MEAN FIELD ANALYSIS OF HYPERGRAPH CONTAGION MODELS
MEAN FIELD ANALYSIS OF HYPERGRAPH CONTAGION MODELS
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DOI：
10.1137/21m1440219
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发表时间：
2022-01-01
影响因子：
1.9
通讯作者：
De Kergorlay, Henry-Louis
中科院分区：
文献类型：
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作者：
Higham, Desmond John;De Kergorlay, Henry-Louis
我们通常以小组形式互动，而不仅仅是成对的。出于这个原因，最近有人提出，信息、观点或疾病的传播应该在超图而不是标准图上建模。超边的使用自然允许在群体大小和感染群体成员的数量方面的非线性传播率，例如当鼓励社会距离时就是这种情况。我们在超图上考虑了一类一般的个体水平的、随机的、敏感的、易感染的模型，并重点讨论了在[G.F.de Arruda，G.Petri，and Y.Moreno，Phys.]中提出的平均场近似。修订决议，2(2020年)，023032]。我们推导了平均场模型预测无传染状态的局部或全局稳定性的谱条件。我们还将这些结果与[D.J.Higham和H.-L.de Kergorlay，Proc.]中导出的精确过程的平均衰变为零的新条件和不同平均场近似的条件进行了比较。A，477(2021年)，20210232]，和(C)微尺度模型的数值模拟。
We typically interact in groups, not just in pairs. For this reason, it has recently been proposed that the spread of information, opinion, or disease should be modeled over a hyper-graph rather than a standard graph. The use of hyperedges naturally allows for a nonlinear rate of transmission, in terms of both the group size and the number of infected group members, as is the case, for example, when social distancing is encouraged. We consider a general class of individuallevel, stochastic, susceptible-infected-susceptible models on a hypergraph, and focus on a mean field approximation proposed in [G. F. de Arruda, G. Petri, and Y. Moreno, Phys. Rev. Res., 2 (2020), 023032]. We derive spectral conditions under which the mean field model predicts local or global stability of the infection-free state. We also compare these results with (a) a new condition that we derive for decay to zero in mean for the exact process, (b) conditions for a different mean field approximation in [D. J. Higham and H.-L. de Kergorlay, Proc. A, 477 (2021), 20210232], and (c) numerical simulations of the microscale model.