  Motivated by foot-and-mouth disease (FMD) outbreak data from Turkey, we
develop a model to estimate disease risk based on a space-time record of
outbreaks. The spread of infectious disease in geographical units depends on
both transmission between neighbouring units and the intrinsic susceptibility
of each unit to an outbreak. Spatially correlated susceptibility may arise from
known factors, such as population density, or unknown (or unmeasured) factors
such as commuter flows, environmental conditions, or health disparities. Our
framework accounts for both space-time transmission and susceptibility. We
model the unknown spatially correlated susceptibility as a Gaussian process. We
show that the susceptibility surface can be estimated from observed,
geo-located time series of infection events and use a projection-based
dimension reduction approach which improves computational efficiency. In
addition to identifying high risk regions from the Turkey FMD data, we also
study how our approach works on the well known England-Wales measles outbreaks
data; our latter study results in an estimated susceptibility surface that is
strongly correlated with population size, consistent with prior analyses.
