Controlling contact network topology to prevent measles outbreaks

Consider an epidemic that propagates in a network of N individuals. The dynamics of the infection are governed by the N-intertwined SIR model, which is a non-linear model. Our goal is to prevent the epidemic by removing (vaccinating) nodes and removing (closing) links. Since vaccinating nodes and closing links are costly, we want to minimize this cost under the constraint of preventing the outbreak. We first show that preventing the outbreak can be guaranteed by ensuring that the maximal eigenvalue lambda-{1} of a specific linear system is negative. This induces a well posed, but highly complex, combinatorial optimization problem. We propose a greedy algorithm that at each step picks the approximately best link to close or the best node to vaccinate, and proceeds to break the network until lambda-{1}<0. We prove that running our algorithm on a coarser and smaller graph of regions, as opposed to individuals, still guarantees that the epidemic is prevented in the large network of size N. We tested our algorithm on an N-intertwined SIR model that was calibrated using real data that includes measles outbreaks and contact frequencies. The contact network was generated based on raw cellular localization data of 17 billion records from Radio Network Controllers that cover 1.8 million users over 2 months. Our encouraging results demonstrate that algorithms that consider the topology of the network can offer great value even in practical scenarios, where the decisions and computations can only be made on the regional level.