Since it was first identified, the epidemic scale of the recently emerged novel coronavirus (2019-nCoV) in Wuhan, China, has increased rapidly, with cases arising across China and other countries and regions. Using a transmission model, we estimate a basic reproductive number of 3.11 (95% CI, 2.39-4.13), indicating that 58-76% of transmissions must be prevented to stop increasing. We also estimate a case ascertainment rate in Wuhan of 5.0% (95% CI, 3.6-7.4). The true size of the epidemic may be significantly greater than the published case counts suggest, with our model estimating 21 022 (prediction interval, 11 090-33 490) total infections in Wuhan between 1 and 22 January. We discuss our findings in the light of more recent information. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.