A study on a modified fractional mathematical model of Listeria infection caused by pre-cooked packaged food by Homotopy analysis method A study on a modified fractional mathematical model of Listeria infection by HAM
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Abstract
This study examines the dynamics of a Listeria bacterium in a packaged food scenario using a mathematical framework that incorporates fractional derivatives in the Caputo sense. The model is solved using two primary methods: the homotopy analysis method (HAM), a semi-analytical approach that provides a series solution for fractional-order nonlinear ordinary differential equations (ODEs), and the Runge-Kutta 4th order (RK4) method, a well-known numerical technique for solving ODE systems. The HAM solution is derived by selecting a convergence control parameter, which produces a series of polynomials, whereas the RK4 method yields a fully numerical solution. The accuracy and dependability of both methods are evaluated by comparing their results to those of an ND Solver. The model's behavior under different parameter values is examined. All computations are carried out using Scilab and Mathematica software. The findings are presented in extensive graphs and tables, and formal theorems are used to demonstrate the convergence of the solution. This comparative method reveals the efficacy of fractional derivative modeling for analyzing bacterial activity in packaged food environments, as well as the effectiveness of HAM and RK4 in handling complex biological systems.
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