Modeling the dynamics of innate immune response to Parkinson disease with therapeutic approach

This paper aims to mathematically model the dynamics of Parkinson's disease with therapeutic strategies. The constructed model consists of five state variables: healthy neurons, infected neurons, extracellularα-syn, active microglia, and resting microglia. The qualitative analysis of the model produced an unstable free equilibrium point and a stable endemic equilibrium point. Moreover, these results are validated by numerical experiments with different initial values. Two therapeutic interventions, reduction of extracellularα-syn and reduction of inflammation induced by activated microglia in the central nervous system, are investigated. It is observed that the latter has no apparent effect in delaying the deterioration of neurons. However, treatment to reduce extracellularα-syn preserves neurons and delays the onset of Parkinson's disease, whether alone or in combination with another treatment.