A Nonstandard Finite Difference Scheme for an SEIQR Epidemiological PDE Model
For researchers in mathematical epidemiology and numerical analysis, this work provides a structure-preserving numerical method for reaction-diffusion epidemic models, though it is an incremental contribution.
The paper develops a nonstandard finite difference scheme for an SEIQR epidemiological PDE model that preserves positivity, boundedness, and stability, with numerical simulations confirming the scheme's effectiveness.
This paper introduces a nonstandard finite difference (NSFD) approach to a reaction-diffusion SEIQR epidemiological model, which captures the spatiotemporal dynamics of infectious disease transmission. Formulated as a system of semilinear parabolic partial differential equations (PDEs), the model extends classical compartmental models by incorporating spatial diffusion to account for population movement and spatial heterogeneity. The proposed NSFD discretization is designed to preserve the continuous model's essential qualitative features, such as positivity, boundedness, and stability, which are often compromised by standard finite difference methods. We rigorously analyze the model's well-posedness, construct a structure-preserving NSFD scheme for the PDE system, and study its convergence and local truncation error. Numerical simulations validate the theoretical findings and demonstrate the scheme's effectiveness in preserving biologically consistent dynamics.