SIR、SIRS和SIRWS流行病模型的几何分析
A geometric analysis of the SIR, SIRS and SIRWS epidemiological models
摘要：
我们研究了SIR、SIRS和SIRWS流行病学模型的快-慢版本。多个时间尺度的行为被引入到解释流行病学途径的一些速率之间的巨大差异。我们的主要目的是表明，快-慢模型，即使在非标准形式，可以研究的几何奇异扰动理论（GSPT）。特别是，不使用李雅普诺夫方法，我们不仅能够分析地方病平衡点的稳定性，但也表明，在某些模型中出现极限环。我们表明，所提出的方法是特别有用的，在更复杂的（高维）模型，如SIRWS模型，我们提供了一个详细的描述，其动力学分析和数值技术相结合。
英文摘要：
We study fast-slow versions of the SIR, SIRS, and SIRWS epidemiological models. The multiple time scale behavior is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is to show that the fast-slow models, even though in nonstandard form, can be studied by means of Geometric Singular Perturbation Theory (GSPT). In particular, without using Lyapunov's method, we are able to not only analyze the stability of the endemic equilibria but also to show that in some of the models limit cycles arise. We show that the proposed approach is particularly useful in more complicated (higher dimensional) models such as the SIRWS model, for which we provide a detailed description of its dynamics by combining analytic and numerical techniques.
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