Objective Since the dawn of human civilization the battle against viruses has never ceased making the prediction of infectious disease data of significant reference value. This paper proposes a novel algorithm to address the limitations of the standard grey wolf algorithm which is prone to local optima and exhibits insufficient global search capability. Methods The wolf pack positions were initialized via the Halton sequence search algorithm to prevent the grey wolf algorithm from becoming trapped in local optima and redundant computations. The Lévy flight and random walk strategies were introduced to optimize the search process of the grey wolf algorithm thereby enhancing the algorithm?? s global exploration capability. The improved grey wolf algorithm was then utilized to optimize the parameters of six machine learning models for prediction. Constrained optimization techniques—specifically the sequential least squares programming SLSQP algorithm and grey wolf optimization GWO algorithm—were employed to determine the optimal ensemble weights for each model. Finally three evaluation functions were applied to score the predictive performance of both individual models and the hybrid model. Results The improved GWO algorithm demonstrated superior performance outperforming other benchmark algorithms in iterative tests. Among the machine learning models optimized by the improved GWO the optimized gradient boosting tree model achieved the best prediction performance. Compared with its unoptimized counterpart its accuracy improved by 52% 52% and 1% in terms of mean absolute error MAE root mean square error RMSE and coefficient of determination R 2 respectively. Conclusion The weighted ensemble model based on GWO-optimized machine learning models achieves outstanding scores yielding a further enhancement in predictive accuracy. The model?? s MAE RMSE and R 2 were 0. 07 0. 24 and 0. 99 respectively. This approach provides a valuable reference for forecasting the number of infectious disease cases.