We introduce a fast simulation technique for modeling epidemics on adaptive networks. Our rejection-based algorithm efficiently simulates the co-evolution of the network structure and the epidemic dynamics. We extend the classical SIS model by incorporating stochastic rules that allow for the association of susceptible nodes and the dissociation of infected nodes. The method outperforms standard baselines in terms of computational efficiency while revealing new emergent patterns in epidemic spread. Code is made available at github.com/GerritGr/icon.