Immunization dynamics on a two-layer network model

We introduced a two-layer network model for the study of the immunization dynamics in epidemics. Spreading of an epidemic is modeled as an excitatory process in a Watts–Strogatz small-world network (infection layer) while immunization by prevention of the disease as a dynamic process in a Barabási–Albert scale-free network (prevention layer). It is shown that prevention indeed turns periodic rages of an epidemic into small fluctuations, and in a certain situation, actually plays an adverse role and helps the disease survive. We argue that the presence of two different characteristic time scales contributes to the immunization dynamics observed.