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

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。

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.