  Human traffic along roads can be a major vector for infectious diseases and
invasive species. Though most road traffic is local, a small number of
long-distance trips can suffice to move an invasion or disease front forward.
Therefore, understanding how many agents travel over long distances and which
routes they choose is key to successful management of diseases and invasions.
Stochastic gravity models have been used to estimate the distribution of trips
between origins and destinations of agents. However, in large-scale systems it
is hard to collect the data required to fit these models, as the number of
long-distance travellers is small, and origins and destinations can have
multiple access points. Therefore, gravity models often provide only relative
measures of the agent flow. Furthermore, gravity models yield no insights into
which roads agents use. We resolve these issues by combining a stochastic
gravity model with a stochastic route choice model. Our hybrid model can be
fitted to survey data collected at roads that are used by many long-distance
travellers. This decreases the sampling effort, allows us to obtain absolute
predictions of both vector pressure and pathways, and permits rigorous model
validation. After introducing our approach in general terms, we demonstrate its
benefits by applying it to the potential invasion of zebra and quagga mussels
(Dreissena spp.) to the Canadian province British Columbia. The model yields an
R-squared value of 0.73 for variance-corrected agent counts at survey
locations.
