Speakers
Description
We present the derivation of a class of reaction-diffusion models for Multiple Sclerosis starting from kinetic equations for the distribution functions of the cell populations involved in the biological processes underlying the evolution of the disease. The kinetic setting for the cell distributions is outlined, detailing interaction operators that account for conservative and non-conservative processes. Under suitable hypotheses of multiple scale processes, an asymptotic diffusive limit of kinetic equations is performed, leading to a system of reaction-diffusion equations for population densities, with general diffusivity and growth functions for some kinds of cells. The Turing instability analysis of such macroscopic system provides necessary conditions for the emergence of spatial patterns in a two-dimensional domain; the shape and stability of such patterns are discussed through a weakly nonlinear analysis, and some numerical simulations are presented in order to confirm theoretical results.
