Multistep navigation of leukocytes: a stochastic model with memory effects.

We present a model for the chemotactically directed migration of neutrophil leukocytes. It reproduces the multistep navigation by memory effects investigated experimentally by E. F. Foxman, J. J. Campbell and E. C. Butcher in 1997. The model consists of a system of stochastic differential equations. The long time behaviour of the corresponding deterministic system is analysed and two approaches for the numerical solution of the full stochastic system are compared. One of them consists in performing direct simulations, the other one is based on a moment approximation of the Fokker-Planck equation and numerical methods for convection-dominated partial differential equations.