(AP) -- The swine flu virus spread to more countries Tuesday, and scientists said the official numbers represent only a fraction of the many thousands of people sickened around the world. At the center of the epidemic, health officials said the worst is over despite more deaths.
Mexico's toll rose Tuesday to 58 deaths and 2,282 confirmed cases of swine flu - a rise of two deaths and 223 more cases since Monday - but Health Secretary Jose Angel Cordova said this reflects a testing backlog: The last confirmed case was May 8.
The more cases Mexico confirms, the less deadly the virus appears, Cordova said. And 92 percent of people sickened or killed in Mexico showed symptoms "before we knew that we were fighting against a new germ," and knew how to properly treat them, he added.
With the virus now spreading worldwide, Swiss pharmaceuticals company Roche Holding AG announced it is donating enough Tamiflu to 5.65 million people to the World Health Organization. Tamiflu is one of two anti-viral drugs known to be effective against swine flu.
Thailand and Finland reported their first confirmed swine cases Tuesday, of people just arrived from Mexico.
Cuba also confirmed its first case - a Mexican student attending a Cuban medical school - despite imposing strict measures on flights and travelers from Mexico in hopes of keeping the virus off the island. The case prompted Fidel Castro to accuse Mexico of hiding the epidemic until after President Barack Obama visited last month.
"Mexican authorities did not inform the world of the presence (of swine flu), while they waited for Obama's visit," he wrote, despite the fact that Obama's April 16 visit came a week before Canadian and U.S. scientists identified swine flu in Mexican patients. The laboratory match prompted Mexico to quickly impose an unprecedented shut down of most aspects of public life for days.
Cuba's Health Ministry said a group of medical students from Mexico began arriving on the island to resume their studies April 25 - four days before Cuban authorities halted airline flights - and that 14 of the students had flu symptoms.
China said it has tracked down and quarantined most passengers who shared flights with the mainland's first case of swine flu - a Chinese graduate student who is said to be improving. The man studied at the University of Missouri, where officials advised people not to panic and to simply keep up basic hygiene.
"They're treating it like the seasonal flu," Columbia/Boone County health department spokeswoman Geni Alexander said. "There's no longer really any need for intense investigation."
The WHO has confirmed more than 5,250 cases in 33 countries. The United States has the most - 2,618 - according to the U.S. Centers for Disease Control and Prevention. Along with those who died in Mexico, swine flu has contributed to the deaths of three people in the U.S., one in Canada and one in Costa Rica.
But a study published Monday in the journal Science suggests there are many more cases than those confirmed by laboratories - anywhere from 6,000 to 32,000 cases in Mexico alone by April 23, the day the epidemic was announced. The flu has since spread around the world.
Researchers also said this swine flu is appears to be substantially more contagious than normal, seasonal flu, and kills between 0.4 percent and 1.4 percent of its victims. But lead author Neil Ferguson of Imperial College, London, said the data remain incomplete: "It's very difficult to quantify the human health impact at this stage," he said.
Ferguson's team also compared the genetic sequences of the viruses in 23 confirmed cases, and came up with an estimate of Jan. 12 for their earliest common ancestor - presumably when person-to-person transmission began. But they said it also could have been anywhere from Nov. 3 to March 2.
Cordova said Mexico's shutdown of schools - lifted Monday in most of the 31 states - had averted an avalanche of cases. "It would have been difficult for us to have controlled this epidemic," said Cordova.
The reopening of kindergartens and primary and middle schools shut since April 24 is another step toward normalcy in Mexico, where businesses, government services, high schools and universities reopened last week. The Education Department said it will extend the school year to make up for lost time.
Mexico's overburdened health system has been strained by the epidemic. Dozens of government doctors and nurses marched and blocked streets in the Gulf coast city of Jalapa to demand higher pay and better working conditions.
"The government asked our help in combatting the influenza epidemic, now we are asking the government to do us justice," said nurse Mariana Cortes, one of the protest organizers.
Mexico also is trying to revive its economy after the epidemic pummeled tourism, the country's third-largest source of legal foreign income. Mexico provided details Monday of a $1.1 billion package to help restaurants, hotels and other businesses, including grace periods for small businesses with outstanding loans, especially in beach resorts and other tourist destinations.
Cordova said there have been no swine flu cases in five top Mexican vacation spots, including Los Cabos, Puerto Vallarta, Cozumel, Mazatlan and Zihuatanejo.
"The tourist destinations are safe in Mexico," he said. "People can return to them with peace of mind."
But with incoming flights virtually empty of tourists, Tourism Secretary Rodolfo Elizondo announced a $90 million publicity campaign to urge Mexicans to vacation at home. He said promoting trips by foreigners now "would be like throwing money away."
Associated Press writers Olga Rodriguez and Alexandra Olson in Mexico City; Miguel Angel Hernandez in Veracruz, Mexico; Maria Cheng in London; and Gillian Wong in Beijing contributed to this report.
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