A Suggestion of a New Measure of Importance of Nodes in Disease-propagation Graphs

One of the most effective ways to protect people from being infected by infectious diseases is through vaccination. However, due to the limitation of vaccine supply, it is usually impractical to vaccinate all of the people in a community. Therefore, how to smartly select a small group of people for targeted vaccination becomes an important issue. Recently, reference [3] deploys a wireless sensor system in a high school in China to collect contacts between students happened within a disease transmission distance. Reference [3] constructs a graph model for disease propagation and presents a measure of importance of nodes, called connectivity centrality, so that targeted vaccination can be performed effectively. We find that although connectivity centrality does provide a nice measure of how a node affects the other nodes during disease propagation, it overemphasizes the contact frequency between nodes and overlooks the number of neighbors of a node. Therefore, in this paper, we suggest a new measure of importance of nodes in disease-propagation graphs. and we show that there exist an infinite number of disease-propagation graphs such that the node selected by our measure is better than that selected by [3].