Competing Epidemics on Graphs - Global Convergence and Coexistence
Competing Epidemics on Graphs - Global Convergence and Coexistence
复制标题
DOI：
10.1109/infocom42981.2021.9488828
复制
发表时间：
2021-04
期刊：
影响因子：
--
通讯作者：
Vishwaraj Doshi;Shailaja Mallick;Do Young Eun
中科院分区：
文献类型：
--
作者：
Vishwaraj Doshi;Shailaja Mallick;Do Young Eun
近年来，著名的易感-易感(SIS)流行病模型有效地捕捉了诸如病毒、传染病甚至谣言/意见等传染病在接触网络(GRAPH)上的传播动态。当涉及到在重叠图上传播的两种这样的传染病之间的竞争时，它们的传播被所谓的双病毒流行病模型所捕获。对这类动力系统的分析包括确定平衡点及其收敛性质，这决定了病毒是消亡还是共存。我们展示了现有的工作如何不能成功地刻画模型参数空间的一个大的子集，包括双病毒系统的竞争力足以达到流行病共存的所有参数。在本文中，我们填补了这一空白，得到了整个模型参数空间的收敛结果；给出了系统全局收敛到三种可能结果的精确条件(充要条件)：无病毒状态、单病毒状态和共存状态--第一个这样的结果。
The dynamics of the spread of contagions such as viruses, infectious diseases or even rumors/opinions over contact networks (graphs) have effectively been captured by the well known Susceptible-Infected-Susceptible (SIS) epidemic model in recent years. When it comes to competition between two such contagions spreading on overlaid graphs, their propagation is captured by so-called bi-virus epidemic models. Analysis of such dynamical systems involve the identification of equilibrium points and its convergence properties, which determine whether either of the viruses dies out, or both survive together. We demonstrate how the existing works are unsuccessful in characterizing a large subset of the model parameter space, including all parameters for which the competitiveness of the bi-virus system is significant enough to attain coexistence of the epidemics. In this paper, we fill in this void and obtain convergence results for the entirety of the model parameter space; giving precise conditions (necessary and sufficient) under which the system globally converges to a trichotomy of possible outcomes: a virus-free state, a single-virus state, and to a coexistence state – the first such result.