Stationary distribution and extinction of a stochastic Alzheimer's disease model

In this paper, a stochastic Alzheimer's disease model with the effect of calcium on amyloid beta is proposed. The Lyapunov function is constructed, followed by the feasibility and positivity and the existence of a stationary distribution for the positive solutions of the proposed model. The sufficient conditions for the extinction of the stochastic Alzheimer's disease model are derived through the Lyapunov function. This indicates that beta-amyloid plaque and the complex of beta-amyloid oligomers with prion protein may go extinct and there is a possibility of a cure for the disease. Furthermore, our numerical simulations show that as the intensity of the random disturbance increases, the time it takes for the disease to go extinct decreases.