New Mathematical Analysis for Nonlinear Simultaneous Differential Equation in Micro-Disk Biosensor Using Hyperbolic Function Method

摘要

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.