Traveling Waves in a Kermack-McKendric Epidemic Model
This study explores the existence of traveling wave solutions in the classical Kermack-McKendrick epidemic model with local diffusive. The findings highlight the critical role of the basic reproduction number $R_0$in shaping wave dynamics. Traveling wave solutions are shown to exist for wave speeds...
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| Format: | Article |
| Language: | English |
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Universidade Estadual do Sudoeste da Bahia (UESB)
2024-12-01
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| Series: | Intermaths |
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| Online Access: | https://periodicos2.uesb.br/index.php/intermaths/article/view/15692 |
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| author | Rassim Darazirar |
| author_facet | Rassim Darazirar |
| author_sort | Rassim Darazirar |
| collection | DOAJ |
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This study explores the existence of traveling wave solutions in the classical Kermack-McKendrick epidemic model with local diffusive. The findings highlight the critical role of the basic reproduction number $R_0$in shaping wave dynamics. Traveling wave solutions are shown to exist for wave speeds $c \geq c^*$ when $R_0> 1$, with $c^*$ denoting the minimal wave speed. Conversely, no traveling waves are observed for $c<c^*$ or $R_0<1$. Numerical simulations are employed to validate the theoretical results, demonstrating the presence of traveling waves for a range of nonlinear incidence functions and offering insights into the spatial spread.
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| format | Article |
| id | doaj-art-e88e0230791c442da106780da049943b |
| institution | DOAJ |
| issn | 2675-8318 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Universidade Estadual do Sudoeste da Bahia (UESB) |
| record_format | Article |
| series | Intermaths |
| spelling | doaj-art-e88e0230791c442da106780da049943b2025-08-20T02:58:41ZengUniversidade Estadual do Sudoeste da Bahia (UESB)Intermaths2675-83182024-12-015210.22481/intermaths.v5i2.15692Traveling Waves in a Kermack-McKendric Epidemic ModelRassim Darazirar0Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, 02000, Chlef, Algeria This study explores the existence of traveling wave solutions in the classical Kermack-McKendrick epidemic model with local diffusive. The findings highlight the critical role of the basic reproduction number $R_0$in shaping wave dynamics. Traveling wave solutions are shown to exist for wave speeds $c \geq c^*$ when $R_0> 1$, with $c^*$ denoting the minimal wave speed. Conversely, no traveling waves are observed for $c<c^*$ or $R_0<1$. Numerical simulations are employed to validate the theoretical results, demonstrating the presence of traveling waves for a range of nonlinear incidence functions and offering insights into the spatial spread. https://periodicos2.uesb.br/index.php/intermaths/article/view/15692Kermack-McKendrick modelminimal wave speedtraveling wavesbasic reproduction number |
| spellingShingle | Rassim Darazirar Traveling Waves in a Kermack-McKendric Epidemic Model Intermaths Kermack-McKendrick model minimal wave speed traveling waves basic reproduction number |
| title | Traveling Waves in a Kermack-McKendric Epidemic Model |
| title_full | Traveling Waves in a Kermack-McKendric Epidemic Model |
| title_fullStr | Traveling Waves in a Kermack-McKendric Epidemic Model |
| title_full_unstemmed | Traveling Waves in a Kermack-McKendric Epidemic Model |
| title_short | Traveling Waves in a Kermack-McKendric Epidemic Model |
| title_sort | traveling waves in a kermack mckendric epidemic model |
| topic | Kermack-McKendrick model minimal wave speed traveling waves basic reproduction number |
| url | https://periodicos2.uesb.br/index.php/intermaths/article/view/15692 |
| work_keys_str_mv | AT rassimdarazirar travelingwavesinakermackmckendricepidemicmodel |