Global Dynamics of a Breast Cancer Competition Model.

In this paper, we present a system of five ordinary differential equations which consider population dynamics among cancer stem cells, tumor cells, and healthy cells. Additionally, we consider the effects of excess estrogen and the body's natural immune response on the aforementioned cell populations. Employing a variety of analytical methods, we study the global dynamics of the full system, along with various submodels.

Global dynamics of a colorectal cancer treatment model with cancer stem cells.

We present and analyze a mathematical model of the treatment of colorectal cancer using a system of nonlinear ordinary differential equations. The model describes the effectiveness of immunotherapy and chemotherapy for treatment of tumor cells and cancer stem cells (CSCs). The effects of CD8T cells, natural killer cells, and interleukin proteins on tumor cells and CSCs under the influence of treatment are also illustrated.