Controlling COVID-19 transmission in universities poses challenges due to the complex social networks and potential for asymptomatic spread. We developed a stochastic transmission model based on realistic mixing patterns and evaluated alternative mitigation strategies. We predict, for plausible model parameters, that if asymptomatic cases are half as infectious as symptomatic cases, then 15% (98% Prediction Interval: 6-35%) of students could be infected during the first term without additional control measures. First year students are the main drivers of transmission with the highest infection rates, largely due to communal residences. In isolation, reducing face-to-face teaching is the most effective intervention considered, however layering multiple interventions could reduce infection rates by 75%. Fortnightly or more frequent mass testing is required to impact transmission and was not the most effective option considered. Our findings suggest that additional outbreak control measures should be considered for university settings.