Yin Shuangshuang, Wu Jianhong, Song Pengfei
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China.
Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics York University, Ontario, Toronto, CA.
Math Biosci Eng. 2023 Jun 12;20(7):13434-13456. doi: 10.3934/mbe.2023599.
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.
在本文中，我们建立了一个具有非对称迁移核的空间异质SEIRS斑块模型。定义了基本再生数$\mathcal{R}{0}$，并根据$\mathcal{R}{0}$研究了全局动力学的阈值型结果。在某些情况下，建立了$\mathcal{R}_{0}$关于异质扩散系数的单调性，但并非在所有情况下都成立。最后，当易感个体的扩散率趋于零时，探讨了地方病平衡点的长期行为。与大多数先前主要关注易感和有症状感染个体迁移的研究不同，我们的研究结果表明暴露和康复者的迁移在疾病动力学中的重要性。
