  Network epidemic simulation holds the promise of enabling fine-grained
understanding of epidemic behavior, beyond that which is possible with
coarse-grained compartmental models. Key inputs to these epidemic simulations
are the networks themselves. However, empirical measurements and samples of
realistic interaction networks typically display properties that are
challenging to capture with popular synthetic models of networks. Our empirical
results show that epidemic spread behavior is very sensitive to a subtle but
ubiquitous form of multi-scale local structure that is not present in common
baseline models, including (but not limited to) uniform random graph models
(Erdos-Renyi), random configuration models (Chung-Lu), etc. Such structure is
not necessary to reproduce very simple network statistics, such as degree
distributions or triangle closing probabilities. However, we show that this
multi-scale local structure impacts, critically, the behavior of more complex
network properties, in particular the effect of interventions such as
quarantining; and it enables epidemic spread to be halted in realistic
interaction networks, even when it cannot be halted in simple synthetic models.
Key insights from our analysis include how epidemics on networks with
widespread multi-scale local structure are easier to mitigate, as well as
characterizing which nodes are ultimately not likely to be infected. We
demonstrate that this structure results from more than just local triangle
structure in the network, and we illustrate processes based on homophily or
social influence and random walks that suggest how this multi-scale local
structure arises.
