The Spatial Equilibrium Model of Elderly Care Facilities with High Spatiotemporal Sensitivity and Its Economic Associations Study

The global population aging poses new challenges in allocating care facilities for the elderly. This demographic trend also influences economic development and the quality of urban life. However, current research focuses on the supply of elderly care facilities and primarily uses administrative divisions as a scale, resulting in low spatiotemporal sensitivity in evaluating the spatial equilibrium of elderly care facilities (SEECF). The relationship between the SEECF and economic development is not clear. In response to these problems, we proposed a spatial equilibrium model of elderly care facilities with high spatiotemporal sensitivity (SEM-HSTS) and explored the spatiotemporal associations between the SEECF and economic development. Considering the spatial accessibility rate of elderly care services (SARecs) and the spatiotemporal supply–demand ratio for elderly care services (STSDRecs), two types of supply–demand relationship factors were constructed. Then, a spatiotemporal accessibility of medical services (STAms) factor was obtained based on a modified two-step floating catchment area (M2SFCA) method. On this basis, the SEM-HSTS was constructed based on the theory of coordinated development. Further, a panel threshold model was employed to evaluate the influence relationships among population aging, SEECF, and gross domestic product (GDP) in different phases. Finally, spatial autocorrelation and Geodetector explored the spatial associations between SEECF and GDP across complex urban land use categories (ULUC). The experimental results at a 100-m grid scale showed that the SEM-HSTS exhibited higher spatiotemporal heterogeneity than the classical accessibility method, with elevated spatiotemporal sensitivity. Effectively identified various spatial imbalances, such as undersupply and resource waste. The panel model captured phased relationship changes, showing that SEECF had inhibitory and promotional effects on GDP in pre- and post-aging societies, with stronger effects as balance approached. Moreover, the combined interaction of ULUC and GDP had a more significant influence on SEECF than any individual factor, with GDP exerting a more significant influence. This study provides an empirical basis for creating resource-efficient elderly care facility systems and optimizing layouts.