Millions of people are affected by Alzheimer's disease, which is a progressive neurodegenerative disorder. It is important to understand the progression dynamics of this disease to be able to minimize the damage that is caused by it. This article provides a mathematical framework to develop strategies to slow down the progression of Alzheimer's disease. Bifurcation analysis is a powerful mathematical tool used to deal with the nonlinear dynamics of any process. Several factors must be considered, and multiple objectives must be met simultaneously. Bifurcation analysis and Multiobjective Nonlinear Model Predictive Control (MNLMPC) calculations are performed on two Alzheimer’s disease models. The MATLAB program MATCONT was used to perform the bifurcation analysis. The MNLMPC calculations were performed using the optimization language PYOMO in conjunction with the state-of-the-art global optimization solvers IPOPT and BARON. The bifurcation analysis revealed the existence of limit points in the models. The limit points were beneficial because they enabled the multiobjective nonlinear model predictive control calculations to converge to the Utopia point in both problems, which is the most beneficial solution. A combination of bifurcation analysis and multiobjective nonlinear model predictive control for Alzheimer’s disease models is the main contribution of this paper.