一类带扩散对流SIS模型的全局吸引子
Global Attractor of the SIS Epidemic Model with Diffusion and Convection
DOI: 10.12677/AAM.2023.124179, PDF,    科研立项经费支持
作者: 李得旺, 梅林锋*：浙江师范大学数学科学学院，浙江 金华
关键词: SIS模型；基本再生数；稳定性；SIS Model； The Basic Reproduction Number； Stability
摘要: 本文研究一类SIS (Susceptible-Infected-Susceptible)反应扩散对流传染病模型。该模型在加入对流项q后，我们可以更好地模拟生物种群在受到被动影响时的动力行为。我们研究了该模型的基本再生数 对模型两类平衡点稳定性的影响。当基本再生数 时，无病平衡点是线性稳定的，当 时，无病平衡点是不稳定的。此时通过动力系统的知识我们证明了正全局吸引子的存在性， 由此也可得到正疾病平衡点的存在性。
Abstract: In this paper, we study a class of SIS reaction diffusion convective infectious disease model. Adding convection term, we can better simulate the outcomes of biological populations. We study the ef-fects of the basic reproduction number on stability of the two types of equilibrium points of the model. When , disease-free equilibrium is linearly stable, while when , disease-free equilibrium is not linearly stable. In the later case, using theory of dynamical systems, we proved the existence of a positive global attractor of the system, and as a consequence, the existence of at least one positive equilibrium.
文章引用：李得旺, 梅林锋. 一类带扩散对流SIS模型的全局吸引子[J]. 应用数学进展, 2023, 12(4): 1722-1731. https://doi.org/10.12677/AAM.2023.124179

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