The state's health director, Dr. David Lakey, at an Austin news conference, called it "highly likely" that the boy contracted the disease in Mexico before his trip to the U.S.
Officials in Brownsville are trying to trace his family's trip to find out how long they were in the area, who they visited and how many people were in the group, said Cameron County Judge Carlos Cascos.
The boy, who was 23 months old, had "underlying health issues" before he flew to Matamoros, Mexico, on April 4 and crossed into Brownsville to visit relatives, state health officials said.
He developed flu symptoms four days later and was taken to a Brownsville hospital April 13 and transferred the following day to Texas Children's Hospital in Houston, where he died Monday night.
The U.S. Centers for Disease Control and Prevention on Wednesday confirmed that he had been infected with the swine flu virus. The cause of the death was pneumonia caused by the virus, Cascos said.
Health officials insisted the boy posed no contagion threat to Houston. He had no contact with other patients at Texas Children's Hospital and none of the staff was exposed, said Dr. Jeffrey Starke, the hospital's director of infectious disease.
This case "shouldn't trigger any undue alarm in the community," Starke told a news conference. "The child did not acquire the virus in Houston, Texas."
Dr. Brian Smith, regional director of the Texas Department of State Health Services, said antiviral treatments were given to family members who had close contact with the child and none had contracted swine flu. He said that with the virus' short incubation period, health officials would have begun seeing secondary cases among the child's close contacts by now, but none has appeared.
Although the boy wasn't initially identified as a swine flu case, Starke said concern grew over the last several days as news of the virus intensified.
Officials refused to release any further information about the boy or his family, including his name or any details on his other health issues, citing privacy laws.
Starke said the child was "critically ill the entire time the child was under our care," and that he was transferred to Houston because the hospital in Brownsville, an impoverished border city of 140,000, couldn't provide the kind of care he needed.
Swine flu is suspected of killing more than 150 people and sickening over 2,600 in Mexico, Canada, New Zealand, Britain, Germany, Spain, Israel and Austria.
The virus has spread to 11 U.S. states from coast to coast. Total American cases surged to nearly 100, including a Marine at the Twentynine Palms base in southern California.
According to the CDC, more than 20,000 children younger than age 5 are hospitalized every year because of seasonal flu. In the 2007-08 flu season, the CDC received reports that 86 children nationwide died from flu complications.
Authorities have confirmed at least 93 swine flu cases in the United States. They've identified 16 cases in Texas, 51 in New York, 14 in California, three in Maine; two in Kansas, two in Massachusetts, and one each in Indiana, Ohio, Arizona and Nevada. The CDC also said Michigan had two, but state officials maintained only one was confirmed.
Texas Gov. Rick Perry announced a disaster declaration Wednesday for the entire state. The declaration will allow officials to begin emergency protective measures and seek reimbursement from the federal government.
Texas officials also are postponing all public high school athletic competition until May 11. Schools serving more than 50,000 kids across Texas were closed.
As for future action, Perry said closing the border with Mexico is an option, but he doesn't want to play a "what-if game."
"There's no need to panic," Perry said. "I urge our citizens to act responsibly in the course of this situation. Heed the advice of local and state health officials."
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