Controlling Contagion Processes in Activity Driven Networks

Abstract

The vast majority of strategies aimed at controlling contagion processes on networks consider the connectivity pattern of the system either quenched or annealed. However, in the real world, many networks are highly dynamical and evolve, in time, concurrently with the contagion process. Here, we derive an analytical framework for the study of control strategies specifically devised for a class of time-varying networks, namely activity-driven networks. We develop a block variable mean-field approach that allows the derivation of the equations describing the coevolution of the contagion process and the network dynamic. We derive the critical immunization threshold and assess the effectiveness of three different control strategies. Finally, we validate the theoretical picture by simulating numerically the spreading process and control strategies in both synthetic networks and a large-scale, real-world, mobile telephone call data set.