Senator McCarthy, a Yanyuwa woman from the NT's Gulf country, revealed at a press conference this morning that her sister was the 30-year-old woman who on Monday tested positive to the virus in the remote community of Robinson River.

"I'd like to say a personal message and that is that to my sister, who is the source of the COVID infection in Robinson River, that our thoughts and prayers are with her and our family, to my uncle and aunties and cousins who have been flown in from Katherine, who are in Howard springs, to stay strong," she said.

"I'm proud of you that you're double vaxxed, proud of you that you're there. And you're in safe hands."

Senator McCarthy said she has not been able to directly contact her sister who is in the care of health staff in the remote community's clinic.

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"I have spoken to the nurse in Robinson River, that was yesterday," she said.

"Clearly the nurse was also in a crowded room. It was difficult to speak directly to my sister. I'm hoping I can do that today."

She said the overcrowding in Robinson River posed a serious problem for containing any outbreak of the virus.

"We have 10 to 12 people to a house. We have people who have 20 people to a house, and the absolute urgency that must be placed on housing and housing for remote homelands and outstations with the federal government to come to the party on this," Senator McCarthy said.

"This is a serious matter. This is a case of life and death here."

Senator McCarthy said providing special accommodation in the community to allow people to isolate is a "no brainer."

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