  A fundamental question during the outbreak of a novel disease or invasion of
an exotic pest is: At what location and date was it first introduced? With this
information, future introductions can be anticipated and perhaps avoided. Point
process models are commonly used for mapping species distribution and disease
occurrence. If the time and location of introductions were known, then point
process models could be used to map and understand the factors that influence
introductions; however, rarely is the process of introduction directly
observed. We propose embedding a point process within hierarchical Bayesian
models commonly used to understand the spatio-temporal dynamics of invasion.
Including a point process within a hierarchical Bayesian model enables
inference regarding the location and date of introduction from indirect
observation of the process such as species or disease occurrence records. We
illustrate our approach using disease surveillance data collected to monitor
white-nose syndrome, which is a fungal disease that threatens many North
American species of bats. We use our model and surveillance data to estimate
the location and date that the pathogen was introduced into the United States.
Finally, we compare forecasts from our model to forecasts obtained from
state-of-the-art regression-based statistical and machine learning methods. Our
results show that the pathogen causing white-nose syndrome was most likely
introduced into the United States 4 years prior to the first detection, but
there is a moderate level of uncertainty in this estimate. The location of
introduction could be up to 510 km east of the location of first discovery, but
our results indicate that there is a relatively high probability the location
of first detection could be the location of introduction.
