A Dynamical Systems Approach to Alzheimer's Disease: A Neural Network Model with Positive Feedback Mechanisms

Alzheimer's disease is a progressive neurodegenerative disorder characterized by a continuous decline in cognitive function. Based on the theory of artificial neural networks, this paper proposes a dynamic model with a positive feedback mechanism to explain the onset and progression of Alzheimer's disease. The model takes the number of neurons, levels of neuroinflammation, and pathological protein load as core state variables and introduces the coupling relationships among them, revealing critical behaviors and self-accelerating mechanisms in disease progression. Through numerical simulations implemented in Python, we analyze the effects of different intervention strategies (anti-inflammatory drugs, anti-Aβ drugs, neuroprotective agents, and combination therapies) on disease trajectories and identify the critical window for treatment. The results indicate that combination therapy is the most effective in delaying the crossing of cognitive thresholds, and the timing of intervention has a decisive impact on efficacy. This study provides a unified theoretical framework for understanding the pathological mechanisms of Alzheimer's disease, guiding early interventions, and developing multi-target treatment strategies.