Novel coronavirus disease (COVID-19) has spread across the world at an unprecedented pace, reaching over 200 countries and territories in less than three months . In response, many governments denied entry to travellers arriving from various countries affected by the virus . While several industries continue to experience economic losses due to the imposed interventions, it is unclear whether the different travel restrictions were successful in reducing COVID-19 importations . Here we develop a comprehensive framework to model daily COVID-19 importations, considering different travel bans . We quantify the temporal effects of the restrictions and elucidate the relationship between incidence rates in other countries, travel flows and the expected number of importations into the country under investigation . As a cases study, we evaluate the travel bans enforced by the Australian government . We find that international travel bans in Australia lowered COVID-19 importations by 87.68% (83.39 - 91.35) between January and June 2020 . The presented framework can further be used to gain insights into how many importations to expect should borders re-open . Authorities may consider the presented information when planning a phased re-opening of international borders.