This study presents a mathematical model of a non-steady-state amperometric biosensor with combined enzyme kinetics and diffusion restrictions, under substrate and product inhibition. An enzymatic reaction with non-Michaelis-Menten dynamics is associated with nonlinear terms in the diffusion equations of the structure.We applied the Laplace Homotopy Perturbation Method (LHPM) to the proposed non-steady-state reaction-diffusion equation and the Akbari-Ganji method (AGM) to the steady state. Approximate analytical solutions for the biosensor concentration profiles, current, sensitivity, and resistance were established for all possible rate constants. Using the MATLAB software, we provide a computational solution and compare the analytical results with the reaction-diffusion equation under consideration. Effective conclusions were observed for all potential values of the variables when examining both the analytical and computational solutions. Furthermore, the key features of enzymatic electrolytic biosensors, including resistance, sensitivity range, efficiency, and reaction time has been examined.