  Vaccination is crucial for the control of epidemics. Yet it is a social
dilemma since non-vaccinators can benefit from the herd immunity created by the
vaccinators. Thus the optimum vaccination level is not reached via voluntary
vaccination at times. Intensive studies incorporate social networks to study
vaccination behavior, and it is shown that vaccination can be promoted on some
networks. The underlying network, however, is often assumed to be static,
neglecting the dynamical nature of social networks. We investigate the
vaccination behavior on dynamical social networks using both simulations and
mean-field approximations. We find that the more robust the
vaccinator-infected-non-vaccinator links are or the more fragile the
vaccinator-healthy-non-vaccinator links are, the higher the final vaccination
level is. This result is true for arbitrary rationality. Furthermore, we show
that, under strong selection, the vaccination level can be higher than that in
the well-mixed population. 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. Our results highlight the dynamical nature
of social network on the vaccination behavior, and can be insightful for the
epidemic control.
