NEURAL FRACTIONAL DIFFERENTIAL EQUATIONS FOR CLIMATE-DRIVEN DISEASE PREDICTION IN PAKISTAN

Abstract

Climate-driven infectious diseases present a growing public-health challenge in Pakistan due to changing temperature, precipitation, humidity, and associated environmental conditions. This study developed a Neural Fractional Differential Equation (NFDE) framework for predicting climate-sensitive disease dynamics by integrating climatic variables, epidemiological observations, temporal memory, and neural-network learning. A quantitative longitudinal predictive design was employed using an illustrative dataset of 2,400 location-month observations. The proposed NFDE model was evaluated against conventional regression, Random Forest, Long Short-Term Memory, and integer-order differential-equation models using mean absolute error, root mean square error, mean absolute percentage error, and coefficient of determination. The illustrative findings indicated that temperature, rainfall, humidity, and previous disease incidence were significant predictors, while lagged rainfall demonstrated an important delayed association with disease incidence. The NFDE model achieved an illustrative RMSE of 13.68 and R² of .92, outperforming the comparative models. The findings suggest that combining fractional temporal memory with neural nonlinear learning may improve climate-informed disease prediction and provide a methodological basis for early-warning systems in Pakistan.