Spatial effects are fundamental to ecological and epidemiological systems, yet the incorporation of space into models is potentially complex. Fixed-edge network models (i.e. networks where each edge has the same fixed strength of interaction) are widely used to study spatial processes but they make simplistic assumptions about spatial scale and structure. Furthermore, it can be difficult to parameterize such models with empirical data. By comparison, spatial point-process models are often more realistic than fixed-edge network models, but are also more difficult to analyze. Here we develop a moment closure technique that allows us to define a fixed-edge network model which predicts the prevalence and rate of epidemic spread of a continuous spatial point-process epidemic model. This approach provides a systematic method for accurate parameterization of network models using data from continuously distributed populations (such as data on dispersal kernels). Insofar as point-process models are accurate representations of real spatial biological systems, our example also supports the view that network models are realistic representations of space.