Background: We investigated the public health and economy outcomes of different levels of social distancing to control a 'second wave' outbreak in Australia and identify implications for public health management of COVID-19. Methods: Individual-based and compartment models were used to simulate the effects of different social distancing and detection strategies on Australian COVID-19 infections and the economy from March to July 2020. These models were used to evaluate the effects of different social distancing levels and the early relaxation of suppression measures, in terms of public health and economy outcomes. Results: The models, fitted to observations up to July 2020, yielded projections consistent with subsequent cases and showed that better public health outcomes and lower economy costs occur when social distancing measures are more stringent, implemented earlier and implemented for a sufficiently long duration. Early relaxation of suppression results in worse public health outcomes and higher economy costs. Conclusions: Better public health outcomes (reduced COVID-19 fatalities) are positively associated with lower economy costs and higher levels of social distancing; achieving zero community transmission lowers both public health and economy costs compared to allowing community transmission to continue; and early relaxation of social distancing increases both public health and economy costs.