Optimizing spatial accessibility and equity of hierarchical older adult care facilities using a multi-modal two-step floating catchment area method: a case study of Lin'an District, Hangzhou

The global aging trend is becoming increasingly pronounced, and the accessibility and equity of older adult care facilities directly influence the health and quality of life of the older adult population, thus representing a critical issue in public health research and policy-making. Using Lin'an District, Hangzhou as an illustrative case, this research examines urban-rural integrated areas specifically, addressing the persistent challenge of supply-demand mismatches in older adult care facility allocation and seeking to optimize their spatial configuration. A comprehensive analytical framework based on the multi-modal two-step floating catchment area (2SFCA) method was established, integrating the Gini coefficient, Lorenz curve, and local spatial autocorrelation analysis to systematically evaluate the spatial accessibility and equity of older adult care facilities. The results demonstrate significant spatial heterogeneity in facility accessibility, revealing a clear distribution pattern characterized by higher accessibility in the eastern urban core and markedly lower accessibility in western rural regions, thereby highlighting notable supply-demand imbalances between urban and rural contexts. Furthermore, the application of local spatial autocorrelation effectively identified key regions characterized by pronounced inequities, notably rural areas in the west suffering severe resource deficiencies and transitional urban-rural zones where supply-demand conflicts prominently occur. The study further investigates critical factors underlying accessibility and equity disparities, including differences in transportation infrastructure, uneven older adult population distributions, and hierarchical classifications of service facilities. Ultimately, the findings provide valuable empirical insights and policy recommendations applicable to urban-rural integration contexts globally, contributing meaningfully to the advancement of age-friendly societies.