Fractional-Order Analysis of Monomer-Oligomer Aggregation Pathways in Alzheimer's Disease

Alzheimer’s disease, a progressive neurodegenerative illness where intermediate forms play a crucial role in neurotoxicity, is associated with the aggregation of amyloid-β(Aβ) peptides into monomers, dimers, trimers, and higher-order structures. This study examines the dynamics of amyloid aggregation using a fractional-order mathematical model based on the Caputo-Fabrizio derivative that takes memory effects into account. Numerical simulations using the fractional Euler technique are used to analyze the model’s positivity and boundedness as well as system behavior. The results show that the aggregation dynamics are highly sensitive to model parameters and fractional order, exhibiting stable convergence in some circumstances and oscillating behavior in others. A Hopf bifurcation is observed with respect to a critical parameter, indicating the transition of the system from stability to periodic oscillations and the onset of instability. The model provides useful information on the complex mechanisms underlying Alzheimer’s disease development.