Screening will be less effective in a growing epidemic, due to an excess of recently-exposed and not-yet-symptomatic travellers (Gostic et al., 2015). In the context of COVID-19, we consider both growing and stable epidemic scenarios, but place greater emphasis on the realistic assumption that the COVID-19 epidemic is still growing. Since late January 2020, the Chinese government has imposed strict travel restrictions and surveillance on population centers heavily affected by COVID-19 (BBC News, 2020; Cellan-Jones, 2020), and numerous other countries have imposed travel and quarantine restrictions on travellers inbound from China. Until about Feb. 20, 2020, these measures had appeared to successfully limit community transmission outside of China, but all the while multiple factors pointed to on-going risk, including evidence that transmission is possible prior to the onset of symptoms (Yu et al., 2020; Hu et al., 2020), and reports of citizens seeking to elude travel restrictions or leaving before restrictions were in place (Ma and Pinghui, 2020; Mahbubani, 2020). Now, in the week following Feb. 20, 2020, new source epidemics have appeared on multiple continents (World Health Organization, 2020a), and the the risk of exportation of cases from beyond the initial travel-restricted area is growing.