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<p>In this work, we want to prove global stability of one time-continuous model and two time-discrete variants for a non-linear, extended three-compartmental model of ethanol metabolism in the human body, which has been recently proposed in one current article (<a href="https://dx.doi.org/10.1002/mma.10858">https://dx.doi.org/10.1002/mma.10858</a>). This means that we show that all trajectories, independent of our non-negative chosen initial values, converge to the ethanol-free equilibrium state. Hence, we extend local stability results of the aforementioned work such that the time-continuous and both proposed time-discrete models possess one unique ethanol-free equilibrium state which is globally asymptotically stable. Here, we mainly apply results of Sundarapandian (<a href="https://dx.doi.org/10.1016/S0893-9659%2801%2900130-6">https://dx.doi.org/10.1016/S0893-9659(01)00130-6</a>) on non-linear cascade systems. Finally, we strengthen our theoretical findings by numerical examples.</p>

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Global asymptotic stability of one time-continuous and two time-discrete models for ethanol metabolism in the human body

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  • 发表日期：

    2025年7月22日

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  • Benjamin Wacker

摘要

In this work, we want to prove global stability of one time-continuous model and two time-discrete variants for a non-linear, extended three-compartmental model of ethanol metabolism in the human body, which has been recently proposed in one current article (https://dx.doi.org/10.1002/mma.10858). This means that we show that all trajectories, independent of our non-negative chosen initial values, converge to the ethanol-free equilibrium state. Hence, we extend local stability results of the aforementioned work such that the time-continuous and both proposed time-discrete models possess one unique ethanol-free equilibrium state which is globally asymptotically stable. Here, we mainly apply results of Sundarapandian (https://dx.doi.org/10.1016/S0893-9659(01)00130-6) on non-linear cascade systems. Finally, we strengthen our theoretical findings by numerical examples.