Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the complex dynamics induced by the network structure. We analyze one recently introduced model and derive important epidemiological quantities for the system. We derive the epidemic threshold and analyze the bifurcation that occurs, and we use asymptotic techniques to derive an approximation for the endemic equilibrium when it exists. We consider the sensitivity of this approximation to network parameters, and the implications for disease control measures are found to be in line with the results of existing studies.

近几十年来，基于网络的流行病传播模型变得越来越流行。尽管此类模型具有丰富的基础，但很少有人提出了用于模拟 SIS 型疾病的低维系统，以设法捕捉由网络结构引起的复杂动态。我们分析了一个最近引入的模型，并为该系统推导出了重要的流行病学数量。我们推导出流行阈值并分析发生的分岔，并使用渐近技术推导出流行均衡存在时的近似值。我们考虑了这种近似对网络参数的敏感性，并且发现对疾病控制措施的影响与现有研究的结果一致。