Hub nodes inhibit the outbreak of epidemic under voluntary vaccination

It is commonly believed that epidemic spreading on scale-free networks is difficult to control and that the disease can spread even with a low infection rate, lacking an epidemic threshold. In this paper, we study epidemic spreading on complex networks under the framework of game theory, in which a voluntary vaccination strategy is incorporated. In particular, individuals face the 'dilemma' of vaccination: they have to decide whether or not to vaccinate according to the trade-off between the risk and the side effects or cost of vaccination. Remarkably and quite excitingly, we find that disease outbreak can be more effectively inhibited on scale-free networks than on random networks. This is because the hub nodes of scale-free networks are more inclined to take self-vaccination after balancing the pros and cons. This result is encouraging as it indicates that real-world networks, which are often claimed to be scale free, can be favorably and easily controlled under voluntary vaccination. Our work provides a way of understanding how to prevent the outbreak of diseases under voluntary vaccination, and is expected to provide valuable information on effective disease control and appropriate decision-making.