  Modelling epidemics is crucial for understanding the emergence, transmission,
impact and control of diseases. Spatial individual-level models (ILMs) that
account for population heterogeneity are a useful tool, accounting for factors
such as location, vaccination status and genetic information. Parametric forms
for spatial risk functions, or kernels, are often used, but rely on strong
assumptions about underlying transmission mechanisms. Here, we propose a class
of non-parametric spatial disease transmission model, fitted within a Bayesian
Markov chain Monte Carlo (MCMC) framework, allowing for more flexible
assumptions when estimating the effect on spatial distance and infection risk.
We focus upon two specific forms of non-parametric spatial infection kernel:
piecewise constant and piecewise linear. Although these are relatively simple
forms, we find them effective. The performance of these models is examined
using simulated data, including under circumstances of model misspecification,
and then applied to data from the UK 2001 foot-and-mouth disease.
