Spreading of epidemics in complex networks with infective medium and spreading delay

In this paper, we propose a new susceptible-infected-susceptible (SIS) model with infective medium and spreading delay (MD-SIS) to study epidemic spreading in networks based on the mean-field theory. Theoretical analysis and simulation results show that the existence of infective medium and spreading delay can significantly enhance the risk of outbreak of epidemics and accelerate the epidemic spreading in the networks. For a given propagation rate, we found that the epidemic prevalence on the homogeneous network varies logarithmically with infection probability of infective medium and spreading delay respectively, and the epidemic prevalence on the scale-free network has a power-law relation with infection probability of infective medium, but a linear relation with spreading delay.