  Mathematical epidemiological models have a broad use, including both
qualitative and quantitative applications. With the increasing availability of
data, large-scale quantitative disease spread models can nowadays be
formulated. Such models have a great potential, e.g., in risk assessments in
public health. Their main challenge is model parameterization given
surveillance data, a problem which often limits their practical usage.
  We offer a solution to this problem by developing a Bayesian methodology
suitable to epidemiological models driven by network data. The greatest
difficulty in obtaining a concentrated parameter posterior is the quality of
surveillance data; disease measurements are often scarce and carry little
information about the parameters. The often overlooked problem of the model's
identifiability therefore needs to be addressed, and we do so using a hierarchy
of increasingly realistic known truth experiments.
  Our proposed Bayesian approach performs convincingly across all our synthetic
tests. From pathogen measurements of shiga toxin-producing Escherichia coli
O157 in Swedish cattle, we are able to produce an accurate statistical model of
first-principles confronted with data. Within this model we explore the
potential of a Bayesian public health framework by assessing the efficiency of
disease detection and -intervention scenarios.
