A Nonstandard Finite Difference Scheme for an SEIQR Epidemiological PDE Model

TL;DR

This paper develops a structure-preserving nonstandard finite difference scheme for a reaction-diffusion SEIQR epidemiological PDE model, ensuring qualitative features like positivity and stability are maintained.

Contribution

It introduces a novel NSFD discretization for the PDE model that preserves key qualitative properties and analyzes its convergence and stability.

Findings

The scheme preserves positivity, boundedness, and stability.

Numerical simulations confirm the scheme's effectiveness.

The method accurately captures spatiotemporal disease dynamics.

Abstract

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.