Clinical trials of a vaccine during an epidemic face particular challenges, such as the pressure to identify an effective vaccine quickly to control the epidemic, and the effect that time-space-varying infection incidence has on the power of a trial. We illustrate how the operating characteristics of different trial design elements maybe evaluated using a network epidemic and trial simulation model, based on COVID-19 and individually randomized two-arm trials with a binary outcome. We show that "ring" recruitment strategies, prioritizing participants at an imminent risk of infection, can result in substantial improvement in terms of power in the model we present. In addition, we introduce a novel method to make more efficient use of the data from the earliest cases of infection observed in the trial, whose infection may have been too early to be vaccine-preventable. Finally, we compare several methods of response-adaptive randomization (RAR), discussing their advantages and disadvantages in the context of our model and identifying particular adaptation strategies that preserve power and estimation properties, while slightly reducing the number of infections, given an effective vaccine.