Modeling Cancer Growth and Treatment
摘要
Cancer can be viewed as an interaction among tumor cells, immune cells, and therapeutic agents. Because the immune response plays a major role in controlling tumor growth, our models include it from the start. We begin by developing a set of Base Tumor–Immune Models that describe how tumor and effector immune cells influence one another. Surgery, radiotherapy, and chemotherapy are added through impulsive or time-dependent forcing terms, and MATLAB simulations are used to see how post-treatment immune strength affects long-term outcomes. The chapter then turns to a melanoma case study. We start with a seven-equation tumor–immune system and apply a quasi–steady-state approximation to obtain a reduced four-equation model that is easier to analyze. We study the equilibria and stability of this reduced system and use simulations to illustrate tumor-free and tumor-persistent behavior. Finally, we relate each model component to the Hallmarks of Cancer to show how biological mechanisms appear in the equations.