Since the arrival of porcine epidemic diarrhea virus (PEDV) in the United States in 2013, elimination and control programmes have had partial success. The dynamics of its spread are hard to quantify, though previous work has shown that local transmission and the transfer of pigs within production systems are most associated with the spread of PEDV. Our work relies on the history of PEDV infections in a region of the southeastern United States. This infection data is complemented by farm‐level features and extensive industry data on the movement of both pigs and vehicles. We implement a discrete‐time survival model and evaluate different approaches to modelling the local‐transmission and network effects. We find strong evidence in that the local‐transmission and pig‐movement effects are associated with the spread of PEDV, even while controlling for seasonality, farm‐level features and the possible spread of disease by vehicles. Our fully Bayesian model permits full uncertainty quantification of these effects. Our farm‐level out‐of‐sample predictions have a receiver‐operating characteristic area under the curve (AUC) of 0.779 and a precision‐recall AUC of 0.097. The quantification of these effects in a comprehensive model allows stakeholders to make more informed decisions about disease prevention efforts.

Since the arrival of porcine epidemic diarrhea virus (PEDV) in the United States in 2013, elimination and control programs have had partial success. The dynamics of its spread are hard to quantify, though previous work has shown that local transmission and the transfer of pigs within production systems are most associated with the spread of PEDV. Our work relies on the history of PEDV infections in a region of the southeastern United States. This infection data is complemented by farm-level features and extensive industry data on the movement of both pigs and vehicles. We implement a discrete-time survival model and evaluate different approaches to modeling the local-transmission and network effects. We find strong evidence in that the local-transmission and pig-movement effects are associated with the spread of PEDV, even while controlling for seasonality, farm-level features, and the possible spread of disease by vehicles. Our fully Bayesian model permits full uncertainty quantification of these effects. Our farm-level out-of-sample predictions have a receiver-operating characteristic area under the curve (AUC) of 0.779 and a precision-recall AUC of 0.097. The quantification of these effects in a comprehensive model allows stakeholders to make more informed decisions about disease prevention efforts.

The dynamics that govern disease spread are hard to model because infections are functions of both the underlying pathogen as well as human or animal behavior. This challenge is increased when modeling how diseases spread between different spatial locations. Many proposed spatial epidemiological models require trade-offs to fit, either by abstracting away theoretical spread dynamics, fitting a deterministic model, or by requiring large computational resources for many simulations. We propose an approach that approximates the complex spatial spread dynamics with a Gaussian process. We first propose a flexible spatial extension to the wellknown SIR stochastic process, and then we derive a moment-closure approximation to this stochastic process. This moment-closure approximation yields ordinary differential equations for the evolution of the means and covariances of the susceptibles and infectious through time. Because these ODEs are a bottleneck to fitting our model by MCMC, we approximate them using a low-rank emulator. This approximation serves as the basis for our hierarchical model for noisy, underreported counts of new infections by spatial location and time. We demonstrate using our model to conduct inference on simulated infections from the underlying, true spatial SIR jump process. We then apply our method to model counts of new Zika infections in Brazil from late 2015 through early 2016.