Abstract
Under the condition of infinite dissemination of the network，it has been proved that the classical epidemic models do not give epidemic thresholds in the infinite scale-free networks. That is，a disease can always propagate on the network no matter how low its spread speed. However，the ability of individuals to spread virus in many real networks is not always infinite. If the maximum dissemination of individuals in the network is set finite，then there should exist a non-zero epidemic threshold for the above epidemic models. The relations between the epidemic threshold and the maximum dissemination，the relations between the degree of infection and the maximum dissemination are discussed，meanwhile the reason why classical epidemic models always over-predict the degree of infections in real networks is explained.
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