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Kaan Hunter has infantile hypophosphatasia - a rare genetic disorder characterised by the abnormal development of bones and teeth.
He is believed to be the only person in New Zealand with the condition.
His mother Tracey Roberts, 26, has taken to Givealittle to fundraise for his treatment - which is not funded in New Zealand.
"We have applied for a grant but are told it is unlikely we will receive it. My baby boy has only just started his life and now needs $100,000 a year just to keep him alive," she wrote.
Without the treatment, baby Kaan has been given between four and six months to live.
"He has very low phosphate, which means he has extremely weak bones that, without treatment, will not be able to handle growing or supporting his body as he grows himself - this is fatal," Roberts wrote.
"He is currently in Starship Hospital, where they are desperately trying to bring his calcium levels down, but this is just a temporary fix."
Roberts said the diagnosis had been "extremely hard" on her and Kaan's three other siblings.
"It will be a hard road ahead but I will not stop fighting to get my little boy the chance at life he so deserves!
"It has broken my heart to hear that I may not be able to afford to keep my child alive, but he is strong and we wont give up on him.
"Any and all support would be so gratefully appreciated by myself and our entire family," the page reads.
Roberts said all funds will go primarily towards funding Kaan's treatments, as well as travel to and from Starship and helping to support his parents and siblings while they fight for his life.
The Givealittle page, set up on Saturday, has currently raised more than $5000.