A mathematical model is considered to determine the effectiveness of disin-
fectant solution for surface decontamination. The decontamination process involved the
diffusion of bacteria into disinfectant solution and the reaction of the disinfectant killing
effect. The mathematical model is a reaction-diffusion type. Finite difference method and
method of lines with fourth-order Runge-Kutta method are utilized to solve the model
numerically. To obtain stable solutions, von Neumann stability analysis is employed to
evaluate the stability of finite difference method. For stiff problem, Dormand-Prince
method is applied as the estimated error of fourth-order Runge-Kutta method. MATLAB
programming is selected for the computation of numerical solutions. From the results
obtained, fourth-order Runge-Kutta method has a larger stability region and better ac-
curacy of solutions compared to finite difference method when solving the disinfectant
solution model. Moreover, a numerical simulation is carried out to investigate the effect
of different thickness of disinfectant solution on bacteria reduction. Results show that
thick disinfectant solution is able to reduce the dimensionless bacteria concentration more
effectively.
This study presents a mathematical model examining wastewater pollutant removal through
an oxidation pond treatment system. This model was developed to describe the reaction
between microbe-based product mPHO (comprising Phototrophic bacteria (PSB)), dissolved
oxygen (DO) and pollutant namely chemical oxygen demand (COD). It consists
of coupled advection-diffusion-reaction equations for the microorganism (PSB), DO and
pollutant (COD) concentrations, respectively. The coupling of these equations occurred
due to the reactions between PSB, DO and COD to produce harmless compounds. Since
the model is nonlinear partial differential equations (PDEs), coupled, and dynamic, computational
algorithm with a specific numerical method, which is implicit Crank-Nicolson
method, was employed to simulate the dynamical behaviour of the system. Furthermore,
numerical results revealed that the proposed model demonstrated high accuracy when
compared to the experimental data.