Accurate epidemiological models require parameter estimates that account for mobility patterns and social network structure. We demonstrate the effectiveness of probabilistic programming for parameter inference in these models. We consider an agent-based simulation that represents mobility networks as degree-corrected stochastic block models, whose parameters we estimate from cell phone co-location data. We then use probabilistic program inference methods to approximate the distribution over disease transmission parameters conditioned on reported cases and deaths. Our experiments demonstrate that the resulting models improve the quality of fit in multiple geographies relative to baselines that do not model network topology.