标题： 一种用于SEIQR流行病学PDE模型的非标准有限差分格式 显示英文标题

标题： A Nonstandard Finite Difference Scheme for an SEIQR Epidemiological PDE Model

摘要： 本文介绍了一种非标准有限差分（NSFD）方法，用于反应扩散SEIQR流行病学模型，该模型捕捉传染病传播的时空动力学。 作为半线性抛物型偏微分方程（PDEs）系统构建的模型，通过引入空间扩散来考虑人口流动和空间异质性，扩展了经典的分 compartment 模型。 所提出的NSFD离散化方法旨在保持连续模型的基本定性特征，如正性、有界性和稳定性，这些特性通常会被标准有限差分方法破坏。 我们严格分析了模型的适定性，为PDE系统构建了一个结构保持的NSFD方案，并研究了其收敛性和局部截断误差。 数值模拟验证了理论结果，并展示了该方案在保持生物上一致动力学方面的有效性。 显示英文摘要

摘要： 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.