* More cases expected across U.S.
* CDC rethinking school closure policy (Adds Napolitano quotes, California prisons paragraphs 12-15)
By Maggie Fox, Health and Science Editor
WASHINGTON, May 4 (Reuters) - The new H1N1 swine flu virus has infected 286 people in 36 U.S. states and it is likely to spread to every state, the U.S. Centers for Disease Control and Prevention reported on Monday.
Most cases remain mild, but 35 people have been hospitalized, the CDC's acting director, Dr. Richard Besser, told a news conference. A toddler who died in Texas last week remains the only death in the United States so far.
In Mexico, officials say they hope cases there will continue to decline, but it was clear the outbreak of the never-before-seen strain of influenza was spreading elsewhere.
Besser said the virus was so clearly everywhere that the CDC might step down its recommendations to test people so that state and federal health officials could spend their limited time and resources elsewhere.
"We are seeing over 700 probable cases in a total of 44 states," Besser said. So far, 99 percent of probable cases have, upon further testing, turned out to be the new H1N1 strain, Besser said.
"This likely represents an underestimation of the total number of cases across the United States," Besser added, because most people with flu-like symptoms -- fever, aching muscles and cough -- are not even getting tested.
Besser said the CDC was even reconsidering the strategy of closing schools where cases turn up. More than 500 U.S. schools have been closed because of outbreaks.
Schools are closed to protect children, and to keep children from spreading an infection in the community. But this virus is looking to be as mild as seasonal flu, which rarely kills children.
"It appears that the virus is already pretty well-established in those communities," Besser said. "So we are looking at the school closure guidance."
DEADLY FLU
That does not mean the virus is harmless, he noted. Seasonal flu infects an estimated 30 million Americans every year, about 10 percent of the population, kills 36,000 and puts 200,000 into the hospital.
"People are hospitalized and die every year with seasonal flu," Besser said. The new virus has killed people in Mexico and will likely kill people in other countries, he said.
California closed all 33 of its state prisons and six juvenile detention centers to routine visitors and other "non-essential activities" until further notice after an adult inmate at a prison in Southern California was diagnosed with a probable case of the H1N1 flu virus.
Besser said he was pleased at how well-prepared state and local officials were for the outbreak -- a result of years of planning for pandemic influenza and other disasters that started with the 2001 anthrax attacks, accelerated when H5N1 avian influenza re-emerged in 2003 and kicked into high gear when the response to Hurricane Katrina in 2005 was so poor.
Experts repeated fears that the virus must be watched because it could come back worse when temperatures start to cool, as happened with the 1918 flu pandemic.
"I think specifically we're viewing this incidence, this flu outbreak as a possible precursor to a subsequent outbreak in the fall," Homeland Security Secretary Janet Napolitano told reporters later. (With additional reporting by Steve Gorman and Toby Zakaria)