Analysis of a heterogeneous SEIRS patch model with asymmetric mobility kernel

Shuangshuang Yin; Jianhong Wu; Pengfei Song; Shuangshuang Yin; Jianhong Wu; Pengfei Song

doi:10.3934/mbe.2023599

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 7: 13434-13456. doi: 10.3934/mbe.2023599

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Analysis of a heterogeneous SEIRS patch model with asymmetric mobility kernel

1.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China
2.
Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics York University, Ontario, Toronto, CA

Academic Editor: Xiang-Sheng Wang

Received: 22 March 2023 Revised: 29 May 2023 Accepted: 07 June 2023 Published: 12 June 2023

In this paper, we establish a spatial heterogeneous SEIRS patch model with asymmetric mobility kernel. The basic reproduction ratio $ \mathcal{R}_{0} $ is defined, and threshold-type results on global dynamics are investigated in terms of $ \mathcal{R}_{0} $. In certain cases, the monotonicity of $ \mathcal{R}_{0} $ with respect to the heterogeneous diffusion coefficients is established, but this is not true in all cases. Finally, when the diffusion rate of susceptible individuals approaches zero, the long-term behavior of the endemic equilibrium is explored. In contrast to most prior studies, which focused primarily on the mobility of susceptible and symptomatic infected individuals, our findings indicate the significance of the mobility of exposed and recovered persons in disease dynamics.
- SEIRS epidemic model,
- asymmetric mobility kernel,
- basic reproduction number,
- spatial heterogeneity
Citation: Shuangshuang Yin, Jianhong Wu, Pengfei Song. Analysis of a heterogeneous SEIRS patch model with asymmetric mobility kernel[J]. Mathematical Biosciences and Engineering, 2023, 20(7): 13434-13456. doi: 10.3934/mbe.2023599

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Abstract

In this paper, we establish a spatial heterogeneous SEIRS patch model with asymmetric mobility kernel. The basic reproduction ratio $ \mathcal{R}_{0} $ is defined, and threshold-type results on global dynamics are investigated in terms of $ \mathcal{R}_{0} $. In certain cases, the monotonicity of $ \mathcal{R}_{0} $ with respect to the heterogeneous diffusion coefficients is established, but this is not true in all cases. Finally, when the diffusion rate of susceptible individuals approaches zero, the long-term behavior of the endemic equilibrium is explored. In contrast to most prior studies, which focused primarily on the mobility of susceptible and symptomatic infected individuals, our findings indicate the significance of the mobility of exposed and recovered persons in disease dynamics.

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