While WHO is reporting about 4,800 confirmed cases in 30 countries, the new analysis estimates there have been between 6,000 and 32,000 cases in Mexico alone.
While there have been 1,626 cases of the flu confirmed in Mexico, the researchers note that there have been more than 11,000 suspected infections.
"Our early analysis would suggest this is going to be an outbreak comparable to that of 20th century pandemics regarding the extent of its spread - it's very difficult to quantify the human health impact at this stage, however," said lead author Neil Ferguson of Imperial College, London.
Ferguson's analysis was released by the journal Science. Normally Science releases its reports on Thursdays but the journal said it was issuing this study early because it contains important public health information.
Meanwhile, on Monday, the World Health Organization's assistant director-general moved to defend the global body against accusations that it stoked unnecessary fear over a flu outbreak that appears to be relatively mild.
"I hope we have come across as trying to present a very balanced picture," Keiji Fukuda told reporters in Geneva.
"I think that one of the things we made clear is that the future is not possible to predict and there are many ways that events could turn out."
"Things could stay relatively mild, things could become more severe. Both of these are possible," he said. "I think without that information both people and countries cannot prepare as well as they can."
Ferguson's researchers said the 2009 H1N1 flu appears to be about equal in severity to the flu of 1957 and less severe than the deadly 1918 version.
The new analysis estimated that between 0.4 percent and 1.4 percent of cases were fatal.
They said the outbreak appears to have originated in mid-February in the village of La Gloria, Veracruz, where over half the population suffered acute respiratory illness, affecting more than 61 percent of under-15-year-olds in the community, the report added.
Using a variety of methods to estimate how easily the virus is transmitted, the researchers said that each case of the flu resulted in between 1.4 and 1.6 infections to others.
Data on the spread and strength of the illness is still incomplete, the researchers stressed. But they said their findings can help policymakers make such decisions as whether to close schools, balancing the cost of such actions against the potential to prevent spread of disease.
The potential spread of the illness in the Southern Hemisphere, which is just beginning its flu season, needs to be closely monitored, Ferguson's team wrote.
WHO's announcement of a Level 5 alert meant that a virus has caused sustained community level outbreaks in at least two countries in one region, and a worldwide pandemic is considered imminent. It alerts countries that do not have the illness yet to prepare for its arrival and institute their pandemic preparedness plans.
The Centers for Disease Control and Prevention reports that there have been 2,618 flu cases in 44 states with three deaths.
WHO Warns Europe To Be On Guard
The number of swine flu infections in Europe could explode in much the same way it has in North America, a senior World Health Organization official said Monday.
Most instances of the disease - which WHO says has reached 4,694 cases in 30 countries but other tallies put much higher - have occurred in Mexico and the United States.
Most cases in Europe, Asia and South America are linked to travelers bringing the virus home with them, but there is a possibility the disease will become established there too, said WHO's flu chief Keiji Fukuda.
"Whether it will develop exactly as it did in the United States and in Canada and in Mexico is anybody's guess, but I think that the potential for it to be established either in Europe or in other places is there," he said.
Mexico Reopens Schools, Tries To Bolster Economy
Mexico welcomed millions of children back to school Monday with masks, thermometers and globs of hand sanitizer.
The reopening of kindergartens and primary and middle schools shut since April 24 was the latest step in Mexico's efforts to restore a sense of normality. Businesses, government services, high schools and universities reopened last week.
But six of Mexico's 31 states put off reopening schools for a week because of local rises in the number of cases, and a seventh ordered a one-day delay.
The federal Education Department said Monday that all 250,000 schools - except some 30,000 in states that did not reopen Monday - had been cleaned and disinfected as 25 million children prepared to return to class.
"It's very important for families to know that the disease is curable; we have enough medicine to treat any cases that arise," Education Secretary Alonso Lujambio Irazabal said. "As soon as we suspect we have a case we are going to offer antivirals to that person, that teacher, that student."
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 14 billion peso ($1.1 billion) package to help restaurants, hotels and other businesses.
At least 10 commercial banks are involved in the plan, promising three-month reprieves for small businesses with outstanding loans in Mexico City and two hard-hit states. Small businesses in beach resorts and other tourist destinations were promised a six-month grace period.
Later in the day, Tourism Secretary Rodolfo Elizondo said the government would launch a 1.2 billion peso ($90 million) publicity campaign this week urging Mexicans to take vacations in their own country.
Noting several nations have issued travel warnings or restricted airline flights to Mexico, Elizondo said that for now trying to promote trips to Mexico by foreigners "would be like throwing money away." He said occupancy rates at Mexico's top beach resorts are averaging between 15 percent and 23 percent.