We use a spatial, stochastic, continuous time SIR model to investigate the dynamics of measles in a "country" of 25 cities. In this model, a person can be born, become infected, recover, immigrate to another city, become vaccinated, or die at any point in time. We are particularly interested in investigating how different vaccine regimes affect the disease's persistence and which, if any, lead to herd immunity. To that end, we study four different vaccination regimes and identify one that minimizes both the number of measles cases and the proportion of the population that must be vaccinated.