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

Shiwen Jing; Hairong Lian; Yiming Tang; Zhaohai Ma; Shiwen Jing; Hairong Lian; Yiming Tang; Zhaohai Ma

doi:10.3934/math.2024389

AIMS Mathematics

2024, Volume 9, Issue 4: 8001-8019. doi: 10.3934/math.2024389

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

School of Science, China University of Geosciences (Beijing), Beijing 100083, China

Received: 23 October 2023 Revised: 24 January 2024 Accepted: 02 February 2024 Published: 26 February 2024
MSC : 35K57, 92D30

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^* $.
- nonlocal dispersal,
- age structure,
- traveling waves,
- SIRS model,
- Laplace transform
Citation: Shiwen Jing, Hairong Lian, Yiming Tang, Zhaohai Ma. Traveling waves for a nonlocal dispersal SIRS epidemic model with age structure[J]. AIMS Mathematics, 2024, 9(4): 8001-8019. doi: 10.3934/math.2024389

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Abstract

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^* $.

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