  In this work we analyze the evolution of voluntary vaccination in networked
populations by entangling the spreading dynamics of an influenza-like disease
with an evolutionary framework taking place at the end of each influenza season
so that individuals take or not the vaccine upon their previous experience. Our
framework thus put in competition two well-known dynamical properties of
scale-free networks: the fast propagation of diseases and the promotion of
cooperative behaviors. Our results show that when vaccine is perfect scale-free
networks enhance the vaccination behavior with respect to random graphs with
homogeneous connectivity patterns. However, when imperfection appears we find a
cross-over effect so that the number of infected (vaccinated) individuals
increases (decreases) with respect to homogeneous networks, thus showing up the
competition between the aforementioned properties of scale-free graphs.
