Stochastic-Deterministic Modeling of Immune Responses and Tumor Evolution Under Therapeutic Influence: Intelligent Predictive Supervised Exogenous Networks

The incredible synergy between monoclonal anti- bodies and interferons in cancer chemotherapy signifies a stride forward in our battle against this inexorable disease. Through meticulous mathematical modeling that delineate the interplay between tumor growth and immune response, this helps in the development of immunomodulatory treatments and aids in counteracting the cost of drug discovery while minimizing the resource-intensive experimental iterations. This study develops a precise and reliable application of numerical as well as artificial intelligence-based treatment methodology via predictive super- vised eXegenious networks for calculable understanding of the movement of the immune response to treatment such as timing, dosing and forecasting therapy retorts to a specific dose. The out- comes of this work underscore the potency of these methodologies in clarifying the pivotal determinants essential to the dynamic of tumor-immune interactions, therapeutic efficacy and the for- mulation of rationalized therapeutic interventions. In the pursuit of unraveling the complexities inherent to the interactions within the tumor-immune-chemotherapy model, this study harnesses the predictive power of nonlinear autoregressive exogenous (NARX) networks, synergistically coalesced with stochastic-deterministic differential modeling, to unfold the hidden intricacies that hold significant potential within this intricate process. Reference data for training, testing and validation of the proposed methodology was generated using Adams numerical method by utilizing baseline parameters derived through experimental data. Error analysis was conducted to verify the authenticity and perfor- mance of the designed framework for different scenarios. The framework demonstrates impressive performance and accuracy, achieving a mean square error between $10^{-11}$ and $10^{-8}$ through iterative refinement.