| Abstract: |
| Contact networks are a paradigmatic model for understanding disease transmission in heterogenous populations. Typical methods approach this via an averaging over nodes of the same degree. We (with Moore and Wang) have show that a modified concept of network dimension can achieve a better prediction of behaviour including endemic state in SIS models. Recent work has shifted attention to transmission on hypergraphs. In this setting the higher order connection are introduced to model higher order interaction process and introduce additional.complication to the analysis. We show that the dynamics observed in these higher order models is always equivalent to dynamics on a lower-order (network) model with time varying disease parameters. While the hypergraphs may be better suited to modelling certain situations they do not introduce dynamical behaviour not present in lower order models. |
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