Global Dynamics of a Pharmacokinetic Compartment Model for Human Ethanol Metabolism and Its Generalization

Abstract

In this work, we revisit a continuous-time two-compartment pharmacokinetic model of human ethanol metabolism originally proposed by Levitt and Levitt. We first establish the positivity and boundedness of the solutions, investigate the existence and uniqueness of a positive equilibrium, and analyze its local and global asymptotic stability. As a result, the global dynamics of the ethanol metabolism model is completely characterized, thereby complementing and extending the analytical results reported in the original benchmark study. Second, we extend the original continuous-time model by replacing the Michaelis--Menten metabolism rate with a general class of metabolism-rate functions that includes many well-known monotone and nonmonotone forms. This extension enhances the flexibility of the model and enables it to capture a wider range of realistic metabolic scenarios. We then investigate the global dynamics of the generalized continuous-time model. Finally, numerical experiments are conducted to support the theoretical findings. The numerical results provide further evidence for the theoretical results.