Homotopy Analysis Method on Listeria Infection Model Caused by Pre-Cooked Package Food

Abstract

In this study, the Listeria infection model involving the fractional derivatives in the Caputo sense is considered and studied through two different techniques called the Homotopy analysis method (HAM) and Runge-Kutta 4th order (RK4) method. HAM is a semi-analytical approach, and the RK4 method is a numerical method proposed for solving fractional order systems of ordinary differential equations (ODEs). We have developed a semi-analytical solution in terms of a series of polynomials by HAM and a numerical solution by the RK4 method for the model. First, we solved the model through HAM by choosing the preferred control parameter and also applied the RK4 method. The model solved by projected methods is compared with the NDSolver solution. The nature of the model is analyzed using different parameters, and the calculations are performed using Mathematica software. The obtained results are expressed in graphs and tables.