  We introduce a Reed-Frost epidemic model with recursive contact tracing and
asymptomatic transmission. This generalizes the branching-process model
introduced by the authors in a previous work [arxiv:2004.07237] to finite
populations and general contact networks. We simulate the model numerically for
two representative examples, the complete graph and the square lattice. On both
networks, we observe clear signatures of a contact-tracing phase transition
from an "epidemic phase" to an "immune phase" as contact-network coverage is
increased. We verify that away from the singular line of perfect tracing, the
finite-size scaling of the contact-tracing phase transition on each network
lies in the corresponding percolation universality class. Finally, we use the
model to quantify the efficacy of recursive contact-tracing in regimes where
epidemic spread is not contained.
