Stochastic models of tumour development and related mesoscopic equations

We consider di erent mathematical models inspired by the
problems of medicine, in particular, the tumour growth and the related
topics. We demonstrate how to starting from an individual-based (microscopic)
description, which characterizes cells' behaviour, derive the socalled
kinetic (mesoscopic) equations, which describe the approximate system
density. Properties of the solutions to the mesoscopic equations (in
particular, their long-time behaviour) re
ect statistical characteristics of
the whole system and demonstrate the corresponding dependence on the
system parameters.