Baló’s concentric sclerosis (BCS) is considered a variant of inflammatory demyelinating disease closely related to multiple sclerosis characterized by a discrete concentrically layered lesion in the cerebal white matter. Khonsari and Calvez (Plos ONE. 2(2007)) proposed a parabolic-elliptic-ODE chemotaxis model for BCS which describes the evolution of the densities of activated macrophages, cytokine and apoptotic oligodendrocytes. Because “classically activated” M1 microglia can produce cytotoxicity, we introduce a linear production term from the activated microglia in the ODE for pro-inflammatory cytotoxic. For the new BCS chemotaxis model, we first investigate the uniform boundedness and global existence of classical solutions, and then get a range of the chemosensitive rate χ where the unique positive equilibrium point is exponentially asymptotically stable.

中文翻译：

---

Boló同心性硬化症趋化模型的整体有界性和稳定性

Baló的同心性硬化症（BCS）被认为是与多发性硬化症密切相关的炎性脱髓鞘疾病的一种变体，其特征是大脑白质中有一个分散的同心分层病灶。Khonsari和Calvez（Plos ONE。2（2007））为BCS提出了抛物线-椭圆-ODE趋化模型，该模型描述了活化的巨噬细胞，细胞因子和凋亡少突胶质细胞密度的演变。由于“经典激活的” M1小胶质细胞可产生细胞毒性，因此我们在ODE中引入了激活小胶质的线性生产术语来表示促炎性细胞毒性。对于新的BCS趋化模型，我们首先研究经典解的一致有界性和全局存在性，然后得出化学敏感率χ的范围 其中唯一的正平衡点呈指数渐近稳定。