Virus propagation of two-dimensional advection dispersion equation in heterogeneous medium: A comparative study

Abstract

In this study we model the virus propagation with mathematical framework that predicts its behavior. Specifically, the advection-dispersion equation (ADE) is employed to understand the dynamics of virus spread and potential remedies. Numerical and Analytical solutions of two-dimensional advection dispersion equation are obtained to describe how the viruses spread from a point source along flow domain in heterogeneous medium. Waterborne disease, associated with contaminated water poses serious health issues. The dispersion co-efficient or flow velocity of the medium reacts inversely with the retardation term. To conceptualize temporal dependence, various combinations of linear, exponential, and asymptotic forms can be used. By introducing new space and time coordinates, the spatial-temporal coefficients of the ADE are simplified to constant values. The numerical solution of the virus transport problem is obtained by FTCS explicit method (Forward Time Central space method) and Laplace Integral transform technique is used to obtain the analytical solution and their graphical representation is made by MATLAB.