The quantitative prediction of neurodegenerative diseases is difficult because they show progressive loss of neurons that is accompanied by complex interactions between protein aggregation, neuroinflammation, oxidative stress, cellular dysfunction, and others. The aim of this study is to create a nonlinear system of ordinary differential equations (ODEs) to account for the dynamics of the disease, by modelling healthy neurons, damaged neurons, toxic protein accumulation, inflammatory response and therapeutic action. Disease progression under different biological conditions is evaluated by stability analysis, equilibrium analysis, sensitivity analysis and numerical simulation by the fourth order Runge–Kutta method. The results show that the decrease of toxic protein aggregation and inflammatory activity is associated with substantial delay in the process of neuronal degeneration and stability of the system in the long run. The proposed mathematical framework will enable understanding of the evolution of disease, pinpoint influential disease parameters for targeted disease intervention, and provide a predictive tool which can be used for planning individualized therapeutic strategies and future computational neuroscience studies.