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Hariadi Wibisono said the results on the 25-year-old woman, who died earlier this week, made her Indonesia's eighth confirmed death from the H5N1 strain of bird flu.
The ministry's director general of disease control, I. Nyoman Kandun, said it was unclear if the man had contact with dead chickens. He died a few days ago, he said.
About 3,500 geese died at a family farm in a development zone in Shishou city in the central province of Hubei, the official Xinhua news agency said, adding that 3,800 poultry were slaughtered within a radius of 3 km.
The news weighed on shares in both Chugai and Roche. Tamiflu is considered one of the best defences against bird flu in humans and is in great demand as fears grow about the spread of the deadly virus.
This is the first known case of H5N1 in the Gulf Arab region but officials could not say whether the bird had the highly pathogenic strain of the virus which has killed more than 60 people in Asia.
The World Health Organisation is to help probe a possible human case of bird flu in southern China, where 6 million birds were slaughtered in an area hit by the country's fourth outbreak of the virus in a month.