The outbreak of coronavirus disease 2019 which originated in Wuhan, China, constitutes a public health emergency of international concern with a very high risk of spread and impact at the global level.We developed data-driven susceptible-exposed-infectious-quarantine-recovered (SEIQR) models to simulate the epidemic with the interventions of social distancing and epicenter lockdown. Population migration data combined with officially reported data were used to estimate model parameters, and then calculated the daily exported infected individuals by estimating the daily infected ratio and daily susceptible population size. As of Jan 01, 2020, the estimated initial number of latently infected individuals was 380.1 (95%-CI: 379.8~381.0). With 30 days of substantial social distancing, the reproductive number in Wuhan and Hubei was reduced from 2.2 (95%-CI: 1.4~3.9) to 1.58 (95%-CI: 1.34~2.07), and in other provinces from 2.56 (95%-CI: 2.43~2.63) to 1.65 (95%-CI: 1.56~1.76). We found that earlier intervention of social distancing could significantly limit the epidemic in mainland China. The number of infections could be reduced up to 98.9%, and the number of deaths could be reduced by up to 99.3% as of Feb 23, 2020. However, earlier epicenter lockdown would partially neutralize this favorable effect.Because it would cause in situ deteriorating, which overwhelms the improvement out of the epicenter. To minimize the epidemic size and death, stepwise implementation of social distancing in the epicenter city first, then in the province, and later the whole nation without the epicenter lockdown would be practical and cost-effective.