Dynamical immunization based on random-walk in time-varying networks

Random-walk describes a simple diffusion process, through which nodes with the larger degree will be traversed with high probability. Thus, it can be applied to the design of immunization strategies for the control of epidemics. As the interaction of individuals dynamically evolves with time, the network information obtained for immunization is limited and dependent on time. In this work, we propose a dynamical immunization method based on the random-walk process in activity-driven (AD) time-varying networks. With the mean-field theory, the epidemic threshold under the random-walk immunization can be effectively predicted. In particular, the role of the immunization observation time, during which the nodes information is measured for the design of immunization strategies is clarified. Simulation experiments show that the accuracy of the predicted threshold strongly depends on the fraction of immunized nodes as well as the immunization observation time. The comparison of the random walk immunization with several classical immunization strategies verifies that random walk immunization is comparable to the acquaintance strategy both in AD networks and in real networks. Our results provide helpful indications for the design of immunization strategies in time-varying networks.