Mariana Bridi da Costa, a 20-year-old Brazilian model
Her father, Agnaldo da Costa, told a Brazilian newspaper that "the concern is over her life".
Miss Bridi was a finalist in the search for Brazil's Miss World contestant in 2006 and 2007.
In 2007 she flew to China to represent her country in the Miss Bikini international competition.
She won a prize there for the most beautiful body, and came sixth out of 50 candidates.
Mr Fontes said Miss Bridi badly needs a transfusion of the uncommon blood type O negative.
He added: "She has always been a great fighter and has a history of perseverance.
"The first time she took part in a beauty contest, in 2006, she travelled for 20 hours on a bus in very plain clothes, and without any preparation, and she ended up coming fourth.
"We need her to show that same kind of fight now.
"In China she took on girls from 50 countries, and came sixth and won the prize for best body.
"This is a desperately sad story and we are calling on potential donors to come forward and give blood."
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