Kinetic Modelling of Autoimmune Diseases

Abstract

In this paper, we review previous results obtained by the authors, concerning the mathematical modelling of autoimmune diseases when the kinetic theory approach is used in order to describe the microscopic interactions between cells. Three cell populations are considered and the distribution function of each population depends on the biological activity variable defining the functional state relevant for that population. We revisit the wellposedness of the kinetic system and focus our study on the numerical simulations with the kinetic system in view of investigating the sensitivity of the solution to certain parameters of the model with biological significance.