve stranded residents. Argentina also chartered a flight to bring Argentines home.

- With files from The Associated Press