  Bipartite networks are composed of two types of nodes and there are no links
between nodes of the same type. Thus the study of epidemic spread and control
on such networks is relevant to sexually transmitted diseases (STDs). When
entire populations of two types cannot be immunized and the effect of
immunization is not perfect, we have to consider the targeted immunization with
immunization rates. We derive the epidemic thresholds of SIR and SIS models
with immunization and illustrate the results with STDs on heterosexual contact
networks.
