The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinInfEdge problem for optimal social distancing involves minimizing the expected number of infections, when we are allowed to break at most B edges; similarly the MinInfNode problem involves removing at most B vertices. These are fundamental problems in epidemiology and network science. While a number of heuristics have been considered, the complexity of this problem remains generally open. In this paper, we present two bicriteria approximation algorithms for the MinInfEdge problem, which give the first non-trivial approximations for this problem. The first is based on the cut sparsification result technique of Karger, which works for any graph, when the transmission probabilities are not too small. The second is a Sample Average Approximation (SAA) based algorithm, which we analyze forthe Chung-Lu random graph model. We also extend some of our results for the MinInfNode problem.