## Description

The numbers of confirmed cases of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection are increasing in many places. Consequently, the number of individuals placed into quarantine is increasing too. The large number of individuals in quarantine has high societal and economical costs. There is ongoing debate about the duration of quarantine, particularly since the fraction of individuals in quarantine who eventually test positive is perceived as being low. We present a mathematical model that uses empirically determined distributions of incubation period, infectivity, and generation time to quantify how the duration of quarantine affects transmission. We use this model to examine two quarantine scenarios: traced contacts of confirmed SARS-CoV-2 cases and returning travellers. We quantify the impact of shortening the quarantine duration in terms of prevented transmission and the ratio of prevented transmission to days spent in quarantine. We also consider the impact of i) test-and-release strategies; ii) reinforced hygiene measures upon release after a negative test; iii) the development of symptoms during quarantine; iv) the relationship between quarantine duration and adherence; and v) the fraction of individuals in quarantine that are infected. When considering the ratio of prevented transmission to days spent in quarantine, we find that the diminishing impact of longer quarantine on transmission prevention may support a quarantine duration below 10 days. This ratio can be increased by implementing a test-and-release strategy, and this can be even further strengthened by reinforced hygiene measures post-release. We also find that unless a test-and-release strategy is considered, the fraction of individuals in quarantine that are infected does not affect the optimal duration of quarantine under our utility metric. Ultimately, we show that there are quarantine strategies based on a test-and-release protocol that, from an epidemiological viewpoint, perform almost as well as the standard 10 day quarantine, but with a lower cost in terms of person days spent in quarantine. This applies to both travellers and contacts, but the specifics depend on the context.