Measuring edge importance to improve immunization performance

The edge heterogeneity has a remarkable influence on disease spreading, but it has seldom been considered in the disease-controlling policies. Based on the gravity model, we propose the edge importance index to describe the influence of edge heterogeneity on immunization strategies. Then the edge importance and contact weight are combined to calculate the infection rates on the I-S (Infected-Susceptible) edges in the complex network, and the difference of the infection rates on strong and weak ties is analyzed. Simulation results show that edge heterogeneity has a significant influence on the performance of immunization strategies, and better immunization efficiency is derived when the vaccination rate of the nodes in the weak I-S edges is increased.