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Coronavirus disease 2019 (COVID-19) is an infectious disease of humans caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Since the first case was identified in China in December 2019 the disease has spread worldwide, leading to an ongoing pandemic. In this article, we present an agent-based model of COVID-19 in Luxembourg, and use it to estimate the impact, on cases and deaths, of interventions including testing, contact tracing, lockdown, curfew and vaccination. Our model is based on collation, with agents performing activities and moving between locations accordingly. The model is highly heterogeneous, featuring spatial clustering, over 2000 behavioural types and a 10 minute time resolution. The model is validated against COVID-19 clinical monitoring data collected in Luxembourg in 2020. Our model predicts far fewer cases and deaths than the equivalent equation-based SEIR model. In particular, with R0 = 2.45, the SEIR model infects 87% of the resident population while our agent-based model infects only around 23% of the resident population. Our simulations suggest that testing and contract tracing reduce cases substantially, but are less effective at reducing deaths. Lockdowns are very effective although costly, while the impact of an 11pm-6am curfew is relatively small. When vaccinating against a future outbreak, our results suggest that herd immunity can be achieved at relatively low coverage, with substantial levels of protection achieved with only 30% of the population fully immune. When vaccinating in the midst of an outbreak, the challenge is more difficult. In this context, we investigate the impact of vaccine efficacy, capacity, hesitancy and strategy. We conclude that, short of a permanent lockdown, vaccination is by far the most effective way to suppress and ultimately control the spread of COVID-19.