University of Guilan Journal of Mathematical Modeling 2345-394X 2026 02 10 A mathematical study on reaction-diffusion model in biomedicine 9429 10.22124/jmm.2026.32423.2938 EN Vembu Ananthaswamy The Madura College (Autonomous -Affiliated to Madurai Kamaraj University, Madurai ) Jeyakumar Anantha Jothi Research Scholar, Research Centre and PG Department of Mathematics, The Madura College (Autonomous) Madurai, Tamil Nadu, India Moorthi Subha Department of Mathematics Fatima College (Autonomous) Madurai, Tamil Nadu, India Journal Article 2025 12 19 The present investigation examines the Michaelis-Menten kinetics response diffusion problem<br />in a planar, spherical framework by employing mathematical model. The substrate concentration<br />is found to have straightforward outcomes with the Michaelis constant, modified Sherwood<br />number, and Thiele modulus. Here, the analytical approximation for the non-dimensional substrate<br />concentration and unitless effectiveness factor are determined via the new approximate<br />analytical methodology for steady-state (Ananthaswamy - Sivasankari method ASM) and Homotopy<br />with Laplace transform method for non-steady state. Additionally, juxtaposition between<br />the analytical approximation and numerical simulation is provided. There is a good correlation<br />between the numerical results and the approximate analytical result. Mathematical modeling Michaelis–Menten kinetics (M-MK) non-linear initial-boundary value problem Homotopy perturbation method new approximate analytical method Numerical simulation https://jmm.guilan.ac.ir/article_9429_013589c99636245bf1e296609211b001.pdf