Stability analysis and numerical simulations of a discrete-time epidemic model
This research investigates a discrete epidemic reaction–diffusion model, focusing on the nuances of both local and global stability. By employing second-order difference schemes alongside L1 approximations, we establish a robust numerical framework for simulating disease spread. The analysis begins...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000452 |
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| author | Iqbal M. Batiha Mohammad S. Hijazi Amel Hioual Adel Ouannas Mohammad Odeh Shaher Momani |
| author_facet | Iqbal M. Batiha Mohammad S. Hijazi Amel Hioual Adel Ouannas Mohammad Odeh Shaher Momani |
| author_sort | Iqbal M. Batiha |
| collection | DOAJ |
| description | This research investigates a discrete epidemic reaction–diffusion model, focusing on the nuances of both local and global stability. By employing second-order difference schemes alongside L1 approximations, we establish a robust numerical framework for simulating disease spread. The analysis begins with a thorough examination of two crucial equilibrium points: the disease-free equilibrium, which signifies complete eradication of the disease, and the endemic equilibrium, where the disease persists within the population. Through this exploration, we seek to identify the specific conditions that can lead to either successful containment or ongoing infection. To assess the global stability of the system, we utilize the Lyapunov method, a powerful analytical technique that enables us to derive sufficient conditions for global asymptotic stability. This rigorous methodology guarantees that, under defined conditions, the system will ultimately reach a stable equilibrium, irrespective of any initial perturbations. Complementing our theoretical framework, we conduct numerical simulations that validate our stability results. These simulations provide deeper insights into the system’s dynamic behavior, illustrating how various parameters and conditions influence its evolution. Moreover, the numerical simulations not only reinforce our theoretical findings but also facilitate the visualization and interpretation of the system’s complex dynamics. This synergy between analytical rigor and numerical validation enhances the reliability of our model, establishing it as a critical tool for understanding epidemic propagation and developing effective control strategies. Our comprehensive investigation thus enriches both the theoretical landscape of reaction–diffusion systems and their practical implications for managing disease outbreaks. |
| format | Article |
| id | doaj-art-3fa56ecad1f448baafd7c376de28e0b6 |
| institution | DOAJ |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-3fa56ecad1f448baafd7c376de28e0b62025-08-20T02:43:20ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-011310111810.1016/j.padiff.2025.101118Stability analysis and numerical simulations of a discrete-time epidemic modelIqbal M. Batiha0Mohammad S. Hijazi1Amel Hioual2Adel Ouannas3Mohammad Odeh4Shaher Momani5Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, United Arab Emirates; Corresponding author at: Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan.Department of Mathematics, College of Sciences, Jouf University, Sakaka, Saudi ArabiaDepartment of Mathematics and Computer Science, University of Oum EL-Bouaghi, Oum El Bouaghi 04000, AlgeriaDepartment of Mathematics and Computer Science, University of Oum EL-Bouaghi, Oum El Bouaghi 04000, AlgeriaDepartment of Mathematics, College of Sciences, Jouf University, Tabarjal, Saudi ArabiaNonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, United Arab Emirates; Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanThis research investigates a discrete epidemic reaction–diffusion model, focusing on the nuances of both local and global stability. By employing second-order difference schemes alongside L1 approximations, we establish a robust numerical framework for simulating disease spread. The analysis begins with a thorough examination of two crucial equilibrium points: the disease-free equilibrium, which signifies complete eradication of the disease, and the endemic equilibrium, where the disease persists within the population. Through this exploration, we seek to identify the specific conditions that can lead to either successful containment or ongoing infection. To assess the global stability of the system, we utilize the Lyapunov method, a powerful analytical technique that enables us to derive sufficient conditions for global asymptotic stability. This rigorous methodology guarantees that, under defined conditions, the system will ultimately reach a stable equilibrium, irrespective of any initial perturbations. Complementing our theoretical framework, we conduct numerical simulations that validate our stability results. These simulations provide deeper insights into the system’s dynamic behavior, illustrating how various parameters and conditions influence its evolution. Moreover, the numerical simulations not only reinforce our theoretical findings but also facilitate the visualization and interpretation of the system’s complex dynamics. This synergy between analytical rigor and numerical validation enhances the reliability of our model, establishing it as a critical tool for understanding epidemic propagation and developing effective control strategies. Our comprehensive investigation thus enriches both the theoretical landscape of reaction–diffusion systems and their practical implications for managing disease outbreaks.http://www.sciencedirect.com/science/article/pii/S2666818125000452Discrete reaction–diffusion dynamicsEpidemic modelLocal–global stability |
| spellingShingle | Iqbal M. Batiha Mohammad S. Hijazi Amel Hioual Adel Ouannas Mohammad Odeh Shaher Momani Stability analysis and numerical simulations of a discrete-time epidemic model Partial Differential Equations in Applied Mathematics Discrete reaction–diffusion dynamics Epidemic model Local–global stability |
| title | Stability analysis and numerical simulations of a discrete-time epidemic model |
| title_full | Stability analysis and numerical simulations of a discrete-time epidemic model |
| title_fullStr | Stability analysis and numerical simulations of a discrete-time epidemic model |
| title_full_unstemmed | Stability analysis and numerical simulations of a discrete-time epidemic model |
| title_short | Stability analysis and numerical simulations of a discrete-time epidemic model |
| title_sort | stability analysis and numerical simulations of a discrete time epidemic model |
| topic | Discrete reaction–diffusion dynamics Epidemic model Local–global stability |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125000452 |
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