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Journal of Vibration Testing and System Dynamics 9(4) (2025) 333--345 | DOI:10.5890/JVTSD.2025.12.003

J. Anantha Jothi$^1$, V. Ananthaswamy$^2$

$^1$ Research Scholar, Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India

$^2$ Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India

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Abstract

This current research work investigates the mathematical models of biosensors. The given models are constructed which depends on non-linear reaction equations pertaining with an enzyme process element. The approximate analytical results for time-dependent conditions of concentrations and current are provided in dimensional for all values of the parameters. The semi-analytical findings for the concentrations of substrate, co-substrate as well as the current are attained by utilising the new homotopy perturbation method (NHPM). On comparing the numerical simulation with our findings, a good fit is reached. The impacts of several parameters, including the substrate's reaction rate constant and co-substrate, diffusion coefficient for substrate and co-substrate, maximal velocity of enzyme reaction and thickness of the active membrane are graphically represented. The effect of numerous parameters on current namely maximal velocity of enzyme reaction, diffusion coefficient for co-substrate and substrate's reaction rate constant are displayed graphically.

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