论文标题
图表上的双 - sis流行病 - 共存平衡的定量分析
Bi-SIS Epidemics on Graphs -- Quantitative Analysis of Coexistence Equilibria
论文作者
论文摘要
我们考虑了一个系统，其中易感感染感染的两种病毒（SIS）类型竞争了一般的覆盖图。尽管此类系统一直是许多最近作品的重点，但它们主要是在收敛分析意义上进行的，没有现有的结果来量化非平处共存平衡（CE），也就是说，当两种竞争性病毒在网络上保持长期存在时。在本文中，我们证明了CE相对于两种病毒的有效感染率的单调性，并以涉及基础图的光谱半径的上限形式对这种均衡进行了首次定量分析，以及相关单病毒系统的正均衡。我们的结果提供了更深入的了解，了解长期感染概率如何受系统参数的影响，我们通过数值结果进一步强调了这一点。
We consider a system in which two viruses of the Susceptible-Infected-Susceptible (SIS) type compete over general, overlaid graphs. While such systems have been the focus of many recent works, they have mostly been studied in the sense of convergence analysis, with no existing results quantifying the non-trivial coexistence equilibria (CE) - that is, when both competing viruses maintain long term presence over the network. In this paper, we prove monotonicity of the CE with respect to effective infection rates of the two viruses, and provide the first quantitative analysis of such equilibria in the form of upper bounds involving spectral radii of the underlying graphs, as well as positive equilibria of related single-virus systems. Our results provide deeper insight into how the long term infection probabilities are affected by system parameters, which we further highlight via numerical results.
