Event Title

A Nonlinear Model of Cancer Tumor Treatment with Cancer Stem Cells

Faculty Mentor

Kristen Abernathy, Ph.D.

College

College of Arts and Sciences

Department

Mathematics

Location

DiGiorgio Campus Center, Room 220

Start Date

24-4-2015 4:05 PM

Description

According to the American Cancer Society, cancer is one of the leading causes of death, second only to heart disease. We present a system of nonlinear, first-order, ordinary differential equations that describes tumor growth based on healthy cell, tumor cell, and cancer stem cell populations. We include terms within our model which reflect the differing effects of chemotherapy and anti-angiogenic therapy to respective cell populations. We perform stability analysis on the equilibrium solutions to predict the long-term behavior of the cell populations. With analysis, it is shown that chemotherapy, with the co-administration of anti-angiogenic treatment, can produce three states: recurrence or persistence of cancer, and a cure state. Results are supported analytically and numerically. Bifurcation diagrams are included to illustrate the different behavior of cell populations depending on the amount of treatment administered.

Comments

Presented at the Mathematical Association of America (MAA) MathFest, August 2014, and the MAA Joint Mathematics Meetings, January 2015

Supported by a grant from the National Science Foundation

Winner, Janet L. Andersen Award for Undergraduate Research in Mathematical or Computational Biology, MathFest, August 2014

This document is currently not available here.

Share

COinS
 
Apr 24th, 4:05 PM

A Nonlinear Model of Cancer Tumor Treatment with Cancer Stem Cells

DiGiorgio Campus Center, Room 220

According to the American Cancer Society, cancer is one of the leading causes of death, second only to heart disease. We present a system of nonlinear, first-order, ordinary differential equations that describes tumor growth based on healthy cell, tumor cell, and cancer stem cell populations. We include terms within our model which reflect the differing effects of chemotherapy and anti-angiogenic therapy to respective cell populations. We perform stability analysis on the equilibrium solutions to predict the long-term behavior of the cell populations. With analysis, it is shown that chemotherapy, with the co-administration of anti-angiogenic treatment, can produce three states: recurrence or persistence of cancer, and a cure state. Results are supported analytically and numerically. Bifurcation diagrams are included to illustrate the different behavior of cell populations depending on the amount of treatment administered.