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

A hybrid gravity and route choice model to assess vector traffic in large-scale road networks