论文标题
SIR，SIR和SIRWS流行病学模型的几何分析
A geometric analysis of the SIR, SIRS and SIRWS epidemiological models
论文作者
论文摘要
我们研究SIR，SIRS和SIRWS流行病学模型的快速慢版本。引入多个时间尺度行为以说明流行病学途径的某些速率之间的巨大差异。我们的主要目的是证明即使以非标准形式以几何奇异扰动理论（GSPT）来研究快速慢模型。特别是，在不使用Lyapunov的方法的情况下，我们不仅能够分析地方性均衡的稳定性，而且还可以表明在某些模型中限制了循环。我们表明，所提出的方法在更复杂（更高维）模型（例如SIRWS模型）中特别有用，为此我们通过结合分析和数值技术来详细描述其动力学。
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.
