Mathematical Modeling of Tumor Growth Dynamics and Chemotherapeutic Response

Abstract

This paper presents a mathematical framework to model tumor growth and its response to chemotherapy within a stabilized vascular environment. The model incorporates interactions between cancerous cells, healthy cells, and chemotherapy agents through a system of differential equations, integrating logistic growth, competitive dynamics, and Holling type II drug-elimination functions. Key properties of the system such as invariance, dissipativity, and equilibrium stability, are analyzed, with a focus on identifying threshold conditions for successful treatment. The model predicts three biologically relevant equilibrium states: cured, cancerous, and coexistence, depending on the chemotherapy infusion rate and drug efficacy. Numerical simulations and bifurcation diagrams illustrate how varying these parameters influence treatment outcomes. A Lyapunov function is employed to confirm the global stability of the cured state, providing strong theoretical support for the effectiveness of continuous chemotherapy under optimal conditions. This work offers valuable insights into optimizing chemotherapy protocols and serves as a foundation for future extensions incorporating tumor resistance, immune response, or spatial factors.