  A generalization of the standard susceptible-infectious-removed (SIR)
stochastic model for epidemics in sparse random networks is introduced which
incorporates contact tracing in addition to random screening. We propose a
deterministic mean-field description which yields quantitative agreement with
stochastic simulations on random graphs. We also analyze the role of contact
tracing in epidemics control in small-world networks and show that its
effectiveness grows as the rewiring probability is reduced.
