A Nonstandard Finite Difference Scheme for an SEIQR Epidemiological PDE Model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918510566834176 |
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| author | Zinihi, Achraf Ehrhardt, Matthias Ammi, Moulay Rchid Sidi |
| author_facet | Zinihi, Achraf Ehrhardt, Matthias Ammi, Moulay Rchid Sidi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_02928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Nonstandard Finite Difference Scheme for an SEIQR Epidemiological PDE Model Zinihi, Achraf Ehrhardt, Matthias Ammi, Moulay Rchid Sidi Quantitative Methods Numerical Analysis Dynamical Systems 92D30, 65M06, 35K57, 37N30 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. |
| title | A Nonstandard Finite Difference Scheme for an SEIQR Epidemiological PDE Model |
| topic | Quantitative Methods Numerical Analysis Dynamical Systems 92D30, 65M06, 35K57, 37N30 |
| url | https://arxiv.org/abs/2508.02928 |