A phenomenological mathematical model for Alzheimer’s disease is formulated and analyzed as a dynamical system. In the model, the formation of amyloid-beta (A \(\beta \) ) proteins is aggregated into three compartments consisting of monomeres, proto-oligomeres, and polymeres, and the net-effect of stimulating and inhibiting feedback loops on the production of monomeres through pro- and anti-inflammatory cytokines is considered. The resulting 4-dimensional nonlinear dynamical system exhibits a uniform dynamical structure irrespective of the numerical values of the parameters with a region of attraction of the trivial equilibrium point (corresponding to no disease) and a region of divergence of the trajectories (corresponding to the presence of the disease) separated by a 3-dimensional stable manifold of a positive equilibrium point acting as stability boundary. Existence and location of this stability boundary are determined by a simple mathematical quantity which expresses the difference between stimulating and inhibiting parameters in the feedback loops and allows a direct interpretation in terms of current treatment approaches.
