Vaccination dilemma on an evolving social network

Vaccination is crucial for the control of epidemics. Yet it is a social dilemma since non-vaccinators benefit from the herd immunity created by the vaccinators. Thus the optimum vaccination level is not reached via voluntary vaccination at times. Social networks have been shown to dramatically alter the vaccination behavior. The underlying network, however, is often assumed to be static, neglecting the dynamical nature of social networks. We address how the dynamics of networks have an impact on the vaccination behavior. We reveal the conditions of the social link rewiring to enhance the vaccination level. We find that the selection intensity can dramatically alter the vaccination level. In addition, we show that vaccination on evolving social network is equivalent to the vaccination in well-mixed population with a rescaled basic reproductive ratio. All the results are based on mean-field approximations verified by simulations. Our results highlight the dynamical nature of social network on the vaccination behavior, and can be insightful for the epidemic control.