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Health Minister Andrew Little admits some people are slipping through the cracks, but says he hasn't had any indication public health officials are falling behind with cases isolating at home with Covid-19.
RNZ has spoken to health leaders who said in one case, a man with the virus slept in a car for six days, because he couldn't safely isolate at home.
Little told Morning Report health officials have told him they're up to the task.
"They certainly are under pressure because the number of people they're dealing with but, I attend the daily briefings that we get about how they're managing the volume that they've got, and they reassure us that they are coping adequately with the volume of work that they've got."
He said the public health team response should be swift after positive test was recorded.
"Once a positive test is returned, the public health is meant to be in contact with the person pretty much straightaway, certainly within hours, so that they can then do the triage, work out where the best place is for that person to be, can they isolate safely at home, do they need to go to an MIQ?"
But he said he had not heard about the man isolating in his car and would have to get more information about the case.
"There are clearly people falling through the cracks. That is unacceptable, but let's gauge the size of the problem before we ascertain what the appropriate response is to it."