Authors

Modified gravity model for assessing healthcare accessibility: problem statement, algorithm, and implementation

Territorial inequality in access to healthcare remains a pressing issue for the healthcare system of the Russian Federation. Significant disparities in transport accessibility, staffing levels, and the spatial distribution of medical facilities complicate evidence-based decision-making, especially in regions with uneven population density and fragmented infrastructure. This creates the need for formalized and reproducible approaches to assessing healthcare accessibility that are adapted to regional specificities and suitable for digital implementation. The aim of this study is to develop a methodology for assessing the potential accessibility of medical facilities, based on a modified gravity model and implemented as an algorithm that accounts for travel time, facility capacity, and overlapping service areas. Unlike traditional models such as 2SFCA and classical gravity models, the proposed approach allows for parameter calibration based on empirical data and incorporates territorial competition for healthcare resources. The methodological foundation includes an exponential distance-decay function and dual normalization by total service supply. The novelty of the methodology lies in the integration of these components into a unified, computable index of potential spatial accessibility suitable for scalable digital implementation. The algorithm was developed in the R programming environment using the OSRM routing engine to calculate travel times over the road network. The model was tested using data from the municipalities of Sverdlovsk oblast. The results (R² = 0.252, mean absolute percentage error MAPE < 28%) confirmed the model’s interpretability and practical relevance. The proposed approach can be used for monitoring healthcare accessibility, identifying underserved areas, and informing spatial resource allocation. Moreover, the methodology can be adapted for other types of social infrastructure. Read more...