论文标题
多组SIS流行与简单和高阶相互作用
Multi-group SIS Epidemics with Simplicial and Higher-Order Interactions
论文作者
论文摘要
本文分析了易感感染感染的（SIS）模型的流行病传播对超图，并以重要的特殊情况的激励，我们将模型引用了Simplicial SIS模型。从经典上讲，多组SIS模型已经假设了跨组传染的成对相互作用，因此在文献中已经进行了广泛的研究。直到最近，才引起了更新的特别关注，以研究高阶相互作用和更通用的图形结构（如单纯形）的研究。 Simpicial SIS模型的平均场近似标量模型的先前工作表明，与经典SIS模型相比，新的动力学行为域是由于新引入的高阶相互作用项而出现的：无病平衡和一个地方性平衡共存，并且都是局部均不稳定的。本文正式确定了多组Simpicial SIS模型中也出现了双重性（作为一种新的流行病学行为）。我们为模型的参数提供了足够的条件，以使其外观和经典多组SIS模型中存在的其他行为域。我们还提供了一种算法来计算地方性平衡的值，并报告了从无疾病域到Bissable域的过渡的数值分析。
This paper analyzes a Susceptible-Infected-Susceptible (SIS) model of epidemic propagation over hypergraphs and, motivated by an important special case, we refer to the model as to the simplicial SIS model. Classically, the multi-group SIS model has assumed pairwise interactions of contagion across groups and thus has been vastly studied in the literature. It is only recently that a renewed special attention has been drawn to the study of contagion dynamics over higher-order interactions and over more general graph structures, like simplexes. Previous work on mean-field approximation scalar models of the simplicial SIS model has indicated that a new dynamical behavior domain, compared to the classical SIS model, appears due to the newly introduced higher order interaction terms: both a disease-free equilibrium and an endemic equilibrium co-exist and are both locally asymptotically stable. This paper formally establishes that bistability (as a new epidemiological behavior) also appears in the multi-group simplicial SIS model. We give sufficient conditions over the model's parameters for the appearance of this and the other behavioral domains present in the classical multi-group SIS model. We additionally provide an algorithm to compute the value of the endemic equilibrium and report numerical analysis of the transition from the disease-free domain to the bistable domain.
