Predicting the demand of elderly care beds by a novel recursive grey Gompertz model: case studies of Jiangsu and Shanghai, China.

BACKGROUND: China is undergoing a rapid demographic transition, with a continuously expanding older adult population driving surging demand for elderly care services, particularly in institutional settings. However, the supply of care resources is marked by regional disparities and structural inefficiencies, failing to meet diverse elderly needs. Scientifically forecasting care resource demand and optimizing allocation are thus urgent priorities. Accurate prediction is crucial, yet often constrained by the limited data availability in this field. METHODS: The study developed a Recursive Grey Gompertz Model (RGGM) to address small-sample forecasting challenges by integrating grey system theory with the Gompertz growth curve. Using historical data on institutional care beds in China, Jiangsu Province, and Shanghai Municipality, the model was applied for fitting and trend projection. Its performance was compared against several established methods-Recursive Grey Model, Gompertz, GM(1,1), Exponential Smoothing, ARIMA, and MLP-using Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) as accuracy metrics. RESULTS: The comparative analysis demonstrated that the RGGM model achieved higher predictive accuracy and reliability than the other benchmark models. The forecast results for the number of elderly care beds using RGGM were associated with lower MAPE and RMSE values, confirming its superior suitability for this forecasting task. Subsequently, the validated RGGM model was used to project the development trend of elderly care beds in China, Jiangsu Province, and Shanghai for the coming years. CONCLUSIONS: The RGGM model introduces a memory factor into its objective function, which assigns a greater weight to newer observations. This mechanism ensures the priority of new information during the modeling process, enhancing the model's adaptability. Furthermore, the model's structural parameters are solved recursively with each new observation, allowing the parameters to inherit information from previous data points. This recursive approach effectively improves prediction accuracy. Accurately predicting the supply of and demand for elderly care resources can assist governments and policymakers in formulating rational elderly service plans, optimizing resource allocation, and ensuring the sustainable development of the elderly care system.