The Discrete SIR Epidemic Reaction–Diffusion Model: Finite-Time Stability and Numerical Simulations
This paper investigates the finite-time stability (FTS) of a discrete SIR epidemic reaction–diffusion (R-D) model. The study begins with discretizing a continuous R-D system using finite difference methods (FDMs), ensuring that essential characteristics like positivity and consistency are maintained...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Computational and Mathematical Methods |
| Online Access: | http://dx.doi.org/10.1155/cmm4/9597093 |
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| author | Issam Bendib Ma’mon Abu Hammad Adel Ouannas Giuseppe Grassi |
| author_facet | Issam Bendib Ma’mon Abu Hammad Adel Ouannas Giuseppe Grassi |
| author_sort | Issam Bendib |
| collection | DOAJ |
| description | This paper investigates the finite-time stability (FTS) of a discrete SIR epidemic reaction–diffusion (R-D) model. The study begins with discretizing a continuous R-D system using finite difference methods (FDMs), ensuring that essential characteristics like positivity and consistency are maintained. The resulting discrete model captures the interplay between spatial heterogeneity, diffusion rates, and reaction dynamics, enabling a robust framework for theoretical analysis. Employing Lyapunov-based techniques and eigenvalue analysis, we derive sufficient conditions for achieving FTS, which is crucial for rapid epidemic containment. The theoretical findings are validated through comprehensive numerical simulations that examine the effects of varying diffusion coefficients, reaction rates, and boundary conditions on system stability. The results highlight the critical role of these factors in achieving FTS of epidemic dynamics. This work contributes to developing efficient computational tools and theoretical insights for modeling and controlling infectious diseases in spatially extended populations, providing a foundation for future research on fractional-order models and complex boundary conditions. |
| format | Article |
| id | doaj-art-c69e6f0d20cd4dbfa825e425aa1dafa7 |
| institution | DOAJ |
| issn | 2577-7408 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Computational and Mathematical Methods |
| spelling | doaj-art-c69e6f0d20cd4dbfa825e425aa1dafa72025-08-20T03:00:23ZengWileyComputational and Mathematical Methods2577-74082025-01-01202510.1155/cmm4/9597093The Discrete SIR Epidemic Reaction–Diffusion Model: Finite-Time Stability and Numerical SimulationsIssam Bendib0Ma’mon Abu Hammad1Adel Ouannas2Giuseppe Grassi3Applied Mathematics & Modeling LaboratoryDepartment of MathematicsDepartment of Mathematics and Computer ScienceDepartment of Innovation EngineeringThis paper investigates the finite-time stability (FTS) of a discrete SIR epidemic reaction–diffusion (R-D) model. The study begins with discretizing a continuous R-D system using finite difference methods (FDMs), ensuring that essential characteristics like positivity and consistency are maintained. The resulting discrete model captures the interplay between spatial heterogeneity, diffusion rates, and reaction dynamics, enabling a robust framework for theoretical analysis. Employing Lyapunov-based techniques and eigenvalue analysis, we derive sufficient conditions for achieving FTS, which is crucial for rapid epidemic containment. The theoretical findings are validated through comprehensive numerical simulations that examine the effects of varying diffusion coefficients, reaction rates, and boundary conditions on system stability. The results highlight the critical role of these factors in achieving FTS of epidemic dynamics. This work contributes to developing efficient computational tools and theoretical insights for modeling and controlling infectious diseases in spatially extended populations, providing a foundation for future research on fractional-order models and complex boundary conditions.http://dx.doi.org/10.1155/cmm4/9597093 |
| spellingShingle | Issam Bendib Ma’mon Abu Hammad Adel Ouannas Giuseppe Grassi The Discrete SIR Epidemic Reaction–Diffusion Model: Finite-Time Stability and Numerical Simulations Computational and Mathematical Methods |
| title | The Discrete SIR Epidemic Reaction–Diffusion Model: Finite-Time Stability and Numerical Simulations |
| title_full | The Discrete SIR Epidemic Reaction–Diffusion Model: Finite-Time Stability and Numerical Simulations |
| title_fullStr | The Discrete SIR Epidemic Reaction–Diffusion Model: Finite-Time Stability and Numerical Simulations |
| title_full_unstemmed | The Discrete SIR Epidemic Reaction–Diffusion Model: Finite-Time Stability and Numerical Simulations |
| title_short | The Discrete SIR Epidemic Reaction–Diffusion Model: Finite-Time Stability and Numerical Simulations |
| title_sort | discrete sir epidemic reaction diffusion model finite time stability and numerical simulations |
| url | http://dx.doi.org/10.1155/cmm4/9597093 |
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