Ro and infection time (i, the time a case remains infectious) are often determined empirically by case tracing and contact tracing in the field. It is usually considered difficult to estimate Ro and i from population data and models, like new and total cases.
It does appear that Ro and i can be estimated graphically by plotting curves with various values for Ro and i such that the curves match the actual data of new and total cases. Restrictions were put in place in Australia on 20 March and the maximum new cases a day occurred on 28 March 2020.
Ro and i change the slope of log new cases graph in opposite directions, so there are a number of 'sets' of Ro and i which fit the actual data equally well. It may be possible to determine which 'set' of Ro and i best agrees with the empiric field data.
Ro and i produce different shapes in the graph of the total cases near the end of the epidemic. Presumably i should have the same value in both graphs. Then R at this time can be more easily estimated and may suggest the effective R while the restrictions are in place.
The efficacy of restrictions appears to be 1- 0.7/2.2 which is 68%.