Related Experiment Video
Updated: Nov 20, 2025

Quantification of Breast Cancer Cell Invasiveness Using a Three-dimensional 3D Model
Published on: June 11, 2014
Global Dynamics of a Breast Cancer Competition Model
Kristen Abernathy1, Zachary Abernathy1, Arden Baxter2
1Winthrop University, 701 Oakland Ave, Rock Hill, SC 29733.
Abstract:
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. We find sufficient conditions on parameter values to ensure cancer persistence in the absence of immune cells, and cancer eradication when an immune response is included. We conclude with a discussion on the biological implications of the resulting global dynamics.
Related Concept Videos
Tumor Progression
Colon cancer is one of the best-documented examples of tumor progression. Early mutation in the APC gene in colon cells causes a small growth on the colon wall called a polyp. With time, this polyp grows into a benign, pre-cancerous tumor. Further...
Cancer Survival Analysis
The Tumor Microenvironment
Mouse Models of Cancer Study
The development of transgenic, knockout, and knock-in mice has led to an exponential increase in their use as model organisms in research,...
Adaptive Mechanisms in Cancer Cells
Some of the advantages that cancer cells have on normal cells include - enhanced ability to divide without terminally differentiating, induce new blood vessel formation,...
Cancer

