A qualitative analysis of a model on alpha-synuclein transport and aggregation in neurons

This study aims to analyze a mathematical model of alpha-synuclein transport and aggregation in neurons qualitatively. Our analysis yielded a unique equilibrium point, which exists always. Also, we derive the criteria for the local and global asymptotic stability of the equilibrium. Moreover, we utilize the closed form of the equilibrium to investigate the effect of the models' parameters on decreasing the long term value of the misfolded alpha-synuclein, which may help in suggesting pharmacological interventions for Parkinson's disease. Furthermore, numerical simulations are illustrated to support the analytic results and sensitivity analysis.