Using Vector Fields in the Modelling of Movements as Flows: A Case Study with Cattle Trade Networks

Livestock production is one of the world’s most important economic activities, involving nearly every country either as a producer or consumer. Indeed, around 1.3 billion people worldwide depend on livestock production. As livestock numbers increase due to the growth in the world population, so does the need for modelling and understanding the patterns in the movement of livestock, which is crucial for understanding global epidemic patterns. Interestingly, the structure of livestock movement is quite similar to other movements, such as human mobility, if we model the phenomena as cases of origin-destination (O-D) flows. Here, we introduce a methodology to better understand the dynamics of mobility patterns by characterising them as these flows while accounting for spatial information. Our approach looks into flows of movements as something that can be derived from networks. We demonstrate the power of our approach on cattle trading by examining a dataset from the Brazilian state of Minas Gerais, the country’s largest cattle production. Our proposal is general and fits to any case in which the network is build from an O-D matrix.