Quantifying Uncertainty and Sensitivity in an Alzheimer’s Disease Model: A Mathematical Approach

Abstract

To understand the dynamics of Alzheimer’s disease, we formulate a generalized mathematical model based on three events: aggregation of disease-related proteins, activation of immune cells and initiation of inflammation. We incorporate functional forms in the model to represent the complex biological interactions between components related to Alzheimer’s disease. We take explicit forms depending on the properties of functions in the model. We describe the system dynamics by locating biologically feasible steady states, determining stability properties and identifying the effective parameters. Parameters are estimated using two methods: biological literature and data fitting. We perform sensitivity and uncertainty analyses to identify the most influential parameters. Partial Rank Correlation Coefficient and scatter plots are used to visualize global sensitivity. Our results reveal that lower activation rate and higher proliferation rate of microglia may contribute to a reduction in toxic protein aggregate levels, thus slowing the disease’s early progression.