Most of real systems such as social, biological and communication systems can be modeled by a complex network. In these networks, elementary units of the system are displayed by nodes and edges represent interactions between them. Disease propagation is one of the dynamical processes on the networks, which deals with the effect of network structure on the disease spreading behavior and the dynamical phase transitions. In other words, the role of network topology in determining the rate and patterns of the spreading process is investigated. The SIS, SIR, SI, and SIRS, are four basic epidemic models which are widely used in describing disease spreading processes. Epidemic threshold is a phase transition between the appearance of epidemic and the lake of it. The aim is finding epidemic threshold for the forenamed models in different networks. Mean-field solution gives an proximate value of the epidemic threshold in the uncorrelated complex networks. But, in the networks with connectivity correlations, the behavior of the epidemic threshold can be described with the network parameters. Our simulation results of the susceptible-infective-recovered (SIR) model on the random, scale-free and small-world networks prove these results. The small-world networks are assortative. It is shown that in these networks, while decreasing the connectivity correlations of the network, with the link randomization method, the value of epidemic threshold tends to the epidemic threshold of the mean-field solution. Keywords: Complex network, spreading process, epidemic threshold, correlation, mean-field