Paper ID: 2202.08296

Controlling Epidemic Spread using Probabilistic Diffusion Models on Networks

Amy Babay, Michael Dinitz, Aravind Srinivasan, Leonidas Tsepenekas, Anil Vullikanti

The spread of an epidemic is often modeled by an SIR random process on a social network graph. The MinINF 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 these problems remains generally open. In this paper, we present two bicriteria approximation algorithms for MinINF, which give the first non-trivial approximations for this problem. The first is based on the cut sparsification result of Karger \cite{karger:mathor99}, and works when the transmission probabilities are not too small. The second is a Sample Average Approximation (SAA) based algorithm, which we analyze for the Chung-Lu random graph model. We also extend some of our results to tackle the MinINFNode problem.

Submitted: Feb 16, 2022