Intense non-pharmaceutical interventions were put in place in China to stop transmission of the novel coronavirus disease (COVID-19). As transmission intensifies in other countries, the interplay between age, contact patterns, social distancing, susceptibility to infection, and COVID-19 dynamics remains unclear. To answer these questions, we analyze contact surveys data for Wuhan and Shanghai before and during the outbreak and contact tracing information from Hunan Province. Daily contacts were reduced 7-8-fold during the COVID-19 social distancing period, with most interactions restricted to the household. We find that children 0-14 years are less susceptible to SARS-CoV-2 infection than adults 15-64 years of age (odd ratio 0.34, 95%CI 0.24-0.49), while in contrast, individuals over 65 years are more susceptible to infection (odd ratio 1.47, 95%CI: 1.12-1.92). Based on these data, we build a transmission model to study the impact of social distancing and school closure on transmission. We find that social distancing alone, as implemented in China during the outbreak, is sufficient to control COVID-19. While proactive school closures cannot interrupt transmission on their own, they can reduce peak incidence by 40-60% and delay the epidemic.