Vol. 11, No. 3, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-4184 (online)
ISSN 1944-4176 (print)
 
Author index
To appear
 
Other MSP journals
A mathematical model of treatment of cancer stem cells with immunotherapy

Zachary J. Abernathy and Gabrielle Epelle

Vol. 11 (2018), No. 3, 361–382
Abstract

Using the work of Shelby Wilson and Doron Levy (2012), we develop a mathematical model to study the growth and responsiveness of cancerous tumors to various immunotherapy treatments. We use numerical simulations and stability analysis to predict long-term behavior of passive and aggressive tumors with a range of antigenicities. For high antigenicity aggressive tumors, we show that remission is only achieved after combination treatment with TGF-β inhibitors and a peptide vaccine. Additionally, we show that combination treatment has limited effectiveness on low antigenicity aggressive tumors and that using TGF-β inhibition or vaccine treatment alone proves generally ineffective for all tumor types considered. A key feature of our model is the identification of separate cancer stem cell and tumor cell populations. Our model predicts that even with combination treatment, failure to completely eliminate the cancer stem cell population leads to cancer recurrence.

Keywords
cancer stem cells, immunotherapy, recurrence, ordinary differential equations, stability
Mathematical Subject Classification 2010
Primary: 34D05, 34D20, 92B05, 92C37
Milestones
Received: 2 September 2014
Revised: 21 April 2016
Accepted: 27 June 2017
Published: 20 October 2017

Communicated by Kenneth S. Berenhaut
Authors
Zachary J. Abernathy
Department of Mathematics
Winthrop University
Rock Hill, SC
United States
Gabrielle Epelle
Department of Mathematics
Winthrop University
Rock Hill, SC
United States