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Extensive non-pharmaceutical and physical distancing measures are currently the primary interventions against coronavirus disease 2019 (COVID-19) worldwide. It is therefore urgent to estimate the impact such measures are having. We introduce a Bayesian epidemiological model in which a proportion of individuals are willing and able to participate in distancing, with the timing of distancing measures informed by survey data on attitudes to distancing and COVID-19. We fit our model to reported COVID-19 cases in British Columbia (BC), Canada, and five other jurisdictions, using an observation model that accounts for both underestimation and the delay between symptom onset and reporting. We estimated the impact that physical distancing (social distancing) has had on the contact rate and examined the projected impact of relaxing distancing measures. We found that, as of April 11 2020, distancing had a strong impact in BC, consistent with declines in reported cases and in hospitalization and intensive care unit numbers; individuals practising physical distancing experienced approximately 0.22 (0.11–0.34 90% CI [credible interval]) of their normal contact rate. The threshold above which prevalence was expected to grow was 0.55. We define the “contact ratio” to be the ratio of the estimated contact rate to the threshold rate at which cases are expected to grow; we estimated this contact ratio to be 0.40 (0.19–0.60) in BC. We developed an R package ‘covidseir’ to make our model available, and used it to quantify the impact of distancing in five additional jurisdictions. As of May 7, 2020, we estimated that New Zealand was well below its …