Traveling wave solutions for a cancer stem cell invasion model

Caleb Mayer; Eric Stachura

doi:10.3934/dcdsb.2020333

Article Contents

2021, Volume 26, Issue 9: 5067-5093. Doi: 10.3934/dcdsb.2020333

This issue Previous Article Stochastic modelling and analysis of harvesting model: Application to "summer fishing moratorium" by intermittent control Next Article Global boundedness of classical solutions to a logistic chemotaxis system with singular sensitivity

Traveling wave solutions for a cancer stem cell invasion model

Caleb Mayer^1, and
Eric Stachura^2, ,

1.
University of Michigan, 540 Thompson Street, Ann Arbor, MI 48104, USA
2.
Department of Mathematics, Kennesaw State University, 850 Polytechnic Lane, Marietta, GA 30060, USA

^*Corresponding author: E. Stachura
^*Corresponding author: E. Stachura

Received: November 30, 2019

Revised: August 31, 2020

Early access: November 2020

Published: September 2021

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Abstract

In this paper we analyze the dynamics of a cancer invasion model that incorporates the cancer stem cell hypothesis. In particular, we develop a model that includes a cancer stem cell subpopulation of tumor cells. Traveling wave analysis and Geometric Singular Perturbation Theory are used in order to determine existence and persistence of solutions for the model.

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Mathematics Subject Classification: Primary: 34C37, 34E17; Secondary: 35C07.

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Figure 1. Profile of traveling wave solution at $ t = 50 $. The qualitative behavior is similar to the results presented in [7] and [22] for only one invasive cell population, the latter reference taking $ \epsilon = 0 $ in their analysis

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Figure 2. Solution profile of (49)-(51) with wavespeed $ c = 1.5 $, $ u^* = 1 $, and $ w^* = 0.6 $

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