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To fully understand intricate enzyme reaction models, one must explore beyond the confines of chemical and biological tools and look toward mathematical modeling and model reduction techniques. Mathematical modeling and model reduction techniques have the potential to provide a vast array of analysis tools for such models. This piece of work entails a review and discussion of a complex noncompetitive inhibitor model. This model is composed of seven non-linear differential equations with constant rates. We propose two efficient model reduction techniques: quasi- steady-state approximation (QSSA) and quasi-equilibrium approximation (QEA). By utilizing the suggested methods, the model equations are segregated into slow and fast subsystems, leading to the attainment of reduced models and slow manifolds with fewer variables and parameters. The outcomes manifest some analytical approximate solutions for the proposed model and establish a profound agreement between model dynamics for both the original and the reduced models. Observing that the reduced models can accurately identify certain critical model parameters is intriguing.
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