Methods and tools of mathematical kinetic theory towards modelling complex biological systems

Abstract

Methods of mathematical kinetic theory have been recently developed to describe the collective behavior of large populations of interacting individuals such that their microscopic state is identified not only by a mechanical variable (typically position and velocity), but also by a biological state (or sociobiological state) related to their organized, somehow intelligent, behavior. The interest in this type of mathematical approach is documented in the collection of surveys edited in [1], in the review papers [2], [3], and in the book [4].