COMPLEX-Analytic Mathematical Modeling of Tumor–Immune Dynamics An AI-Enhanced Framework for Predictive Oncology and Disease Progression

Abstract

In this study, an integrated complex-analytic mathematical and AI framework was developed to examine the dynamics of tumor and immune cells and predict disease progression in a 600-observation, 24-variable oncology dataset. The data included tumor characteristics, immune-cell markers, inflammatory markers, molecular markers, derived tumor–immune indices, treatment response, and progression outcomes. A coupled nonlinear dynamical model was employed to describe tumor growth, immune-mediated killing, equilibrium conditions and stability behavior, and five machine-learning algorithms were tested for predicting tumor progression. 27.0% of cases had disease progression, with the results showing. Progression was correlated with increased PD-L1, Treg cells, Ki-67, and tumor volume and decreased CD8+ T cells, NK cells, and immune balance. In the mathematical analysis a locally asymptotically stable coexistence equilibrium was found, suggesting that the immune activity is sufficient to limit the growth of the tumor. In the predictive models, Gradient Boosting performed best in terms of accuracy (90.8%) and specificity (97.7%) and had the best cross-validated ROC-AUC, whereas Random Forest had the best cross-validated ROC-AUC. Treg cells, tumor volume, LDH, PD-L1, Ki-67, and CD8+ T cells were identified as top predictors of progression using SHAP analysis. Overall, it illustrates the added value of mechanistic modelling and explainable AI to predictive oncology and the need to validate the framework with real-world longitudinal clinical datasets.