Department of Mathematics, North University of China, Taiyuan 030051, Shanxi, China.
Math Biosci Eng. 2022 Aug 5;19(11):11217-11231. doi: 10.3934/mbe.2022523.
In this paper, a two-patch SIS model with saturating contact rate and one-directing population dispersal is proposed. In the model, individuals can only migrate from patch 1 to patch 2. The basic reproduction number $ R_0^1 $ of patch 1 and the basic reproduction number $ R_0^2 $ of patch 2 is identified. The global dynamics are completely determined by the two reproduction numbers. It is shown that if $ R_0^1 < 1 $ and $ R_0^2 < 1 $, the disease-free equilibrium is globally asymptotically stable; if $ R_0^1 < 1 $ and $ R_0^2 > 1 $, there is a boundary equilibrium which is globally asymptotically stable; if $ R_0^1 > 1 $, there is a unique endemic equilibrium which is globally asymptotically stable. Finally, numerical simulations are performed to validate the theoretical results and reveal the influence of saturating contact rate and migration rate on basic reproduction number and the transmission scale.
本文提出了一个具有饱和接触率和单向人口扩散的两斑块 SIS 模型。在该模型中，个体只能从斑块 1 迁移到斑块 2。斑块 1 的基本再生数$R_0^1$和斑块 2 的基本再生数$R_0^2$被确定。全局动力学完全由两个再生数决定。结果表明，如果$R_0^1 < 1$且$R_0^2 < 1$，则无病平衡点全局渐近稳定；如果$R_0^1 < 1$且$R_0^2 > 1$，则存在边界平衡点全局渐近稳定；如果$R_0^1 > 1$，则存在唯一的地方平衡点全局渐近稳定。最后，通过数值模拟验证了理论结果，并揭示了饱和接触率和迁移率对基本再生数和传播规模的影响。
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