title: Global dynamics of a colorectal cancer treatment model with cancer stem cells.
abstract: 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 CD8+T cells, natural killer cells, and interleukin proteins on tumor cells and CSCs under the influence of treatment are also illustrated. Using the method of localization of compact invariant sets, we present conditions on treatment parameters to guarantee a globally attracting tumor clearance state. Numerical simulations using estimated parameters from the literature are included to showcase various global dynamics of the model.
authors.affiliation: Winthrop University, Bancroft Hall, Rock Hill, SC 29733, United States.
authors.forename: Kristen
authors.initials: K
authors.lastname: Abernathy
authors.affiliation: Winthrop University, Bancroft Hall, Rock Hill, SC 29733, United States.
authors.forename: Zachary
authors.initials: Z
authors.lastname: Abernathy
authors.affiliation: High Point University, United States.
authors.forename: Kelsey
authors.initials: K
authors.lastname: Brown
authors.affiliation: Sewanee: The University of the South, United States.
authors.forename: Claire
authors.initials: C
authors.lastname: Burgess
authors.affiliation: Saint Mary's College, United States.
authors.forename: Rebecca
authors.initials: R
authors.lastname: Hoehne
keywords: Applied mathematics; Mathematical biosciences