A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion

In this paper, we propose an efficient numerical method for a comprehensive infection model that is formulated by system of nonlinear coupling advection-diffusion-reaction equations. Using some subtle mixed explicit-implicit treatments, construct linearized and decoupled discrete scheme. Moreover, the proposed scheme capable preserving positivity variables, which essential requirement under consideration. The uses cell-centered finite difference spatial discretization, thus, it easy to implement. diffusion terms are treated implicitly improve robustness A semi-implicit upwind approach discretize advection terms, distinctive feature resulting preserve variables without any restriction on mesh size time step size. We rigorously prove unique existence solutions positivity-preserving property requirements It worthwhile note these properties proved using variational principles rather than conventional approaches matrix analysis. Numerical results also provided assess performance