A bone marrow transplant led to the fatal infection, said Mrs Hughes.
She said her brother had just one paper left to complete his Masters degree in Maori studies at Auckland University. He had also graduated with a Bachelor of Arts from the university last March and was working part-time as a waiter at Sails restaurant before becoming ill.
Mrs Hughes described her brother as a "larger than life" figure, who thought of his illness as "a blip on the horizon".
"He's just a friendly, compassionate guy - nothing was too much trouble. He was my big, fantastic incredible, larger-than-life brother.
"Right up until probably a week-and-a-half ago, he was making his next lot of plans. He had the world map out," Mrs Hughes said.
MasterChef judge Simon Gault said he enjoyed working with Burden on the programme's first season.
"He was great to work with. He was never a minute without a laugh or a joke - great sense of humour."
In his younger years, Burden honed his skills in front of the camera by signing up with a modelling agency.
A service celebrating his life is due to be held at Auckland University's MacLaurin Chapel on Wednesday at 11am.
A follow-up memorial service in his home town of Napier has been planned for Monday next week.