  We study a susceptible-vaccinated--infected--recovered (SVIR)
epidemic-spreading model with diversity of infection rate of the individuals.
By means of analytical arguments as well as extensive computer simulations, we
demonstrate that the heterogeneity in infection rate can either impede or
accelerate the epidemic spreading, which depends on the amount of vaccinated
individuals introduced in the population as well as the contact pattern among
the individuals. Remarkably, as long as the individuals with different
capability of acquiring the disease interact with unequal frequency, there
always exist a cross point for the fraction of vaccinated, below which the
diversity of infection rate hinders the epidemic spreading and above which
expedites it. The overall results are robust to the SVIR dynamics defined on
different population models; the possible applications of the results are
discussed.
