Solution of bacteria- surface decontamination model by using separation of variables

Abstract

The aim of this study is to investigate the application of the Fourier series method to solve a known mathematical model of surface disinfection and in order to determine its effectiveness. The mathematical model is based on the reaction-diffusion partial differential equation due to the diffusion of the bacteria into the disinfectant solution when the decontamination process begins and the reaction of the disinfectant killing effect on the bacteria. Analytical and approximate solution for the model is carried out using Fourier series. The infinite Fourier series is approximated twice by choosing finite terms of the series and by approximating some of the eigenvalues of the solution. Mathematica programming software is selected to execute the numerical computations. The obtained results are compared with the exact initial condition and a previous study. Simulation of the results demonstrate that the Fourier series method is able to approximate the solution of the surface disinfection model.