The current restrictions in Australia appear to be edging closer to 90% effective in reducing the infection rate. The number of new cases a day is dropping towards low numbers.
So the question is: Given that the restrictions are hurting the economy, what level of reduction in infection rate should Australia aim for in lifting the restrictions? The short answer is one that keeps the apparent infection rate R0 below 1. And since the 'natural' R0 of the virus appears to be about 2.2 the restriction should at least achieve a 54.6% reduction in the infection rate to bring the apparent R0 to 1 or less.
The graph produced by the infection model, below, shows the same thing as does the zoomed out version lower down. The 'wobbles' in the graph are artifacts caused by the sudden change in level of restrictions, rather than a more likely 'wash-in' of the effects over a few days.
If restrictions are eased till they are only 54%, or less, effective at reducing the infection rate, then it simply sets off another exponential rise in new cases. The rise is either slow but very prolonged (years) or sudden and overwhelming. The good news is that if the eased restrictions are 55% effective or better, the new cases of infection steadily drops. But that level of restrictions would need to be maintained. If the restrictions were eased till they were still 60% effective at reducing the infection rate, new cases could be very low by September, and contact tracing could be very effective as long as the border was kept secure against surprise re-entry of the virus from elsewhere.