Mathematical modelling of autoimmunity

Maria Piedade Ramos

November 26, 2019

A mathematical model describing the microscopic interactions between cells that are involved in autoimmunity was recently developed (Ramos, M.P.M., Ribeiro, C. & Soares, A.J., “A kinetic model of T cell autoreactivity in autoimmune diseases”, J. Math. Biol. (2019)), using a kinetic theory approach. In this model three different cell populations were considered, namely self-antigen presenting cells, self-reactive T cells and the set of immunosuppressive cells consisting of regulatory T cells and Natural Killer cells. The cells of the interacting populations are characterized by a microscopic functional state or activity variable which defines the specific biological function of each cell. The equations of the model then constitute a nonlinear system of integro-differential type that describes the evolution of the distribution functions associated to the cell populations. In this talk we will explain the mathematical and biological basis of our model, present ongoing work involving both the extension of our model to include an artificial inlet representing an external drug therapy and the investigation of optimal treatment strategies using optimal control theory. Furthermore, we will discuss future work in the context of mathematical modeling of autoimmunity.