Susceptible–infected epidemics on evolving graphs

Abstract

The evoSIR model is a modification of the usual SIR process on a graph G in which S − I connections are broken at rate ρ and the S connects to a randomly chosen vertex.The evoSI model is the same as evoSIR but recovery is impossible. In [14] the critical value for evoSIR was computed and simulations showed that when G is an Erdős-Rényi graph with mean degree 5, the system has a discontinuous phase transition, i.e., as the infection rate λ decreases to λc, the fraction of individuals infected during the epidemic does not converge to 0. In this paper we study evoSI dynamics on graphs generated by the configuration model. We show that there is a quantity ∆ determined by the first three moments of the degree distribution, so that the phase transition is discontinuous if ∆ > 0 and continuous if ∆ < 0.

Time Complexity of Broadcast and Consensus for Randomized Oblivious Message Adversaries

“…In contrast to the above works, in this paper we study a more randomized message adversary, considering a stochastic model where adversarial graphs are partially chosen uniformly at random. While a randomized perspective on dynamic networks is natural and has been considered in many different settings already, existing works on random dynamic communication networks, e.g., on the radio network model [14], on rumor spreading [5], as well as on epidemics [11], do not consider oblivious message adversaries. Note, however, that the information dissemination considered in this paper is similar to the SI model for virus propagation, with results having implications in both directions [15].…”