Ana Jacinta Soares
CMAT, Universidade do Minho
Biological systems are usually described at the macroscopic level, by considering the relevant interacting populations that are involved in the system. However, it is well known that a detailed description at the cellular level could be more appropriate in understanding the complex dynamics of many diseases. In particular, the kinetic theory offers a very rich approach, since it is able to describe not only the cellular dynamics and the biological expression of cells but also the global behaviour of the populations by averaging the unknown variables of the kinetic system and passing to the corresponding hydrodynamic limit. In this talk, we present a mathematical model based on a kinetic theory approach for describing the behaviour of autoimmune diseases. We study the mathematical properties of the model and show some numerical results illustrating typical patterns of some autoimmune diseases.
[Work in collaboration with R. Della Marca, M.P. Ramos, C. Ribeiro]