Fifteen people have been told to go home in the past 24 hours.

Police intercepted more than 35 people in cars - including some towing caravans and boats - and turned them back as needed.

Three people have been arrested or summoned to appear in court over COVID-19 related offences, the force confirmed on Friday.

"This Easter, if you are away from your primary residence and try to go to your shack and you don't have a valid excuse, you will not only be turned around, but you could be charged and face a substantial fine," Acting Assistant Commissioner Jo Stolp said.

Premier Peter Gutwein told residents on Thursday not to leave their homes unnecessarily, with fines of up to $16,800 or six months' jail.

Helicopters are monitoring people's movements, hovering over regional communities including Bicheno, Friendly Beaches, Coles Bay, Dunalley and Primrose Sands.

Officers are also patrolling on foot in Bridport, St Helens, Longford, Great Lake, Port Sorell, Somerset and Smithton among the areas.

Tasmania had recorded 111 cases of the virus as of Thursday night, with 48 of those people recovering.