  In this paper, we develop a new nonconservative kinetic framework to be
applied for the study of immune system dysregulation. From the modeling
viewpoint, the new kinetic model regards a system, composed of stochastically
interacting agents, under the action of an eternal force field. According to
the application perspectives of this paper, the external force field has a
specific analytical shape. In this case, some analytical results are proved,
i.e. existence, uniqueness, positivity and boundedness of solution of the
related Cauchy problem, under suitable assumptions, at least locally in time.
Then, the models is refined to be implemented for the study of treatment
strategies in case of autoimmune response. Specifically, we distinguish the
autonomous case from the nonautonomous one, representing absence or delivery of
drugs, respectively. The former allows to gain some stability results, still in
terms of Hopf bifurcations. Whereas, the latter is qualitatively studied.
Numerical simulations are provided for both schemes. They show the adherence of
this new framework to the realistic scenarios, confirming its impact and
potentiality.
