Twenty-nine people have died in Thailand and Vietnam since the latest outbreak began in January.
But while health officials stressed it was an isolated case, and the WHO said it "would not pose a significant public health risk," the case has renewed fears that bird flu could mutate with human influenza to create a deadlier version of the disease.
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Bird flu, also known as the H5N1 virus, is principally an avian disease, and was first caught in humans in Hong Kong, 1997. Almost all human cases come from contact with birds, though there were unconfirmed reports of possible human to human spread of the disease.
According to Thailand's Ministry of Public Health, Pranee Thongchan, 26, died of the virus September 20 soon after her daughter Sakuntala, 11, apparently died of the same illness, though she was cremated before tests could be conducted.
Pranee Thongchan "either contracted the virus from the environment in the village where the chickens died, or from the sick daughter who she was taking care of very closely at the hospital for a long period of time".
"This probable human-to-human transmission of avian influenza was related to a single index case and was limited within a family, and there is no evidence to suggest that the virus has mutated or re-assorted," the statement said.
Pranee's sister, Pranom - who also looked after Sakuntala in hospital - was confirmed as suffering from bird flu on Monday, and is now recovering in a hospital isolation ward.
Though the ministry earlier said neither Pranom or Pranee had been in contact with any established source of bird flu, such as infected fowl, it was later reported that Pranom, the aunt, had handled chicken carcasses at her house.
The aunt's three-year-old son has now recovered from suspected H5 flu, but nine more people in the province are suspected cases, including a 13-year-old who has died.
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The government said every province has been ordered to follow strict safety measures to avoid an epidemic, like reporting sick birds and screening and treating patients suspected to be infected.
In a joint statement on Monday, the UN Food and Agriculture Organization and the World Organization for Animal Health called the avian influenza epidemic in Asia "a crisis of global importance.
"Recent outbreaks in China, Thailand, Vietnam, Cambodia, and Malaysia show that the virus continues to circulate in the region, and will probably not be eradicated in the near future," the statement said.
