Romina Travaglini
CMAT
ANAP group seminar
The study of systems involving a huge number of interacting agents (as particles, cells or individuals) can be described, at mesoscopic level, by means of kinetic equations. We show how, assuming that the all the possible interactions occur at different time scales, it is possible perform a hydrodynamic limit, obtaining macroscopic reaction-diffusion equations for the number densities of the constituents. This procedure can be applied to the study of autoimmune diseases, for which interactions among self-antigen presenting cells, self-reactive T cells and immunosuppressive cells have been described by means of systems of integro-differential equations. We extend these models considering the motion of T-cells due to chemotaxis, stimulated by cytokines. Moreover, we adapt them to the scenario of Multiple Sclerosis, implementing the degradation of myelin performed by T-cells, resulting in the appearance of demyelinated plaques. We finally inquire about the formation or such lesions performing a Turing instability analysis of the problem and basing the discussion on microscopic parameters of the model.