Social Bubbles and Superspreaders: Source Identification for Contagion Processes on Hypertrees

Previous work has shown that for contagion processes on extended star networks (trees with exactly one node of degree > 2), there is a simple, closed-form expression for a highly accurate approximation to the maximum likelihood infection source. Here, we generalize that result to a class of hypertrees which, although somewhat structurally analogous, provides a much richer representation space. In particular, this approach can be used to estimate patient zero sources, even when the infection has been propagated via large group gatherings rather than person-to-person spread, and when it is spreading through interrelated social bubbles with varying degrees of overlap. In contact tracing contexts, this estimator may be used to identify the source of a local outbreak, which can then be used for forward tracing or for further backward tracing (by similar or other means) to an upstream source.