On a Generalized Compartment Model for Ethanol Metabolism in the Human Body

We introduce a generalized continuous-time compartment model of ethanol metabolism in the human body that extends a recently developed framework. In the proposed model, we replace the Michaelis-Menten mechanism of the liver's ethanol metabolism rate with a general class of nonlinear rate functions. This modification provides greater modeling flexibility and enables the model to capture a wider range of hepatic ethanol metabolism dynamics. The qualitative behavior of the proposed ethanol metabolism model is analyzed rigorously. More specifically, we investigate the positivity and boundedness of solutions, as well as the global asymptotic stability (GAS) of the unique equilibrium point using an appropriate quadratic Lyapunov function.
Second, we formulate a discrete-time counterpart of the proposed continuous-time model and investigate its dynamical properties. We show that, under an appropriate condition on the time step size, the discrete-time model faithfully reproduces the qualitative dynamical behavior of the corresponding continuous-time system.
Lastly, we conduct a series of numerical experiments employing several ethanol metabolism rate functions to support the theoretical results.