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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Main Author: Rassim Darazirar
Format: Article
Language:English
Published: Universidade Estadual do Sudoeste da Bahia (UESB) 2024-12-01
Series:Intermaths
Subjects:
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
description 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.
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