In this paper, we develop a nonconservative kinetic framework to be applied to the study of immune system dysregulation. From the modeling viewpoint, the 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, existence, uniqueness, positivity, and boundedness of solution of the related Cauchy problem, at least locally in time. Then, the model 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 the absence or delivery of drugs, respectively. The former allows us to gain some stability results. Whereas, the latter is qualitatively studied. Numerical simulations are provided for both schemes.

中文翻译：

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外力场作用下的非保守动力学模型用于模拟自身免疫反应的医学治疗


在本文中，我们开发了一个非保守动力学框架，应用于免疫系统失调的研究。从建模的角度来看，该模型认为是一个在永恒力场作用下由随机相互作用的主体组成的系统。根据本文的应用视角，外力场具有特定的解析形状。在这种情况下，一些分析结果被证明，相关柯西问题的解的存在性、唯一性、正性和有界性，至少在时间上是局部的。然后，对该模型进行完善，以用于研究自身免疫反应的治疗策略。具体来说，我们将自主案例与非自主案例区分开来，分别代表药物的缺失或输送。前者使我们能够获得一些稳定性结果。而后者是定性研究的。两种方案都提供了数值模拟。