Background: To prevent the catastrophic health and economic consequences from COVID-19 epidemics, nations had to respond with swift public health interventions to achieve no community transmission outside of quarantine. However, the exact characteristics of an outbreak that trigger these measures are poorly defined. We aimed to assess the critical timing and extent of interventions in Australia. Methods: We developed a practical model using existing epidemics data in Australia. We quantified the effective combinations of public health interventions and the critical number of daily cases for intervention commencement. We assessed the impact of increasing transmissibility from new variants and the effect of vaccination coverage on the critical timing and extent of interventions. Findings: We found that in the past COVID-19 outbreaks in four Australian states, the number of reported cases on the day that interventions commenced strongly predicted the size and duration of the outbreaks. In the early phase of an outbreak, containing a wild-type dominant epidemic to a low level (≤10 cases/day) required effective combinations of social distancing and face mask use interventions to be commenced before the number of daily reported cases reaches 6 cases. Containing epidemics from alpha variant would require more stringent interventions that commenced earlier. For delta variant, public health interventions alone will not contain the epidemic, unless with a moderate vaccination coverage (≥50%). Interpretation: Our study highlights the importance of early and decisive action in the initial phase of an outbreak if governments aimed for zero community transmission. Vaccination is essential for containing variants.Funding Information: LZ is supported by the National Natural Science Foundation of China (grant number: 8191101420), Thousand Talents Plan Professorship for Young Scholars (Grant number: 3111500001); Xi’an Jiaotong University Basic Research and Profession Grant (Grant number: xtr022019003) and Xi’an Jiaotong University Young Talent Support Program (Grant number: YX6J004). The study is supported by Bill and Melinda Gates Foundation. Declaration of Interests: The authors declare no competing interests.