Propagation of Chaos in the Nonlocal Adhesion Models for Two Cancer Cell Phenotypes

We establish a quantitative propagation of chaos for a large stochastic systems of interacting particles. We rigorously derive a mean-field system, which is a diffusive cell-to-cell nonlocal adhesion model for two different phenotypes of tumors, from that stochastic system as the number of particles tends to infinity. We estimate the error between the solutions to a N-particle Liouville equation associated with the particle system and the limiting mean-field system by employing the relative entropy argument.