"It's been a dark couple of days," Brown, 34, tells PEOPLE in an exclusive statement, "but the outpouring of support has been tremendous. It's truly what will keep me fighting."
After collapsing while filming a new reality show, Brown, 32, underwent two emergency surgeries – one procedure to remove a tumor blocking her colon on Aug. 17 and another three days later due to complications from the first operation.
She is currently in the ICU of a New York City hospital in stable condition where she's expected to stay for about two weeks.
Brown, who chronicled her fight with ovarian cancer in a candid blog for PEOPLE.com, added, "I'm so fortunate to have a platform as I know I'm not the only one out there going through something like this."
"I promise to keep trucking along if for nothing else but others who need to know it is possible to beat this horrible disease once and for all!" says Brown.
Those close to her know she's a woman of her word. "She's a fighter," her sister Megan told PEOPLE. "It's definitely an uphill battle, but I know if anybody can do it it's her."
"Diem is in such high spirits today thanks to the love and support people have shown since this news was announced," says her longtime friend Alicia Quarles.
"I've seen Diem battle this horrific disease and come out victorious twice before," she adds. "It is unfair and surreal that once again she is being put in this position."
But friends and family are fired up to help her through what lies ahead, says Quarles. They have also set up a support page for Brown on MedGift, a gift registry Brown started to help those suffering from any illness.