| Description |
One of the main obstacles to treating cancer is its ability to evolve and resist treatment. In this project, we are primarily interested mathematically modeling how the cancer microenvironment interacts with cancer cells and affects cancer's response to therapy. We aim to develop the mathematical model in the context of estrogen-receptor-positive (ER+) breast cancer, endocrine therapy, and cancer-associated fibroblasts (CAFs). The system is described with ordinary differential equations (ODEs) to investigate the impacts that cancer cells and CAFs have on each other's population dynamics. ODEs are a simple, yet powerful tool to model physical phenomena and can help us understand and study cancer. The proposed models explore two different proposed scenarios of Cancer-CAF dynamics. First, we consider the case when cancer cells can recruit CAFs from an endless supply of fibroblasts. We also consider the case when there is a constant total population of Fibroblasts, which can switch between healthy and cancer-associated. In each respective scenario, the stability of fixed points is analyzed to determine the impacts of endocrine treatment and CAFs on the long-term behavior of cancer. In both models, we find saddle points and bifurcations dependent on estrogen availability in the system. We hope that the model will be able to provide insight into how ER+ breast cancer develops resistance to endocrine therapy. |
