Predicting the number of care beds for older people by a novel grey Verhulst cosine self-memory model: two case studies of Jiangsu and Shanghai, China

Accurate prediction of care resource demands for older people is critical for the Chinese government in policy formulation and resource optimization. To enhance prediction accuracy, this study proposes a grey Verhulst cosine self-memory model (GVC-SM), designed to forecast future trends in care resource demand for older people with greater precision. The GVC-SM model integrates the grey Verhulst cosine model with the self-memory principle of dynamic system. The cosine component effectively captures short-term cyclical fluctuations in the data, reflecting shifts in care resource demands for older people. The self-memory equation addresses the limitations of traditional dynamic equations, which rely on a single initial condition, by leveraging multi-time historical data. This enhances the model's robustness and predictive accuracy. The model is well-suited for time series exhibiting short-term fluctuations within S-type saturation growth processes. In this study, data on care beds for older people from China, Jiangsu, and Shanghai were used for modeling and analysis. The GVC-SM model was compared with classical grey prediction models, statistical methods (quadratic exponential smoothing), and machine learning techniques (neural networks). The accuracy of the models was assessed using the Mean Absolute Percentage Error (MAPE) indicator. The GVC-SM model outperformed traditional grey, statistical, and machine learning models in terms of fitting and multi-step rolling predictions. It more accurately captured both the long-term growth trend and short-term fluctuations in care beds demand for older people, with significantly lower prediction errors than other methods, demonstrating superior forecasting capability. The results indicate that the GVC-SM model provides more accurate predictions for the future development of care resources for older people in China. The GVC-SM model combines cosine term and self-memory mechanism, significantly improves the processing ability of short-term fluctuations and random changes, enhances the memory and utilization efficiency of historical data, and thus improves the prediction accuracy of care resources for older people. This model provides a scientific basis for the government to deal with aging, and can better guide the planning and allocation of care resources for older people, improve the quality of care services for older people, and help China's aging strategy.