The source of two cases of coronavirus in the Devonport area will remain unknown, Public Health director Mark Veitch says.
He said an extensive investigation into workplaces, social gatherings, living areas and the movements of the two women over a two-week period had been undertaken over a number of days.
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"We haven't been able to identify a setting where we can confidently say where they caught their infection," Dr Veitch said.
He said he would alert the media if any revelation of a source for either case emerged.
Dr Veitch said community transmission of the virus was inevitable in the medium to longer term.
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Public Health on Wednesday night revealed two interstate travellers, who had been on an extensive tour of Tasmania two weeks ago, had tested positive to coronavirus.
The pair had visited Port Arthur by bus, MONA by ferry, Freycinet Marine Farm, Kate's Berry Farm near Swansea, Bridestowe Lavender Farm, Pyengana Cheese Factory, and Ashgrove Farm.
They had gone on the Batman River Cruise on March 21.
The pair, a man in his 20s and a man in his 70s, were in the state from March 12 until March 22.
Dr Veitch said there was a low risk the infection would be transferred to others in the same venue as the infected travellers but the risk was higher if they had been on a bus trip or on other transport with them.
Premier Peter Gutwein said more measures to flatten the curve of coronavirus spread will be announced later on Thursday.
These will constitute additional restrictions on movement by the state's population.
"The state will get through this...but we need to work together to ensure we get to the other side," Mr Gutwein said.
Health Minister Sarah Courtney said there had been one more positive test to coronavirus, bringing the state's tally to 72.
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