Bi-SIS Epidemics on Graphs - Quantitative Analysis of Coexistence Equilibria
Bi-SIS Epidemics on Graphs - Quantitative Analysis of Coexistence Equilibria
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DOI：
10.1109/cdc51059.2022.9992411
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
Vishwaraj Doshi;Jie Hu;Do Young Eun
中科院分区：
文献类型：
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作者：
Vishwaraj Doshi;Jie Hu;Do Young Eun
我们考虑一个系统，其中两个病毒的易感-感染-易感（SIS）类型的竞争一般，重叠的图形。虽然这样的系统一直是最近的许多作品的焦点，他们主要是在收敛分析的意义上进行了研究，没有现有的结果量化的非平凡的共存平衡（CE）-也就是说，当两个竞争病毒保持长期存在的网络。在本文中，我们证明了单调性的CE相对于有效的两种病毒的感染率，并提供了第一个定量分析的形式，涉及谱半径的基础图形，以及相关的单病毒系统的正平衡的上界，这样的平衡。我们的研究结果提供了更深入的了解长期感染概率如何受到系统参数的影响，我们通过数值结果进一步强调。
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.