<p>This study presents an analytical investigation of substrate concentration profiles in immobilized enzyme systems exhibiting hysteresis behavior under enzyme flow calorimetry conditions. A mathematical model is formulated using the ordinary differential equations that incorporate nonlinear substrate inhibition kinetics together with diffusion parameters. Closed-form analytical expressions for the dimensionless substrate concentration at steady state are derived for planar, cylindrical, and spherical particle geometries using the Hosoya Polynomial Approximation Method (HPAM). The solution is expressed in terms of a quadratic polynomial basis constructed from path-graph Hosoya polynomials, whose coefficients are determined by satisfying the governing nonlinear boundary value problem at selected collocation points. The accuracy of HPAM is rigorously assessed by comparing its predictions against numerical solutions obtained via the fourth-order Runge–Kutta (RK4) method and against results from the Homotopy perturbation method (HPM). For all six parameter cases examined, HPAM achieves an average percentage deviation from the RK4 numerical solution as low as 0.0004% for planar particles (Table 1, β = 0.1) and below 1.69% even under the most demanding Thiele modulus conditions (Table 4, Ω = 260). In every case, HPAM outperforms HPM, which reaches deviations exceeding 10% under comparable conditions. A sensitivity analysis reveals that increasing the Thiele modulus Ω or decreasing the dimensionless inhibition parameter β amplifies the concentration gradient within the particle, a trend captured faithfully by the proposed method. The simplicity, accuracy, and broad applicability of HPAM makes it a valuable analytical tool for modeling reaction–diffusion systems in immobilized enzyme bioreactor design and kinetic parameter estimation.</p>