Involve: A Journal of Mathematics

  • Involve
  • Volume 11, Number 3 (2018), 361-382.

A mathematical model of treatment of cancer stem cells with immunotherapy

Zachary J. Abernathy and Gabrielle Epelle

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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.

Article information

Source
Involve, Volume 11, Number 3 (2018), 361-382.

Dates
Received: 2 September 2014
Revised: 21 April 2016
Accepted: 27 June 2017
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513775073

Digital Object Identifier
doi:10.2140/involve.2018.11.361

Mathematical Reviews number (MathSciNet)
MR3733964

Zentralblatt MATH identifier
1379.34046

Subjects
Primary: 34D05: Asymptotic properties 34D20: Stability 92B05: General biology and biomathematics 92C37: Cell biology

Keywords
cancer stem cells immunotherapy recurrence ordinary differential equations stability

Citation

Abernathy, Zachary J.; Epelle, Gabrielle. A mathematical model of treatment of cancer stem cells with immunotherapy. Involve 11 (2018), no. 3, 361--382. doi:10.2140/involve.2018.11.361. https://projecteuclid.org/euclid.involve/1513775073


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