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Games 2018, 9(3), 61; https://doi.org/10.3390/g9030061

Game Theoretical Model of Cancer Dynamics with Four Cell Phenotypes

1
Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, NC 27109, USA
2
Department of Mathematics and Computer Science, Western Carolina University, Cullowhee, NC 28723, USA
3
Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 30 June 2018 / Revised: 25 August 2018 / Accepted: 29 August 2018 / Published: 2 September 2018
(This article belongs to the Special Issue Mathematical Biology and Game Theory)
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Abstract

The development of a cancerous tumor requires affected cells to collectively display an assortment of characteristic behaviors that contribute differently to its growth. A heterogeneous population of tumor cells is far more resistant to treatment than a homogeneous one as different cell types respond dissimilarly to treatments; yet, these cell types are also in competition with one another. This paper models heterogeneous cancer cell interactions within the tumor mass through several game theoretic approaches including classical normal form games, replicator dynamics, and spatial games. Our concept model community consists of four cell strategies: an angiogenesis-factor-producing cell, a proliferative cell, a cytotoxin producing cell, and a neutral stromal cell. By comparing pairwise strategic interactions, invasibility and counter-invasibility, we establish conditions for dominance and the existence of both monomorphic and polymorphic equilibria. The spatial game supports co-occurrence among multiple subpopulations in accordance with biological observations of developing tumors. As the tumor progresses from primarily stromal cells to a more malignant state, angiogenic and cytotoxic cells form clusters while proliferative cells are widespread. The clustering of certain subpopulations suggests insight into the behaviors of cancer cells that could influence future treatment strategies. View Full-Text
Keywords: evolutionary game theory; cancer; replicator dynamics; spatial dynamics; heterogeneous populations; biomathematical modeling evolutionary game theory; cancer; replicator dynamics; spatial dynamics; heterogeneous populations; biomathematical modeling
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Hurlbut, E.; Ortega, E.; Erovenko, I.V.; Rowell, J.T. Game Theoretical Model of Cancer Dynamics with Four Cell Phenotypes. Games 2018, 9, 61.

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