Game Theoretical Model of Cancer Dynamics with Four Cell Phenotypes

Elena Hurlbut, Ethan Ortega, Igor V. Erovenko and Jonathan T. Rowell
Additional contact information
Elena Hurlbut: Department of Mathematics and Statistics, Wake Forest University, Winston-Salem, NC 27109, USA
Ethan Ortega: Department of Mathematics and Computer Science, Western Carolina University, Cullowhee, NC 28723, USA
Igor V. Erovenko: Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402, USA
Jonathan T. Rowell: Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402, USA

Games, 2018, vol. 9, issue 3, 1-16

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.

Keywords: evolutionary game theory; cancer; replicator dynamics; spatial dynamics; heterogeneous populations; biomathematical modeling (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2073-4336/9/3/61/pdf (application/pdf)
https://www.mdpi.com/2073-4336/9/3/61/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jgames:v:9:y:2018:i:3:p:61-:d:167307

Access Statistics for this article

Games is currently edited by Ms. Susie Huang

More articles in Games from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().