Abstract
In this paper, a non-steady-state amperometric biosensor with the mixed enzyme kinetics and diffusion limitations under the inhibitions of substrate and product is modeled mathematically. The non-steady-state reaction-diffusion equations of the system
consist non-linear terms related to an enzymatic reaction of non-Michaelis-Menten kinetics. We have presented the approximate analytical solutions for the concentrations of substrate and product in non-steady and steady-state models using
the new approach of Homotopy perturbation method (HPM). The provided expression is presented for all potential diffusion and kinetic parameter values. Analytical expressions of the biosensor current and sensitivity are also presented and
discussed. In addition, we also provided numerical solutions for the proposed model by utilizing the pdepe tool in MATLAB software. When comparing the analytical solution with the numerical solution, a satisfactory result is noted for
all the possible values of the parameters. Furthermore, the influence of diffusion and kinetic parameters on both the current and the sensitivity are discussed. Analytical expressions for the limiting cases of biosensor enzyme kinetics
are presented in this research article. Additionally, an analytical expression for determining the effective thickness of the membrane is derived and presented.
