Neurodegenerative diseases can be classified into three broad categories. Demyelinating diseases (including MS or ADEM), diseases of neuronal dysfunction (including early-stage Alzheimer's and mild cognitive impairment), and diseases of neuronal death (including Alzheimer's disease, Huntington's Disease, and many others). In each of these conditions, cognitive decline is a key feature of the progression of the illness. In this study, we present a novel method to model cognitive decline as the performance of an arbitrary neural network designed to execute a classification task, tested for robustness in a node and edge deletion trial. Edge deletion modeled demyelination, node deletion modeled the death of the neuron, and general neuronal dysfunction was modeled with additive noise. Network performance rapidly declined by the deletion of more nodes and edges, with more robustness to edge deletion than node deletion. Networks with larger hidden nodes and edges in the predefined architecture were found to be more resistant to performance decline than smaller networks. The addition of noise also precipitated a decline in performance but this decline was more gradual than with node and edge deletion. These experiments were compared to models of cognitive dysfunction from clinical data in the literature and found to contain similar profiles.