Title: Global dynamics of a cancer stem cell treatment model

Authors: K. Abernathy; Z. Abernathy; R. Dougherty-Bliss; C. Mayer; H. Whiteside

Addresses: Winthrop University, 701 Oakland Ave, Rock Hill, SC 29733, USA ' Winthrop University, 701 Oakland Ave, Rock Hill, SC 29733, USA ' Winthrop University, 701 Oakland Ave, Rock Hill, SC 29733, USA ' Winthrop University, 701 Oakland Ave, Rock Hill, SC 29733, USA ' Winthrop University, 701 Oakland Ave, Rock Hill, SC 29733, USA

Abstract: We provide global stability arguments for a cancer treatment model with chemotherapy and radiotherapy that accounts for the cancer stem cell hypothesis. Employing the method of localisation of compact invariant sets, we resolve the global dynamics of the no-treatment, constant radiation, and combination chemotherapy and radiotherapy cases. In our analysis of the combination treatment model, we show that the presence of a chemotherapy agent lowers the required radiation strength for a globally stable cure state.

Keywords: cancer stem cells; global stability; cancer treatment; localisation of compact invariant sets.

DOI: 10.1504/IJDSDE.2019.100566

International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.2, pp.176 - 186

Received: 12 Apr 2017
Accepted: 15 Dec 2017

Published online: 27 Jun 2019 *

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