Mathematical Modeling And Artificial Intelligence For Predictive Analysis In Complex Biological And Computational Systems

Abstract

Complex biological and computational systems involve nonlinear interactions, dynamic feedback, uncertainty, and multiscale processes that make accurate prediction difficult using a single modeling approach. Mathematical models provide mechanistic interpretability, whereas artificial intelligence supports flexible prediction from complex data. This research develops a hybrid SEIR–AI framework for predictive analysis using COVID-19 transmission dynamics in India as a representative case study. Publicly available data from Our World in Data were used, with seven-day smoothed new cases selected as the primary prediction target. An SEIR compartmental model was fitted to represent susceptible, exposed, infectious, and recovered or removed population dynamics. A Random Forest model was then used for AI-only prediction and for residual correction in the hybrid model. The hybrid framework was evaluated against a naive baseline, SEIR-only model, and AI-only model using MAE, RMSE, MAPE, and . Results showed that the naive baseline performed best during the low-transmission testing period, but the hybrid SEIR–AI model improved RMSE and MAPE compared with the SEIR-only and AI-only models. The findings indicate that hybrid mathematical–AI modeling can improve mechanistic prediction while preserving biological interpretability, supporting its broader use in biomathematics, epidemiology, digital health, and complex biological forecasting.