Human traffic along roads can be a major vector for infectious diseases and invasive species. Understanding how many agents travel  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 develop a combined stochastic gravity and route choice model for road traffic. We introduce this hybrid approach in general terms and demonstrate its benefits by applying it to the potential invasion of zebra and quagga mussels (Dreissena spp.) to the Canadian province British Columbia (BC). The spread of these mussels is facilitated by traffic of boaters transporting propagules from invaded to uninvaded lakes. The model allows absolute predictions of agent traffic and yields insights into which roads agents use. Applying the approach, we identify the most significant sources of potential mussel vectors and the waterbodies in BC that are threatened most. Furthermore, we show the roads along which most boaters enter BC. The hybrid model can be fitted with survey data collected at roads that are used by many long-distance travellers. This decreases the required sampling effort so that more data are available to fit the model. As a consequence, the model yields accurate predictions even in large-scale systems, and the model can be validated rigorously. The model's predictions can be used to understand the spread and facilitate the management of infectious diseases and invasive species .
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 .
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(BC). The spread of these mussels is facilitated by traffic of boaters transporting propagules from invaded to uninvaded lakes. The model allows absolute predictions of agent traffic and yields insights into which roads agents use. Applying the approach, we identify the most significant sources of potential mussel vectors and the waterbodies in BC that are threatened most. Furthermore, we show the roads along which most boaters enter BC. The hybrid model can be fitted with survey data collected at roads that are used by many long-distance travellers. This decreases the required sampling effort so that more data are available to fit the model. As a consequence, the model yields accurate predictions even in large-scale systems, and the model can be validated rigorously. The model's predictions can be used to understand the spread and facilitate the management of infectious diseases and invasive species
. The model yields an R-squared value of 0.73 for variance-corrected agent counts at survey locations