  Spatial connectivity is an important consideration when modelling infectious
disease data across a geographical region. Connectivity can arise for many
reasons, including shared characteristics between regions, and human or vector
movement. Bayesian hierarchical models include structured random effects to
account for spatial connectivity. However, conventional approaches require the
spatial structure to be fully defined prior to model fitting. By applying
penalised smoothing splines to coordinates, we create 2-dimensional smooth
surfaces describing the spatial structure of the data whilst making minimal
assumptions about the structure. The result is a non-stationary surface which
is setting specific. These surfaces can be incorporated into a hierarchical
modelling framework and interpreted similarly to traditional random effects.
Through simulation studies we show that the splines can be applied to any
continuous connectivity measure, including measures of human movement, and that
the models can be extended to explore multiple sources of spatial structure in
the data. Using Bayesian inference and simulation, the relative contribution of
each spatial structure can be computed and used to generate hypotheses about
the drivers of disease. These models were found to perform at least as well as
existing modelling frameworks, whilst allowing for future extensions and
multiple sources of spatial connectivity.
