Gaussian process forecasts

White-nose syndrome has been decimating populations of several bat species since its first occurrence in the Northeastern United States in the winter 2006-2007. The spread of the disease has been monitored across the continent through the collaboration of many organizations. Inferring the rate of spread of the disease and predicting its arrival at new locations is critical when assessing the current and predicting the future status and trends of bat species. We developed a model of disease spread that simultaneously achieves high-predictive performance, computational efficiency, and interpretability. We modeled white-nose syndrome spread using Gaussian process variations to infer the spread rate of the disease front, identify areas of anomalous time of arrival, and provide future forecasts of the expected time of arrival throughout North America. Cross-validation of model predictive performance identified a stationary Gaussian process without an additional residual error process as the best-supported model. Results indicated that white-nose syndrome is likely to spread throughout the entire continental United States by 2030. These annually updatable model predictions will be useful in determining the horizon over which disease management actions must take place as well as in status and trend assessments of disease-affected bats.