A qualitative analysis of an Aβ-monomer model with inflammation processes for Alzheimer’s disease

We introduce and study a new model for the progression of Alzheimer's disease incorporating the interactions of Aβ-monomers, oligomers, microglial cells and interleukins with neurons through different mechanisms such as protein polymerization, inflammation processes and neural stress reactions. In order to understand the complete interactions between these elements, we study a spatially-homogeneous simplified model that allows to determine the effect of key parameters such as degradation rates in the asymptotic behavior of the system and the stability of equilibriums. We observe that inflammation appears to be a crucial factor in the initiation and progression of Alzheimer's disease through a phenomenon of hysteresis, which means that there exists a critical threshold of initial concentration of interleukins that determines if the disease persists or not in the long term. These results give perspectives on possible anti-inflammatory treatments that could be applied to mitigate the progr..., Numerical generations are obtained through Matlab Software by using the solver ode45., , # A qualitative analysis of an Aβ-monomer model with inflammation processes for Alzheimer’s disease Access this dataset on Dryad: This data set contains the table of parameters and the codes of the numerical methods applied to solve the bi-monomeric ODE system.\ The parameter values were chosen just to test the structural variables of our system such as the degradation rate of mononers and the initial concentration of interleukins. ## Description of the data and file structure Parameters.xlsx : Table with test parameter values of the system used in the simulations. We focused on the order of magnitude. The scripts to produce the figures are the following: Bifurcation_d.m : Script to generate the bifurcation diagram for degradation of monomers (Figure 2). This script solves a system of equations to compute the steady states of the systems for different values of the degradation rate of monomers through the fzero method of MATLAB. Critical_I_d.m : Script to generate the critical cu...我们提出并研究了一种全新的阿尔茨海默病进展模型，该模型纳入了β淀粉样蛋白单体（Aβ-monomers）、寡聚体（oligomers）、小胶质细胞（microglial cells）以及白细胞介素（interleukins）与神经元之间的相互作用，涵盖蛋白质聚合、炎症反应及神经应激反应等多种作用机制。 为全面阐明上述组分间的完整相互作用，我们构建了空间均质简化模型，可用于确定关键参数（如降解速率）对系统渐近行为及平衡态稳定性的影响。 我们观察到，通过滞后现象，炎症似乎是阿尔茨海默病起始与进展的关键影响因素——即存在临界初始白细胞介素浓度阈值，可决定该疾病能否长期存续。上述研究结果为开发可缓解疾病进展的潜在抗炎治疗方案提供了研究视角。[原文此处截断为“mitigate the progr...”] 数值仿真结果通过MATLAB软件的ode45求解器生成。 # 针对阿尔茨海默病炎症反应的β淀粉样蛋白单体模型的定性分析 本数据集可在Dryad平台获取： 该数据集包含系统参数表及用于求解双单体常微分方程（Ordinary Differential Equation, ODE）系统的数值方法代码。 本次选用的参数值仅用于测试系统的结构变量，例如单体降解速率及白细胞介素初始浓度。 ## 数据与文件结构说明 Parameters.xlsx：包含仿真所用系统的测试参数值表格，研究重点关注参数的数量级。 用于生成图表的脚本如下： Bifurcation_d.m：用于生成单体降解速率相关的分岔图（图2）。该脚本通过MATLAB的fzero方法求解方程组，以计算不同单体降解速率下系统的稳态解。 Critical_I_d.m：用于生成临界[原文未完成内容]