On a mathematical model with a free boundary for the dynamics of the Tumor-Immune system interaction

Mathematical models of tumor growth are essential for accurately monitoring and predicting the spatiotemporal dynamics of tumor development. In this work, we present a mathematical model designed to describe the early stages of interaction between immune cells and tumor cells through a system of partial differential equations. The model is structured in terms of size and space, incorporating the migration of tumor antigen-specific cytotoxic effector cells toward the tumor microenvironment via a chemotactic mechanism.