This paper presents a mathematical model of breast cancer composed of six compartments: one representing tumor cells, two representing cytokine populations, and three representing immune cell types. The proposed framework is original in that it integrates cytokine-mediated (IL-2 and IFN-) feedback loops, immune effector dynamics, and chemotherapeutic drug kinetics within a unified six-compartment structure. This coupling of tumor-immune-drug interactions, calibrated specifically for breast cancer, distinguishes the model from existing mathematical tumor-immune systems. To maintain simplicity and avoid unnecessary complexity, the study initially considers the interaction between tumor cells and the two cytokine groups. The results show that cytokines alone are insufficient to eliminate tumor cells. The analysis then extends to the interaction between tumor cells and the three immune cell types. Graphical simulations demonstrate that tumor cells can still evade immune cell responses. A dynamical analysis is conducted, proving the uniqueness and nonnegativity of the model solutions and identifying two types of equilibrium points. The existence conditions for each equilibrium are discussed. A transcritical bifurcation analysis (TBA) indicates that the tumor-free equilibrium loses stability at a critical tumor growth rate of 0.25 per day, beyond which a stable positive tumor state emerges. Comparison with clinical tumor growth data shows that the model accurately captures tumor dynamics, achieving a goodness-of-fit of 98.46 percent using nonlinear least squares (NLS) fitting. The full model, which incorporates immune cells, tumor cells, and a chemotherapeutic agent, is then presented. Mathematical techniques are applied to reduce the system, and the Adomian Decomposition Method (ADM) is used for analysis. The convergence of ADM in the context of the model is established and proved. Graphical results indicate that tumor cells can be eliminated under this treatment strategy. Phase-plane (PP) and vector field (VF) analyses reveal oscillatory immune responses and regulatory feedback among immune cells, while surface plots highlight the sensitivity of tumor suppression to key parameters. The findings suggest that effective treatment requires both reducing tumor proliferation and enhancing immune-mediated lysis. A sensitivity analysis (SA) identifies the most influential parameters in tumor control.
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