Modeling Interactions Between Various Cell Populations in a Cancerous System

We create two models based on systems of ordinary differential equations (ODEs) to study how normal, benign, metastatic, and immune cell populations evolve in a patient with cancer. The first, one-patch, model is used to simulate the cell populations in a single fixed area. Using stability analysis for this model, we determine a healthy equilibrium point with no tumor cells and derive necessary and sufficient conditions for stability. This model is also used to show the effects of immunotherapy on a cancerous system. To capture the effects of metastatic cancer, a two-patch model is introduced. It looks at the cell populations in two different areas of the body. A healthy equilibrium is also found for this model and sufficient conditions for stability are provided.