Hydrodynamic limit of a stochastic model of proliferating cells with chemotaxis

Abstract

A hybrid stochastic individual-based model of proliferating cells with chemotaxis is presented. The model is expressed by a branching diffusion process coupled to a partial differential equation describing concentration of a chemotactic factor. It is shown that in the hydrodynamic limit when number of cells goes to infinity the model converges to the solution of nonconservative Patlak-Keller-Segel-type system. A nonlinear mean-field stochastic model is defined and it is proven that the movement of descendants of a single cell in the individual model converges to this mean-field process.