From the mathematical kinetic theory of active particles to multiscale modelling of complex biological systems

The mathematical approach proposed in this paper refers to the modelling of large systems of interacting entities whose microscopic state includes not only mechanical variables (typically position and velocity), but also specific activities of the single entity. Their number is sufficiently large to describe the overall state of the system by a suitable probability distribution over the microscopic state. The first part of the paper is devoted to the derivation of mathematical structures which can be properly used to model a variety of models in different fields of applied sciences. Then, some research perspectives are focused on applications to biological systems.