Mean Field Analysis of Hypergraph Contagion Model

Desmond J Higham, Henry-louis De Kergorlay

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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 modelled over a hypergraph 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 individual-level, stochastic, susceptible-infected-susceptible models on a hypergraph, and focus on a mean field approximation proposed in [Arruda et al., Phys. Rev. Res., 2020]. 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 [Higham and de Kergorlay, Proc. Roy. Soc. A, 2021], and (c) numerical simulations of the microscale model.
Original languageEnglish
Pages (from-to)1987-2007
JournalSiam Journal on Applied Mathematics
Volume82
Issue number6
Early online date9 Dec 2022
DOIs
Publication statusPublished - 31 Dec 2022

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