Ramos M P Machado, Ribeiro C, Soares A J
Centro de Matemática, Universidade do Minho, Guimarães, Portugal.
Centro de Matemática, Universidade do Minho, Braga, Portugal.
J Math Biol. 2019 Dec;79(6-7):2005-2031. doi: 10.1007/s00285-019-01418-4. Epub 2019 Sep 9.
We construct a mathematical model of kinetic type in order to describe the immune system interactions in the context of autoimmune disease. The interacting populations are self-antigen presenting cells, self-reactive T cells and the set of immunosuppressive cells consisting of regulatory T cells and Natural Killer cells. The main aim of our work is to develop a qualitative analysis of the model equations and investigate the existence of biologically realistic solutions. Having this goal in mind we describe the interactions between cells during an autoimmune reaction based on biological considerations that are given in the literature and we show that the corresponding system of integro-differential equations has finite positive solutions. The asymptotic behaviour of the solution of the system is also studied. We complement our mathematical analysis with numerical simulations that study the sensitivity of the model to parameters related to proliferation of immunosuppressive cells, destruction of self-antigen presenting cells and self-reactive T cells and tolerance of SRTCs to self-antigens.
我们构建了一个动力学类型的数学模型，以描述自身免疫性疾病背景下的免疫系统相互作用。相互作用的群体包括自身抗原呈递细胞、自身反应性T细胞以及由调节性T细胞和自然杀伤细胞组成的免疫抑制细胞集合。我们工作的主要目的是对模型方程进行定性分析，并研究生物学上现实解的存在性。出于这个目标，我们基于文献中给出的生物学考虑描述了自身免疫反应期间细胞之间的相互作用，并表明相应的积分 - 微分方程组具有有限正解。还研究了该系统解的渐近行为。我们通过数值模拟对数学分析进行补充，这些模拟研究了模型对与免疫抑制细胞增殖、自身抗原呈递细胞和自身反应性T细胞破坏以及自身反应性T细胞对自身抗原的耐受性相关参数的敏感性。
