We describe a two-component positive-feedback system that could account for the large reduction of acetylcholine that is characteristic of patients with Alzheimer's disease (AD). One component is beta-amyloid-induced apoptosis of cholinergic cells, leading to a decrease in acetylcholine. The other component is an increase in the concentration of beta-amyloid in response to a decrease in acetylcholine. We describe each mechanism with a differential equation, and then solve the two equations numerically. The solution provides a description of the time course of the reduction of acetylcholine in AD patients that is consistent with epidemiological data. This model may also provide an explanation for the significant, but lesser, decrease of other neurotransmitters that is characteristic of AD.