齐次网络上SIRS流行病模型的几何分析
A geometric analysis of the SIRS epidemiological model on a homogeneous network
摘要：
本文研究了齐次图上的SIRS流行病模型的一个快-慢版本，该模型是通过应用矩封闭方法得到的。我们使用GSPT来研究该模型，考虑到感染期比免疫的平均持续时间短得多。我们表明，动态发生通过一系列的快速和缓慢的流动，可以通过2维地图，在某些假设下，可以近似为1维地图。使用这种方法，与数值分歧工具，我们表明，该模型可以产生周期解，不同的是相应的模型的基础上均匀混合。
英文摘要：
We study a fast-slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
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