Modeling and Forecasting Long-Term Memory Dynamics in Diabetes Outpatient Attendance: Case Studies from Sudan

Diabetes mellitus represents an increasing public health problem in Sudan, notably in remote areas as observed in Blue Nile State with an unsatisfactory attendance to outpatient services that affects the quality of care and health planning. The objective of this study was to model and predict monthly diabetes outpatient attendance using the long-memory time series methodology, for better prediction and estimation of resource allocation. Monthly attendance data from January 2015 to December 2024 (n = 120) were obtained from the Blue Nile State Ministry of Health. After data cleaning and diagnostic testing, ARFIMA models were estimated via maximum likelihood. Competing short-memory models (ARIMA and SARIMA) were also developed for comparison. Model selection was based on information criteria and out-of-sample forecasting accuracy. The best-fitting ARFIMA (1, 0.32, 1) model estimated a statistically significant fractional differencing parameter (d = 0.32, p < 0.001), indicating the long-memory nature of outpatient demand. For 2023–2024, ARFIMA was superior to ARIMA and SARIMA in out-of-sample forecasts with RMSE = 31.7, MAE = 25.8, and MAPE = 7.3%. Our findings show that by incorporating persistence, there is a significant gain in the predictive ability for chronic disease care. Forecast reliability for outpatient diabetes demand. These results suggest that ARFIMA-based methods could be incorporated into health planning processes in order to minimize staffing shortages and supply stockouts while facing uncertain population needs. Seasonal fraction models incorporating exogenous factors may be evaluated for improvement.