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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Mathematical Study on Reaction-Diffusion Process in Amperometric Biosensor

Journal of Applied Nonlinear Dynamics 15(3) (2026) 615--627 | DOI:10.5890/JAND.2026.09.007

V. Ananthaswamy$^1$, J. Anantha Jothi$^2$, M. Subha$^3$

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

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

$^3$ Department of Mathematics, Fatima College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India

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Abstract

This article investigates the mathematical models of amperometric biosensors. The given models is constructed which depends on diffusion equations of the non-linear element pertaining with an enzyme process. The approximate analytical solutions for both time - independent and time - dependent conditions of concentrations are provided in non-dimensional and dimensional for all values of the parameters. The semi-analytical expressions for the substrate, product concentrations and current are attained by utilising the new homotopy perturbation method (NHPM). The new homotopy perturbation technique is employing to solve the biosensors models like non-linear reaction-diffusion model in amperometric biosensors, potentiometric biosensors and michaelis-menten kinetics. On comparing the numerical simulation with our findings, a good fit is reached. The impacts of several parameters, including the Thiele modulus, saturation parameter, maximal enzymatic rate, the ratio of diffusion coefficients, Michaelis constant, substrate concentration in the bulk solution and thickness of the enzyme membrane are graphically represented for concentration and current.

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