Vector fields as a framework for modelling the mobility of commodities

Farokhnejad, Sima, S. da Mata, Angélica, Macedo, Mariana and Menezes, Ronaldo (2025) Vector fields as a framework for modelling the mobility of commodities. PLOS ONE. (Submitted)

Abstract

Commodities, including livestock, flow through trade networks across the world, with trajectories that can be effectively captured using mobility pattern modelling approaches similar to those used in human mobility studies. However, documenting these movements comprehensively presents significant challenges; it can be unrealistic, costly, and may conflict with data protection regulations. As a result, mobility datasets typically contain inherent uncertainties due to sparsity and limitations in data collection methods. Origin-destination (OD) representations offer a powerful framework for modelling movement patterns and are widely adopted in mobility studies. However, these matrices possess inherent structural limitations: locations absent from the OD framework lack spatial information regarding potential mobility directions and intensities. This spatial incompleteness creates analytical gaps across different geographical granularities, constraining our ability to fully characterise movement patterns in underrepresented areas. In this study, we introduce a vector-field-based method to address these persistent data challenges, transforming OD data into vector fields that capture spatial flow patterns more comprehensively, enabling us to also study mobility directions in a robust manner. We utilise cattle trade data from Minas Gerais, Brazil, as our case study for commodity flows. This region's extensive livestock trading network makes it an ideal test case for our vector-field methodology. Cattle movements are particularly significant as they directly impact disease transmission, including foot-and-mouth disease. Accurately modelling these flows enables more effective disease surveillance and control strategies, with implications for both animal health and economic stability. Our vector-field approach reveals fundamental patterns in commodity mobility and can infer movement information for unrepresented locations; a critical factor in modelling scenarios such as disease spread. Our approach offers an alternative to traditional network-based models, enhancing our capacity to infer mobility patterns from incomplete datasets and advancing our understanding of large-scale commodity trades.

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