I'm pretty sure that Melbourne isn't running some undetected pandemic:
- There are between 15,000 and 20,000 tests a day being done in Victoria. That's 5 times higher than in Queensland - see the Qld health table below.
- Despite testing 15,000 people a day, the positive rate in Victoria is now just 0.1%. If insufficient testing was being done that rate would be more like 20%. It's also about a third of the positive rate a month or so ago, 0.3%, which was in any case considered pretty good.
Department of Health and Human Services Victoria | Coronavirus testing data by local government area
So, yeah, I'm pretty confident that the Vic numbers are accurate.
Returning to the Qld traveller, there are just 175 active cases in Victoria, of whom 167 are in Melbourne, all of whom who would be in isolation. It really is unlikely that she landed in Victoria and was immediately infected.
Given that she's asymptomatic she could have been positive for weeks:
"She's not showing any symptoms of COVID-19 and that's why it's challenging for us to identify when she may have been infectious."
Oh, and then there's this:
Chair of the Northern Australia Primary Health Limited and Townsville general practitioner, Dr Michael Clements, said the traces and case should be a wake-up call.
"We should use it not as a fear mongering step but as a reminder that we are still vulnerable," Dr Clements said.
"Unfortunately, what we have seen in north Queensland and in large parts of Queensland is a complacency.
"We haven't had any cases here for so long now that we've seen testing rates drop.
"We've seen social distancing almost thrown out the window.
"Our biggest danger is complacency and thinking that we've beaten it.
"If we carry on as if it's not going to happen to us it'll spread like wildfire and we will be locked off to the rest of the world."
Testing
Region Samples tested Persons tested Tests per 100,000 persons Total Last 24 hours Total Last 24 hours Queensland 1,174,703 5,280 955,185 3,241 18,673 

