Premier Annastacia Palaszczuk says Queensland is months away from a peak in coronavirus infections, as the state’s tally climbed again.

The total number of cases is 873 since the outbreak began, up after 39 new cases were confirmed overnight.

Four Queenslanders have died.

“We haven’t even started to climb the curve. We are about two or three weeks behind NSW and the peak could be in July, August, September,” the Premier told ABC radio on Friday.

“We will continue to see increases of cases.”

More info on how we’re asking people to treat the rules around gatherings. #coronavirusaustralia pic.twitter.com/PAJUeiInCI

— Annastacia Palaszczuk (@AnnastaciaMP) April 2, 2020

She said 80 to 85 per cent of cases were still linked to overseas travel as Queenslanders return home from high-risk countries.

Queensland imposed even tighter border controls overnight, with unauthorised travellers being turned back at the state’s border with NSW.

The Premier said 16 people had been turned around since midnight.

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.

Water barriers and check points have been stepped up at Coolangatta, the Gold Coast’s southernmost suburb.

And water barriers have been used to close off some streets to stop people trying to avoid checkpoints.

• Related: Queensland rolls out barriers to unauthorised arrivals

There is also 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 their point of origin on the next available flight.

Australia has now recorded more than 5100 coronavirus cases, including 25 deaths.

Social isolation should help limit the scale of the winter flu season but authorities are urging people get their shots now.

“We don’t want an outbreak of flu at the same time we have an outbreak of COVID-19,” Queensland Chief Health Officer Jeannette Young said on Friday.

Dr Young said there was “very, very limited local transmission” of coronavirus in Queensland and the situation was nothing like the community transmission that was going on in NSW and Victoria.

“We’re such a dispersed state … in this case it’s very very much an advantage,” she told reporters.

“(It) means that we won’t see the peak of the impact of this virus across the whole state at the same time. We’ll be able to provide support within the state, wherever it’s needed.”

Four additional jets have been put on stand-by to rapidly move people around the state should that be necessary.

Health workers abused

Health Minister Steven Miles expressed disgust at reports of Queensland Health workers being “vilified, threatened and treated abhorrently” when out in public in their uniforms.

“They are heroes. They are are people who go to work every day to take care of us. So thank them, don’t yell at them,” he said.

The Premier has warned of a tough six months ahead, as Queenslanders deal with rules that urge them not to leave their homes unless it’s truly necessary.

But Ms Palaszczuk has pulled back slightly on the Prime Minister’s advice that households must limit visitors to just one non-resident at a time.

“You can have two additional people to your house, and when you go outside you can only have two people,” Ms Palaszczuk said on Thursday.

“Don’t have strangers to your house, so I think if everyone abides by those rules we’ll be okay.”

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 Friday.

–with AAP