Global and local targeted immunization in networks with community structure

Immunization plays an important role in the field of epidemic spreading in complex networks. In previous studies, targeted immunization has been proved to be an effective strategy. However, when extended to networks with community structure, it is unknown whether the superior strategy is to vaccinate the nodes who have the most connections in the entire network (global strategy), or those in the original community where epidemic starts to spread (local strategy). In this work, by using both analytic approaches and simulations, we observe that the answer depends on the closeness between communities. If communities are tied closely, the global strategy is superior to the local strategy. Otherwise, the local targeted immunization is advantageous. The existence of a transitional value of closeness implies that we should adopt different strategies. Furthermore, we extend our investigation from twocommunity networks to multi-community networks. We consider the mode of community connection and the location of community where epidemic starts to spread. Both simulation results and theoretical predictions show that local strategy is a better option for immunization in most cases. But if the epidemic begins from a core community, global strategy is superior in some cases.