Five challenges for spatial epidemic models

• Spatial models will become more important as geolocated data become the norm for infectious disease.
• Network models can be thought of as a unifying framework within which metapopulation models and individual-based models are contained.
• Work is needed on threshold parameters for spatial models, partly because they often do not produce exponential growth.
• Accurately predicting the impact of interventions requires models to be constructed with the appropriate resolution.

Infectious disease incidence data are increasingly available at the level of the individual and include high-resolution spatial components. Therefore, we are now better able to challenge models that explicitly represent space. Here, we consider five topics within spatial disease dynamics: the construction of network models; characterising threshold behaviour; modelling long-distance interactions; the appropriate scale for interventions; and the representation of population heterogeneity.