A sensitivity analysis of a mathematical model for the synergistic interplay of amyloid beta and tau on the dynamics of Alzheimer’s disease

We propose a mathematical model for the onset and progression of Alzheimer's disease based on transport diffusion equations. treat brain neurons as continuous medium structure them by their degree malfunctioning. Three different mechanisms are assumed to be relevant temporal evolution disease: i) agglomeration soluble Amyloid beta, ii) effects phosphorylated tau protein iii) neuron-to-neuron prion-like transmission disease. these processes system Smoluchowski equations beta concentration, an equation dynamics kinetic-type distribution function malfunctioning neurons. The latter contains integral term describing random jump process localized in particularly sensitive areas brain. interested investigating synergistic interplay output our numerical simulations, although 2D with over-simplified geometry, is good qualitative agreement clinical findings concerning both brain, which varies from early advanced stages,