The beauty queen was crowned Miss Venezuela at the age of 17 in 2000, and the following year she was third runner-up in the Miss Universe pageant in Puerto Rico.
Miss Ekvall, who also worked as an actress and TV presenter, wrote a book, Fuera de Foco (Out of Focus), about her struggle with cancer, which included images by Venezuelan photographer Roberto Mata.
I hate to see photos in which I come out ugly. But you know what? Nobody ever said cancer is pretty or that I should look like Miss Venezuela when I have cancer.
In an interview last year, she told the newspaper El Nacional: "I needed to send the message of the need for cancer prevention."
Her cover portrait showed her without makeup and her head shaved. The book also included images of her while going through chemotherapy.
"I hate to see photos in which I come out ugly," she said at the time. "But you know what? Nobody ever said cancer is pretty or that I should look like Miss Venezuela when I have cancer."
In her book, Ms Ekvall described her joy at the birth of her daughter saying: "that happiness, although (the daughter) may not know it or understand it, keeps me alive today."
The book included emails that she wrote to friends providing updates on her treatment and thanking them for their support, as well as short essays by relatives and friends reflecting on her ordeal.
Her father, Eric Ekvall, recalled in the book that his mother, also named Eva, had died of the same type of cancer at age 39.
"Those who know Eva know she doesn't give up," he wrote of his daughter. "She fights for what she wants."
Ms Ekvall's remains were cremated in Houston, where she was in hospital, and are being taken home to Venezuela where her funeral will be held.
Although her mother is Jamaican and her father is American of Swedish and Hungarian descent, she once said: "I feel more Venezuelan than anybody."
Her husband posted a photo on Twitter on Sunday of a close-up of his hand holding hers, resting on a bed, with the words "Always together ... I love you wife."