Amperometric biosensors and coupled enzyme nonlinear reactions processes: A complete theoretical and numerical approach

•Mathematical model for biosensor acting in trigger mode is discussed.•Nonlinear differential equations are solved and validated with simulation results.•Transient current, sensitivity, resistance and gain expressions are derived.•The influence of various system parameters on biosensor response has been examined. The transient response of amperometric enzyme-based biosensors working in trigger mode is discussed. Nonlinear time-dependent partial differential equations for Michaelis–Menten reaction kinetics are solved analytically using a new approach of homotopy perturbation technique. The simple and closed-form analytical expression for concentration profiles are provided. Subsequently, the biosensor's current, sensitivity, resistance, and amplification are derived from the concentration profiles. The current response is predicted under steady-state conditions when T→∞, proving the validity of the mathematical analyses. The limiting situations of catalytic sites (unsaturation and saturation) are considered. The compatibility of analytical results with simulation and limiting case results can be observed from the graphs and tables presented. The existence of the moving boundary between the two categories of catalytic sites is also discussed.