The misconformation and aggregation of the protein Amyloid-Beta (A\(\beta \)) is a key event in the propagation of Alzheimer’s Disease (AD). Different types of assemblies are identified, with long fibrils and plaques deposing during the late stages of AD. In the earlier stages, the disease spread is driven by the formation and the spatial propagation of small amorphous assemblies called oligomers. We propose a model dedicated to studying those early stages, in the vicinity of a few neurons and after a polymer seed has been formed. We build a reaction–diffusion model, with a Becker–Döring-like system that includes fragmentation and size-dependent diffusion. We hereby establish the theoretical framework necessary for the proper use of this model, by proving the existence of solutions using a fixed point method.

蛋白质淀粉样蛋白-β (A \(\beta \) )的错误构象和聚集是阿尔茨海默病 (AD) 传播的关键事件。识别出不同类型的组件，在 AD 晚期沉积长纤维和斑块。在早期阶段，疾病传播是由称为低聚物的小无定形组装体的形成和空间传播驱动的。我们提出了一个模型，专门用于研究在几个神经元附近和聚合物种子形成之后的早期阶段。我们构建了一个反应-扩散模型，其中包含一个 Becker-Döring-like 系统，其中包括碎裂和大小相关的扩散。通过使用不动点方法证明解的存在，我们在此建立了正确使用该模型所需的理论框架。