Four Queenslanders have died, three of whom had contracted the virus after returning from trips on cruise ships.

Premier Annastacia Palaszczuk has warned Queensland is still months off approaching its infection peak.

“We haven’t even started to climb the curve,” she told ABC radio today.

“We are about two or three weeks behind NSW and the peak could be in July, August, September.”

“We will continue to see increases of cases.”

The Premier said 80 to 85 per cent of cases were still linked to overseas travel as Queenslanders continue to return home.

Queensland imposed even tighter border controls overnight, after hundreds of people ignored pre-existing closures and continued to cross the state’s border with NSW.

The premier said 16 people had been turned around since midnight in a bid to crackdown on non-essential travel between the two states.

Under the new rules Queenslanders are being let in, along with freight services.

Everyone else is being refused entry unless they hold a government permit proving they are travelling for essential reasons, such as work or medical appointments.

The has also been an increased police presence at the Brisbane airport.

Non-residents who don’t have an entry permit will not be allowed to leave the airport, and will be returned to where they arrived from on the next available flight.

The state is also closing most national parks, walking tracks and 4WD areas.

The parks will be closed to the public, along with hiking tracks, picnic areas, camping areas, swimming holes and lookouts from today.