Modeling neuroimmune dynamics in neurodegeneration: A nonlinear ODE framework for stability and transition analysis

Neuroinflammation is an important factor in the pathogenesis and pathophysiology of neurodegenerative diseases, but the mechanistic insights into neuron-immune system relationships are still incomprehensive. This paper fills this gap with the creation of a nonlinear ordinary differential equation model describing the interconnected behavior of healthy neurons, infected neurons, extracellular signaling molecules, microglia, and T-cells. It will aim at examining the parameters of immune activation and neuronal degradation and their impact on neuroimmune stability and the development of disease. The stability and sensitivity analysis are some methods by which we understand the behavior of the system using the Runge–Kutta (RK45) numerical solver. The findings indicate that there are a variety of equilibrium points, threshold shifts, and nonlinear feedback processes, which drive changes between healthy and inflammatory regimes. Sensitivity analysis determines the parameters that are important in controlling neuronal resilience, whereas phase-space and time-series plots depict the important transitions toward neuronal collapse or recovery. The results offer quantitative information on neuroimmune regulation and can be used to inform experimental studies and treatment approaches aimed at inhibiting neuroimmune regulation in neurodegenerative disorders.