Improved targeted immunization strategies based on two rounds of selection

In the case of high degree targeted immunization where the number of vaccine is limited, when more than one node associated with the same degree meets the requirement of high degree centrality, how can we choose a certain number of nodes from those nodes, so that the number of immunized nodes will not exceed the limit? In this paper, we introduce a new idea derived from the selection process of second-round exam to solve this problem and then propose three improved targeted immunization strategies. In these proposed strategies, the immunized nodes are selected through two rounds of selection, where we increase the quotas of first-round selection according the evaluation criterion of degree centrality and then consider another characteristic parameter of node, such as node's clustering coefficient, betweenness and closeness, to help choose targeted nodes in the second-round selection. To validate the effectiveness of the proposed strategies, we compare them with the degree immunizations including the high degree targeted and the high degree adaptive immunizations using two metrics: the size of the largest connected component of immunized network and the number of infected nodes. Simulation results demonstrate that the proposed strategies based on two rounds of sorting are effective for heterogeneous networks and their immunization effects are better than that of the degree immunizations.