Game Theory Cancer Models of Cancer Cell-Stromal Cell Dynamics using Interacting Particle Systems

2020 ◽  
Vol 15 (03) ◽  
pp. 171-193
Author(s):  
Yinan Zheng ◽  
Yusha Sun ◽  
Gonzalo Torga ◽  
Kenneth Pienta ◽  
Robert Austin

We describe an evolutionary game theory model that has been used to predict the population dynamics of interacting cancer and stromal cells. We first consider the mean field case assuming homogeneous and nondiscrete populations. Interacting Particle Systems (IPS) are then presented as a discrete and spatial alternative to the mean field approach. Finally, we discuss cases where IPS gives results different from the mean field approach.

2020 ◽  
Vol 405 ◽  
pp. 109181 ◽  
Author(s):  
Martin Burger ◽  
René Pinnau ◽  
Claudia Totzeck ◽  
Oliver Tse ◽  
Andreas Roth

1997 ◽  
Vol 34 (2) ◽  
pp. 346-362 ◽  
Author(s):  
Shui Feng

A result for the propagation of chaos is obtained for a class of pure jump particle systems of two species with mean field interaction. This result leads to the corresponding result for particle systems with one species and the argument used is valid for particle systems with more than two species. The model is motivated by the study of the phenomenon of self-organization in biology, chemistry and physics, and the technical difficulty is the unboundedness of the jump rates.


1997 ◽  
Vol 34 (02) ◽  
pp. 346-362 ◽  
Author(s):  
Shui Feng

A result for the propagation of chaos is obtained for a class of pure jump particle systems of two species with mean field interaction. This result leads to the corresponding result for particle systems with one species and the argument used is valid for particle systems with more than two species. The model is motivated by the study of the phenomenon of self-organization in biology, chemistry and physics, and the technical difficulty is the unboundedness of the jump rates.


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