Evolutionary vaccination dynamics with internal support mechanisms

This paper reports internal support mechanisms (i.e., without external intervention) to enhance the vaccine coverage in the evolutionary vaccination dynamics. We present two internal support mechanisms, one is global support mechanism in which each individual pays a support cost to build up a public fund and then the public fund is divided by all vaccinated individuals, while another is local support mechanism in which each individual pays a support cost and then this support cost will be divided by its immediate vaccinated neighbors. By means of extensive computer simulations, we show that, in the same strength of support cost, the heterogeneous (local) support mechanism can encourage more people to take vaccination than the homogeneous (global) support mechanism. And then, we study the most general case that includes supporters and troublemakers together, where supporters (troublemakers) mean that the individuals join (do not join) the internal support mechanism, in the population. We surprisingly find that, in scale-free networks, the voluntary vaccination dynamics with the local support mechanism will not degrade into the original voluntary vaccination dynamics, and the vaccination level can still be effectively improved. In view of most social networks are of scale-free degree distribution, we study further in empirical networks and find that the vaccination level can still be improved in the absence of external intervention.