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 population...

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Published inDifferential equations and dynamical systems Vol. 28; no. 4; pp. 791 - 805
Main Authors Abernathy, Kristen, Abernathy, Zachary, Baxter, Arden, Stevens, Meghan
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.10.2020
Springer Nature B.V
Subjects
Breast cancer
Cancer
Computer Science
Differential equations
Dynamics
Engineering
Estrogens
Immune system
Mathematics
Mathematics and Statistics
Ordinary differential equations
Original Research
Stem cells
Ordinary differential equations
Breast cancer
Tumor-immune dynamics
Global dynamics
Estrogen
Online AccessGet full text
ISSN0971-3514
0974-6870
DOI10.1007/s12591-017-0346-x

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Summary: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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ISSN:0971-3514
0974-6870
DOI:10.1007/s12591-017-0346-x