Spatial accessibility indices in the framework of point processes. An application to veterinarian shortage

In a wide range of scientific fields, studying accessibility indices is essential for understanding how easily people can reach spatially distributed activities or resources, including employment opportunities, services, education, and, in particular, healthcare. Within the One Health framework, the health of humans, animals, and their shared environment is interdependent, making ad-equate veterinary care essential for safeguarding public health. The decline in the availability of veterinary healthcare in France adversely affects the health of food-producing animals. With this particular application in mind, and more broadly for supply-to-demand indices, we first reformulate the classical 2SFCA index within the framework of spatial point process theory and propose a new version that addresses its shortcomings. This enables us to define a popula-tion version of the classical as well as the new 2SFCA indices and to construct confidence bands for assessing their variability. In the application, we com-pute accessibility-to-veterinarian indices, and assess whether the spatial con-figuration of clinics and farms complies with a threshold recommended by the authorities.