Disease extinction for susceptible–infected–susceptible models on dynamic graphs and hypergraphs

Abstract

We consider stochastic, individual-level susceptible–infected–susceptible models for the spread of disease, opinion, or information on dynamic graphs and hypergraphs. We set up “snapshot” models where the interactions at any time are independently and identically sampled from an underlying distribution that represents a typical scenario. In the hypergraph case, this corresponds to a new Gilbert-style random hypergraph model. After justifying this modeling regime, we present useful mean field approximations. With an emphasis on the derivation of spectral conditions that determine long-time extinction, we give computational simulations and accompanying theoretical analysis for the exact models and their mean field approximations.