Abstract In this study, a mathematical model of immobilized enzyme system, which follows the Michaelis-Menten kinetics for micro-disk biosensor is discussed. It is based on substrate and hydrogen peroxide profile with enzyme reaction within the biosensor under steady state condition. Accordingly, simple and compact analytical expression for substrate as well as hydrogen peroxide concentrations and electrode current for micro-disk biosensor are obtained. In addition, it acquired as a function of reaction diffusion parameter and saturated parameter using hyperbolic function method. Therefore, this hyperbolic function analysis of the proposed model is an efficient tool to predict the Michaelis-Menten constant. Furthermore, to confirm the validity and accuracy of the proposed method, the results are compared with those obtained by using well-established Homotopy analysis method and Modified Adomian decomposition method. The numerical results obtained are provided by the highly reputed program pdex2 and pdex4 in MATLAB. Tabular compilations of concentrations and current are also explored for typical values of the governing parameters.

中文翻译：

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微盘生物传感器非线性联立微分方程新数学分析的双曲函数法

摘要 本研究讨论了微盘生物传感器中遵循Michaelis-Menten动力学的固定化酶系统数学模型。它基于底物和过氧化氢曲线，在稳态条件下生物传感器内发生酶反应。因此，获得了用于微盘生物传感器的基板以及过氧化氢浓度和电极电流的简单而紧凑的分析表达式。此外，使用双曲线函数法获得了作为反应扩散参数和饱和参数的函数。因此，所提出模型的这种双曲函数分析是预测 Michaelis-Menten 常数的有效工具。此外，为了确认所提出方法的有效性和准确性，将结果与使用完善的同伦分析方法和修正的 Adomian 分解方法获得的结果进行比较。得到的数值结果由 MATLAB 中著名的程序 pdex2 和 pdex4 提供。还探索了浓度和电流的表格汇编以获取控制参数的典型值。