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 |
| Subjects: | |
| Online Access: | https://periodicos2.uesb.br/index.php/intermaths/article/view/15692 |
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| Summary: | 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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| ISSN: | 2675-8318 |