The number of casual contacts of a COVID-positive case in the North has grown to 51 people.
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As previously reported, 17 close contacts of the 15-year-old Newnham boy have recorded negative COVID tests so far.
Acting Premier Jeremy Rockliff said these close contacts would be tested again over the weekend as they reached the seven-day mark of contact with the boy.
Public Health director Mark Veitch said more casual contacts had been identified through contact tracing.
He said these new contacts were present at the Launceston Airport on October 2 when the boy flew in from Victoria.
Of the casual contact group, seven negative results have been returned.
Dr Veitch said it remained possible that one of the close contacts would test positive for the Delta strain.
"But they would have been in quarantine up until that time and should pose no risk to the community," he said.
Dr Veitch said testing numbers remained low in the Mowbray and Newnham area.
He said even fully vaccinated people in these suburbs should be tested for the mildest of COVID-19 symptoms.
"Vaccination will reduce the symptoms that people have, but it doesn't always stop you getting infected," Dr Veitch said.
"If you have symptoms, go and get tested.
"If there has been spread into the community somehow, cases could occur anytime from now to over the next week or so."
Mr Rockliff said 62 per cent of eligible Tasmanians had received two doses of the COVID-19 vaccine.
He said the state was on the path to pass the 80-per-cent mark over the weekend for eligible Tasmanians who had received the first dose of the vaccine.
Mr Rockliff said the government was developing a small towns vaccination program to ensure all Tasmanians had a chance to access the vaccine.
Acting state controller Dale Webster said the small towns program would be done in conjunction with the Royal Flying Doctors Service.
"They have a bus and the bus will roll into the local town and will be there for a day," he said.
Mr Webster said people would be able to walk up to the bus and be vaccinated.
He said the town itinerary still needed to be established.
Mr Rockliff said it remained a concern that 95,000 eligible Tasmanians were yet to receive their first jab.
He said 101 general practitioners were approved to administer vaccinations as were 105 community pharmacies and state-run clinics.