Authorities only became aware of three Logan men allegedly making a false declaration to drive home from Victoria after one of them asked for a COVID-19 test the next day.

Police will allege the trio – a 29-year-old from Slacks Creek, a 23-year-old from Waterford and a 25-year-old from Loganlea – had spent several weeks in Melbourne but displayed false ‘G’ pass declarations on their vehicle.

As Queensland Health was on Sunday trying to shut down a COVID-19 cluster started by three women in Logan, after an ill-fated trip to Melbourne, the three men allegedly used a falsified border notice to cross the border at Coolangatta.

An exasperated Premier Annastacia Palaszczuk today pleaded with people to be honest with authorities.

“We don’t want people to do this, it’s not right,” Palaszczuk said.

Chief Health Officer Jeannette Young said one of the men sought a COVID-19 test on Monday, admitting to the Melbourne trip, and “that’s what set off the alarm”.

The three men are in hotel quarantine while they, and Queensland Health, await the outcome of tests, expected on Tuesday afternoon. That will determine the extent of contact tracing in and around Logan, an area already on high alert after two of the three women returned from Melbourne with COVID-19 and infected three others, including one who worked with children and another who worked in aged care.

No new cases of COVID-19 were reported overnight, despite extensive testing, however there remains a risk that people have contracted the virus and may be passing it on without knowing.

“We’ve still got another six days to go until we can feel that we’ve safely got through that latest cluster,” Young said.

Victoria has recorded 439 new cases of coronavirus and 11 more deaths. Premier Daniel Andrews confirmed the deaths on Tuesday, bringing the state’s toll from COVID-19 to 147 and the national toll to 232.

All of the 11 deaths are linked to outbreaks in aged care facilities.

Deputy Police Commissioner Steve Gollschewski said the three men had been issued with notices to appear in court and it should be of “grave concern” to Queenslanders that they were not upfront about their movements.

Over the past week, 10 people have been issued with notices to appear in court, and the movements of some 400 others remain under investigation. Gollschewski said he was disappointed that “people in our community are still telling lies”.

Palaszczuk said that while only a “small minority” of Queenslanders were undermining the efforts to keep the state safe their deception could have tragic outcomes.

Opposition Leader Deb Frecklington said the “honour system at the border is clearly not working”.

“We believe a reverse onus of proof should now be put on people entering Queensland where they must prove they have not been to a hotspot,” Frecklington said in a statement.

“We can’t risk the lives and livelihoods of Queenslanders because of lax border controls.”

Treasurer Cameron Dick took to Twitter to respond to Frecklington’s criticism, writing: “This is the same leader of the same party that wanted Queensland’s borders open 1 July. To everyone.”

Palaszczuk, Young and Gollschewski have said they are constantly looking at ways to improve COVID-19 controls.

Melbourne’s rising death toll comes as Victoria settles into a new stage four lockdown in Melbourne, bringing with it expensive fines for people not self-isolating.

Mr Andrews on Tuesday announced a coronavirus isolation crackdown with more police, Defence and Health department personnel.

Infected people caught breaching the rules for a second time will be slapped with a $4957 on the spot fine, which will grow to $20,000 if the matter goes to court.

An additional 250 police, 500 ADF and 300 health staff will monitor the compliance.

“That team is growing substantially and that means every single positive case will be door-knocked multiple times, random and repeated doorknocks,” Mr Andrews told reporters.

It comes after new research revealed the state’s earlier stage three restrictions in Melbourne potentially saved the lives of hundreds of people.

Research from the Burnet Institute, published in the Medical Journal of Australia on Tuesday, found the state’s response to the second wave of COVID-19 averted 9000 to 37,000 cases between July 2 and 30.

Based on the World Health Organisation’s mortality rate of 3.4 per cent, the restrictions potentially saved 1258 lives.

Among stage three restrictions was the lockdown of 12 hotspot postcodes, the complete quarantine of several public housing towers in Flemington and North Melbourne and the closure of state borders in early July.

A six-week lockdown was announced for residents of metropolitan Melbourne and Mitchell Shire from July 9, then the compulsory use of masks in public settings was introduced.

Researchers said the reproduction rate of the virus before lockdown was 1.75.

Last week, Mr Andrews said that number was hovering about 1.0.

Under the latest restrictions, residents of metropolitan Melbourne must follow an 8pm-5am curfew and can’t travel more than 5km from home for shopping or exercise.

Regional Victoria is now moving to stage three restrictions, with restaurants, cafes, bars and gyms to shut from midnight on Wednesday.