In this paper, a new susceptible-infected-susceptible model with infective medium is proposed, which describes epidemics (e.g. malaria) transmitted by infective media (e.g. mosquitoes) on various complex networks. The dynamic behaviours of the model on a homogeneous network and a heterogenous scale-free network are considered, respectively, where the absence of the threshold on the scale-free network is demonstrated. Then, analytical and simulated results are given to show that the proportional immunization strategy to the new model is very effective on scale-free networks. Furthermore, it is shown that the immune density of nodes depends not only on the infectivity between individual persons, but also on the infectivity between persons and mosquitoes. This reveals that the absence of a critical immunization threshold not only is due to the unbounded connectivity fluctuation of the underlying scale-free network, but also is determined by the path of the epidemic spreading.