SIR epidemics on evolving graphs.

We consider evoSIR, a variant of the SIR model, on ErdH os-Renyi random graphs in which susceptibles with an infected neighbor break that connection at rate $rho$ and rewire to a randomly chosen individual. We compute the critical infection rate $lambda_c$ and the probability of a large epidemic by showing that they are the same for the delSIR model in which $S-I$ connections are deleted instead of rewired. The final size of a large delSIR epidemic has a continuous transition. Simulations suggest that the final size of a large evoSIR epidemic is discontinuous at $lambda_c$.