Traveling waves for a nonlocal dispersal SIRS epidemic model with age structure

This paper focuses on a SIRS infectious model of nonlocal dispersal adopted with age structure. We primarily investigate the existence and nonexistence of traveling wave solutions connecting the disease-free equilibrium state and the endemic equilibrium state. To be more precise, we obtain the exist...

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Published inAIMS mathematics Vol. 9; no. 4; pp. 8001 - 8019
Main Authors Jing, Shiwen, Lian, Hairong, Tang, Yiming, Ma, Zhaohai
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
age structure
laplace transform
nonlocal dispersal
sirs model
traveling waves
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Summary:This paper focuses on a SIRS infectious model of nonlocal dispersal adopted with age structure. We primarily investigate the existence and nonexistence of traveling wave solutions connecting the disease-free equilibrium state and the endemic equilibrium state. To be more precise, we obtain the existence of traveling wave solutions by constructing suitable upper and lower solutions and then applying Schauder's fixed point theorem when $ R_0 > 1 $ and $ c > c^* $. In addition, we prove the nonexistence of traveling wave solutions by applying the Laplace transform for $ R_0 > 1 $ and $ 0 < c < c^* $.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024389