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
