Contact tracing and epidemics control in social networks.

A generalization of the standard susceptible-infectious-removed 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 that yields quantitative agreement with stochastic simulations on random graphs. Both the stochastic simulations and the mean-field equations show secondary epidemics if the contact tracing is not performed with sufficient strength. 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.