A mathematical study of the influence of media on the asymptotic dynamics of diseases
This study explores the asymptotic behavior of a stochastic epidemic model that accounts for the impact of media coverage. The initial focus lies on determining the conditions leading to the exponential extinction of the disease. Additionally, we investigate the weak convergence of the probability d...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003681 |
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| author | Lahcen Boulaasair Hassane Bouzahir N. Seshagiri Rao Salma Haque Nabil Mlaiki |
| author_facet | Lahcen Boulaasair Hassane Bouzahir N. Seshagiri Rao Salma Haque Nabil Mlaiki |
| author_sort | Lahcen Boulaasair |
| collection | DOAJ |
| description | This study explores the asymptotic behavior of a stochastic epidemic model that accounts for the impact of media coverage. The initial focus lies on determining the conditions leading to the exponential extinction of the disease. Additionally, we investigate the weak convergence of the probability distribution of the stochastic process N(t), representing the total population, to a one-dimensional stochastic process with density calculated through the Fokker–Planck equation. Subsequently, we demonstrate the persistent nature of the disease and utilize Has’minskii theory to establish the presence of a unique ergodic stationary distribution for our stochastic epidemic model. Finally, numerical simulations are conducted to validate the theoretical findings. |
| format | Article |
| id | doaj-art-e1ab7f42469c45868d1cac5b3fc4ef63 |
| institution | DOAJ |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-e1ab7f42469c45868d1cac5b3fc4ef632025-08-20T02:50:09ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210098210.1016/j.padiff.2024.100982A mathematical study of the influence of media on the asymptotic dynamics of diseasesLahcen Boulaasair0Hassane Bouzahir1N. Seshagiri Rao2Salma Haque3Nabil Mlaiki4ISTI Lab, ENSA, Ibn Zohr University, Agadir, MoroccoISTI Lab, ENSA, Ibn Zohr University, Agadir, MoroccoDepartment of Mathematics & Statistics, School of Applied Science & Humanities, Vignan’s Foundation for Science, Technology & Research, Vadlamudi 522213, Andhra Pradesh, IndiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia; Corresponding author.This study explores the asymptotic behavior of a stochastic epidemic model that accounts for the impact of media coverage. The initial focus lies on determining the conditions leading to the exponential extinction of the disease. Additionally, we investigate the weak convergence of the probability distribution of the stochastic process N(t), representing the total population, to a one-dimensional stochastic process with density calculated through the Fokker–Planck equation. Subsequently, we demonstrate the persistent nature of the disease and utilize Has’minskii theory to establish the presence of a unique ergodic stationary distribution for our stochastic epidemic model. Finally, numerical simulations are conducted to validate the theoretical findings.http://www.sciencedirect.com/science/article/pii/S2666818124003681Disease dynamicsMedia coverageExponential extinctionPersistence in meanFokker–Planck equationStationary distribution |
| spellingShingle | Lahcen Boulaasair Hassane Bouzahir N. Seshagiri Rao Salma Haque Nabil Mlaiki A mathematical study of the influence of media on the asymptotic dynamics of diseases Partial Differential Equations in Applied Mathematics Disease dynamics Media coverage Exponential extinction Persistence in mean Fokker–Planck equation Stationary distribution |
| title | A mathematical study of the influence of media on the asymptotic dynamics of diseases |
| title_full | A mathematical study of the influence of media on the asymptotic dynamics of diseases |
| title_fullStr | A mathematical study of the influence of media on the asymptotic dynamics of diseases |
| title_full_unstemmed | A mathematical study of the influence of media on the asymptotic dynamics of diseases |
| title_short | A mathematical study of the influence of media on the asymptotic dynamics of diseases |
| title_sort | mathematical study of the influence of media on the asymptotic dynamics of diseases |
| topic | Disease dynamics Media coverage Exponential extinction Persistence in mean Fokker–Planck equation Stationary distribution |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003681 |
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