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Global Dynamics of a Breast Cancer Competition Model

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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.

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Authors and Affiliations

  1. Winthrop University, 701 Oakland Ave, Rock Hill, SC, 29733, USA

    Kristen Abernathy & Zachary Abernathy

  2. Rollins College, 1000 Holt Ave, Winter Park, FL, 32789, USA

    Arden Baxter

  3. Drake University, 2507 University Ave, Des Moines, IA, 50311, USA

    Meghan Stevens

Authors
  1. Kristen Abernathy
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  2. Zachary Abernathy
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  3. Arden Baxter
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  4. Meghan Stevens
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Corresponding author

Correspondence to Zachary Abernathy.

Additional information

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1358534. Additionally, this project is supported by an Institutional Development Award (IDeA) from the National Institute of General Medical Sciences (2 P20 GM103499 15) from the National Institutes of Health. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or the National Institutes of Health.

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Abernathy, K., Abernathy, Z., Baxter, A. et al. Global Dynamics of a Breast Cancer Competition Model. Differ Equ Dyn Syst 28, 791–805 (2020). https://doi.org/10.1007/s12591-017-0346-x

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