Summary Linking information on a movement network with space–time data on disease incidence is one of the key challenges in infectious disease epidemiology. In this article, we propose and compare two statistical frameworks for this purpose, namely, parameter-driven (PD) and observation-driven (OD) models. Bayesian inference in PD models is done using integrated nested Laplace approximations, while OD models can be easily fitted with existing software using maximum likelihood. The predictive performance of both formulations is assessed using proper scoring rules. As a case study, the impact of cattle trade on the spatiotemporal spread of Coxiellosis in Swiss cows, 2004–2009, is finally investigated.