Mathematics Department, King Abdulaziz University, Jeddah, Saudi Arabia.
Phys Biol. 2022 Aug 18;19(5). doi: 10.1088/1478-3975/ac8516.
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, extracellular-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 extracellular-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 extracellular-syn preserves neurons and delays the onset of Parkinson's disease, whether alone or in combination with another treatment.
本文旨在通过治疗策略对帕金森病的动力学进行数学建模。所构建的模型由五个状态变量组成：健康神经元、感染神经元、细胞外突触、活性小胶质细胞和静止小胶质细胞。模型的定性分析产生了一个不稳定的自由平衡点和一个稳定的地方病平衡点。此外，这些结果通过不同初始值的数值实验进行了验证。研究了两种治疗干预措施，即减少细胞外突触和减少中枢神经系统中活性小胶质细胞引起的炎症。结果表明，后者对延缓神经元恶化没有明显效果。然而，无论单独使用还是与另一种治疗方法联合使用，减少细胞外突触的治疗方法都能保护神经元并延缓帕金森病的发作。
