Modeling the antigen recognition by B-cell and T-cell receptors through thermostatted kinetic theory methods

The activation and the resulting response of the immune system to antigens comprise different complex processes and cells. This paper aims at modeling the processes of recognition and learning of the immune system by means of the thermostatted kinetic theory methods. Specifically, the thermostatted kinetic framework is firstly generalized for taking into account that in some processes of proliferation of the cells, the rate is also function of the degree of information exchanged amongst cells. In particular, within the new framework, a mathematical model is proposed for miming the recognition process of the immune system through the definition of interactions between the cytotoxic and humoral components of the adaptive immune system via T- and B-cells. The model validation is obtained by performing a sensitivity analysis on the parameters which depicts the main emerging phenomena and the different phases of the recognition and learning of the immune system.